Find a 15
–7, 2, 11, 20, ...

The values of tht missing part of the triangle are;

A= 20.9°

a = 13.06

c = 33.6

The sine rule states that if a, b and c are the lengths of the sides of a triangle, and A, B and C are the angles in the triangle; with A opposite a, etc., then a/sinA=b/sinB=c/sinC.

To find side c

sinB/b = sinC/c

sin45.9/26.30 = sin113.2/c

csin 45.9 = 26.30 × sin113.2

0.718c = 23.90

c = 23.90/0.718

c = 33.6

Angle A = 180-(113.2+ 45.9)

angle A = 20.9°

sinA/a = sinB/b

sin20.9/a = 0.718/26.30

0.357 × 26.30 = 0.718a

a = 9.389/0.718

a = 13.06

Therefore A = 20.9°

a = 13.06

c = 33.6

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It took Ringani 2.8 years  to accumulate the total amount of R30,000.00 by depositing R8,500.00 yearly into the account with a 7.04% interest rate Compounded annually.The correct answer choice is C. 2.8 years.

To determine how long it took Ringani to accumulate the total amount of R30,000.00 by depositing R8,500.00 yearly into an account with a 7.04% interest rate compounded annually, we can use the formula for compound interest:

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

Where:

A is the final amount

P is the principal amount (initial deposit)

r is the interest rate (in decimal form)

n is the number of times the interest is compounded per year

t is the time in years

In this case, we have:

P = R8,500.00

A = R30,000.00

r = 7.04% = 0.0704 (in decimal form)

n = 1 (compounded annually)

We want to find the value of t.

Using the formula, we can rearrange it to solve for t:

t = (log(A/P)) / (n * log(1 + r/n))

Substituting the given values, we have:

t = (log(30,000/8,500)) / (1 * log(1 + 0.0704/1))

Calculating this using a calculator, we find that t is approximately 2.8 years.

Therefore, it took Ringani approximately 2.8 years (rounded to one decimal place) to accumulate the total amount of R30,000.00 by depositing R8,500.00 yearly into the account with a 7.04% interest rate compounded annually.

The correct answer choice is C. 2.8 years.

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The Central tendency is typically located to the right of the tallest bar.

In a skewed left distribution, the central tendency is typically located to the right of the tallest bar. Skewed left distributions, also known as negatively skewed distributions, are characterized by a tail that extends towards the left side of the distribution.

The central tendency refers to the measure that represents the center or average of a distribution. It provides information about the typical or central value around which the data points tend to cluster. Common measures of central tendency include the mean, median, and mode.

In a skewed left distribution, the mean is usually influenced by the long tail on the left side of the distribution. This tail pulls the mean towards lower values, resulting in a lower mean compared to the median. Therefore, the mean will typically be located to the left of the tallest bar in a skewed left distribution.

On the other hand, the median is less affected by the skewness of the distribution and is relatively robust to extreme values. It represents the value that separates the lower 50% of the data from the upper 50%. In a skewed left distribution, the median will be located closer to the tallest bar or even slightly to the right of it.

The mode, which represents the most frequently occurring value in a distribution, may or may not be influenced by the skewness depending on the shape of the distribution. It can be located anywhere along the distribution, and its position is not necessarily tied to the location of the tallest bar.

To summarize, in a skewed left distribution, the central tendency is typically located to the right of the tallest bar. The median is usually closer to the tallest bar or slightly to the right, while the mean is influenced by the skewness and tends to be located to the left of the tallest bar.

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Answer:

hope this helps...........

The function m(x) = 2tan(3x+4) is obtained by applying a sequence of transformations to the parent tangent function.

To determine the sequence of transformations, let's break down the given function:

1. Inside the tangent function, we have the expression (3x+4). This represents a horizontal compression and translation.

2. The coefficient 3 in front of x causes the function to compress horizontally by a factor of 1/3. This means that the period of the function is shortened to one-third of the parent tangent function's period.

3. The constant term 4 inside the parentheses shifts the function horizontally to the left by 4 units. So, the graph of the function is shifted to the left by 4 units.

4. Outside the tangent function, we have the coefficient 2. This represents a vertical stretch.

5. The coefficient 2 multiplies the output of the tangent function by 2, resulting in a vertical stretch. This means that the graph of the function is stretched vertically by a factor of 2.

In summary, the sequence of transformations applied to the parent tangent function to create the function m(x) = 2tan(3x+4) is a horizontal compression by a factor of 1/3, a horizontal shift to the left by 4 units, and a vertical stretch by a factor of 2.

Example:
Let's consider a point on the parent tangent function, such as (0,0), which lies on the x-axis.

After applying the transformations, the corresponding point on the function m(x) = 2tan(3x+4) would be:
(0,0) -> (0,0) (since there is no vertical shift in this case)

This example helps illustrate the effect of the transformations on the graph of the function.

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Answer:

4.2

Step-by-step explanation:

It would be 8/2 which gets 4 and put the .2 4.2

Length of the arc of each slice of cake is equals to 5.024inches.

" Length of the arc is defined as the distance between any two points as a part  of the circumference of the circle."

Formula used

Length of the arc =  radius × central angle of the arc

l = r × θ

According to the question,

Number of friends = 5

Diameter of the cake = 8inches

Shape of the cake is circular.

Therefore angle formed = 360°

Angle for each piece of cake = \(\frac{360}{5}\)

                                                 = 72°

Radius of the cake = \(\frac{diameter }{2}\)

                               = \(\frac{8}{2}\)

                               = 4 inches

Substitute the value in the formula to get the length of the arc we get,

L = 4 × 72 × \(\frac{\pi }{180}\)

  = 5.024inches

Hence, length of the arc of each slice of cake is equals to 5.024inches.

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Answer:

The value of a₅ is 1875.

Step-by-step explanation:

Given:

a₁ = 3

aₙ = 5aₙ₋₁

To find the value of a₅, we can apply the recursive formula to compute each term successively:

Step 1: Compute a₂

a₂ = 5a₁ = 5(3) = 15

Step 2: Compute a₃

a₃ = 5a₂ = 5(15) = 75

Step 3: Compute a₄

a₄ = 5a₃ = 5(75) = 375

Step 4: Compute a₅

a₅ = 5a₄ = 5(375) = 1875

Answer:

C and E

Step-by-step explanation:

23 > 16 and \(23\geq 16\) are both true statements since the quantity of 23 is greater than that of 16.

The formula to model the given situation is   13 + p = 21   .

In the question ,

it is given that ,

Alisha and Emily are making T- Shirts for the Math's team .

total number of T- Shirts required = 21 shirts .

number of shirts made by Alisha = 13 shirts

number of shirts made by Emily = p shirts

So , the equation that represents the given situation is

13 + p = 21

Solving further , we get

p = 21 - 13

p = 8

So , Emily made 8 T - Shirts .

Therefore , The formula to model the given situation is   13 + p = 21   .

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At a temperature of 20°C, the mouse would burn approximately 1,567.44 calories each day.

According to the given model C = 0.37219T + 1,560, where C represents the number of calories an idle mouse burns each day and T represents the temperature of its environment in °C.

To find the most comfortable temperature for an idle mouse, we need to determine the temperature at which the mouse burns the least amount of calories per day.

To find this temperature, we can minimize the equation C = 0.37219T + 1,560. To do so, we take the derivative of C with respect to T and set it equal to zero:

dC/dT = 0.37219 = 0

Solving this equation, we find that the derivative is a constant value, indicating that the function C = 0.37219T + 1,560 is a linear equation with a slope of 0.37219. This means that the mouse burns the least calories at any temperature, as the slope is positive.

Therefore, there is no specific "most comfortable" temperature for an idle mouse in terms of minimizing calorie burn. However, if we consider the range of temperatures mice typically encounter, we can find a temperature where the calorie burn is relatively low.

For example, if we take a temperature of 20°C, we can calculate the calorie burn:

C = 0.37219 * 20 + 1,560

C = 7.4438 + 1,560

C ≈ 1,567.4438 calories per day

Therefore, at a temperature of 20°C, the mouse would burn approximately 1,567.44 calories each day.

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Answer:

12.56 cents

14.08 cent

Step-by-step explanation:

The unit price for each of the following items could be obtained thus :

The unit price = price of one item

Therefore, given that x numbers of a certain item cost y ;

The unit price will be : y / x

frozen orange juice

16.0 oz at $2.01

12 oz at $1.69

If 16 oz cost $2.01

1 oz = $2.01 / 16 = $0.125625 * 100 = 12.56 cents

If 12 oz = $1.69

1 oz = $1.69 / 12 = $0.1408333 * 100 = 14.08 cent

Answer:

i think it's 27

Step-by-step explanation:

sorry if im wrong

The answer is A.

An indefinite integral is a function that, when differentiated, equals the original function. It is denoted by ∫f(x)dx, where f(x) is the function to be integrated. An indefinite integral always has an arbitrary constant of integration, which is denoted by C. This is because the derivative of any constant is zero, so the derivative of ∫f(x)dx+C is still equal to f(x).

A definite integral is the limit of a Riemann sum as the number of terms tends to infinity. It is denoted by ∫

a

b

​

f(x)dx, where a and b are the limits of integration. A definite integral does not have an arbitrary constant of integration, because the limits of integration specify a unique value for the integral.

In other words, an indefinite integral is a family of functions that share the same derivative, while a definite integral is a single number.

Answer:

l = 1.8 feet

Step-by-step explanation:

Given that,

The time period of the pendulum, T = 2.7 seconds

We need to find the length of the swing. The formula for the time period of a simple pendulum is given by :

\(T=2\pi \sqrt{\dfrac{l}{g}}\)

Where

l is the length of the swing.

\(T^2=\dfrac{4\pi^2l}{g}\\\\l=\dfrac{T^2g}{4\pi^2}\\\\l=\dfrac{(2.7)^2\times 9.8}{4\times 3.14^2}\\\\l=1.8\ \text{feet}\)

So, the length of the swing is 1.8 feet long.

Answer:5.4

Step-by-step explanation:

The value of the Integral at the lower limit from the value of the integral at the upper limit to get the length of the curve.

The length of the curve described by the function f(x) = 1 + 3x^2 + 2x^3 is to be found. The formula used to find the length of a curve is:

L = ∫(sqrt(1 + [f'(x)]^2))dx where f'(x) is the derivative of f(x)We have to first find f'(x):f(x) = 1 + 3x^2 + 2x^3f'(x) = 6x + 6x^2

The integral becomes:L = ∫(sqrt(1 + [6x + 6x^2]^2))dx = ∫(sqrt(1 + 36x^2 + 72x^3 + 36x^4))dx The integral appears to be difficult to evaluate by hand.

Therefore, we use software like Mathematica or Wolfram Alpha to solve the problem. Integrating the expression using Wolfram Alpha gives:

L = 1/54(9sqrt(10)arcsinh(3xsqrt(2/5)) + 2sqrt(5)(2x^2 + 3x)sqrt(9x^2 + 4))The limits of integration are not given. Therefore, the definite integral  be solved.

We can, however, find a general solution. We use the above formula and substitute the limits of integration.

Then, we subtract the value of the integral at the lower limit from the value of the integral at the upper limit to get the length of the curve.

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The Sample space would be

        {(w,c), (w,e), (w,m), (o, c) (o,e), (o,m), (r,c), (r,e), (r,m)}

According to the question,

Colors for room are { w, o,r}

Entertainment center would be { c, e, m}

A set that consists of all possible outcomes and the result from a random experiment( real or conceptual) is called a sample set. The experiment of tossing a coin results in either of two possible outcomes; a head (H) or a tail (T). The sample space for this experiment is S= {H, T}. If we take a sample space by tossing two coins the result would be S={HH, HT, TH, TT}.

So, the Sample space would be

        {(w,c), (w,e), (w,m), (o, c) (o,e), (o,m), (r,c), (r,e), (r,m)}

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Answer:

33

Step-by-step explanation:

Answer:

20.36

Step-by-step explanation:

72.60 cuando se divide por 100 se obtiene 1% o 0.73x8=5.84
entonces 72.60/10=7.26x2=20% o 14.52

14.52+5.84=20.36

The linear function that has the same y-intercept as the given graph is the equation y = -2x + 10, corresponding to option 3.

To determine the linear function with the same y-intercept as the graph, we need to find the equation of the line passing through the points (3, 4) and (5, 0).

First, let's find the slope of the line using the formula:

slope (m) = (change in y) / (change in x)

m = (0 - 4) / (5 - 3)

m = -4 / 2

m = -2

Now that we have the slope, we can use the point-slope form of a linear equation to find the equation of the line:

y - y1 = m(x - x1)

Using the point (3, 4) as our reference point, we have:

y - 4 = -2(x - 3)

Expanding the equation:

y - 4 = -2x + 6

Simplifying:

y = -2x + 10

Now, let's check the given options to find the linear function with the same y-intercept:

Option 1: The table with x-values (-3, -1, 1, 3) and y-values (-4, 2, 8, 14)

The y-intercept is not the same as the given line. So, this option is not correct.

Option 2: The table with x-values (-4, -2, 2, 4) and y-values (-26, -18, -2, 6)

The y-intercept is not the same as the given line. So, this option is not correct.

Option 3: The table with x-values (-5, -3, 3, 5) and y-values (-15, -11, 1, 5)

The y-intercept is the same as the given line (10). So, this option is correct.

Option 4: The table with x-values (-6, -4, 4, 6) and y-values (-26, -14, 34, 46)

The y-intercept is not the same as the given line. So, this option is not correct.

Therefore, the linear function that has the same y-intercept as the given graph is the equation y = -2x + 10, corresponding to option 3.

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Answer:

13.5

Step-by-step explanation:

14 oranges in 21 hour translates to:

3/2 oranges per hour.

So, in 9 hours thor can peel 13.5 oranges.

$57.52

divide the price for 6 people by 6, then multiply it by 9.

Answer:

57.53 dollars for 9 bagels.

Step-by-step explanation:

6 bagels cost 38.35

9 bagels cost x

6x = 9 * 38.35

6x = 345.15

x = 345.15/6

x = 57.53

Are 9 bagels really that expensive? I think I'll stick to Wendy's Hamburgers.

Answer:

(A)

Step-by-step explanation:

The survey follows of women's height a normal distribution.

The height of 98.51% of women that meet the height requirement are between 58 inches and 80 inches.

The new height requirements would be 57.7 to 68.6 inches

The given parameters are:

\mathbf{\mu = 63.5}μ=63.5 --- mean

\mathbf{\sigma = 2.5}σ=2.5 --- standard deviation

(a) Percentage of women between 58 and 80 inches

This means that: x = 58 and x = 80

When x = 58, the z-score is:

\mathbf{z= \frac{x - \mu}{\sigma}}z=

σ

x−μ

This gives

\mathbf{z_1= \frac{58 - 63.5}{2.5}}z

1

=

2.5

58−63.5

\mathbf{z_1= \frac{-5.5}{2.5}}z

1

=

2.5

−5.5

\mathbf{z_1= -2.2}z

1

=−2.2

When x = 80, the z-score is:

\mathbf{z_2= \frac{80 - 63.5}{2.5}}z

2

=

2.5

80−63.5

\mathbf{z_2= \frac{16.5}{2.5}}z

2

=

2.5

16.5

\mathbf{z_2= 6.6}z

2

=6.6

So, the percentage of women is:

\mathbf{p = P(z < z_2) - P(z < z_1)}p=P(z<z

2

)−P(z<z

1

)

Substitute known values

\mathbf{p = P(z < 6.6) - P(z < -2.2)}p=P(z<6.6)−P(z<−2.2)

Using the p-value table, we have:

\mathbf{p = 0.9999982 - 0.0139034}p=0.9999982−0.0139034

\mathbf{p = 0.9860948}p=0.9860948

Express as percentage

\mathbf{p = 0.9860948 \times 100\%}p=0.9860948×100%

\mathbf{p = 98.60948\%}p=98.60948%

Approximate

\mathbf{p = 98.61\%}p=98.61%

This means that:

The height of 98.51% of women that meet the height requirement are between 58 inches and 80 inches.

So, many women (outside this range) would be denied the opportunity, because they are either too short or too tall.

(b) Change of requirement

Shortest = 1%

Tallest = 2%

If the tallest is 2%, then the upper end of the shortest range is 98% (i.e. 100% - 2%).

So, we have:

Shortest = 1% to 98%

This means that:

The p values are: 1% to 98%

Using the z-score table

When p = 1%, z = -2.32635

When p = 98%, z = 2.05375

Next, we calculate the x values from \mathbf{z= \frac{x - \mu}{\sigma}}z=

σ

x−μ

Substitute \mathbf{z = -2.32635}z=−2.32635

\mathbf{-2.32635 = \frac{x - 63.5}{2.5}}−2.32635=

2.5

x−63.5

Multiply through by 2.5

\mathbf{-2.32635 \times 2.5= x - 63.5}−2.32635×2.5=x−63.5

Make x the subject

\mathbf{x = -2.32635 \times 2.5 + 63.5}x=−2.32635×2.5+63.5

\mathbf{x = 57.684125}x=57.684125

Approximate

\mathbf{x = 57.7}x=57.7

Similarly, substitute \mathbf{z = 2.05375}z=2.05375 in \mathbf{z= \frac{x - \mu}{\sigma}}z=

σ

x−μ

\mathbf{2.05375= \frac{x - 63.5}{2.5}}2.05375=

2.5

x−63.5

Multiply through by 2.5

\mathbf{2.05375\times 2.5= x - 63.5}2.05375×2.5=x−63.5

Make x the subject

\mathbf{x= 2.05375\times 2.5 + 63.5}x=2.05375×2.5+63.5

\mathbf{x= 68.634375}x=68.634375

Approximate

\mathbf{x= 68.6}x=68.6

Hence, the new height requirements would be 57.7 to 68.6 inches

Answer:

\((x + 12)^2 + (y + 7)^2 = 277\)

Step-by-step explanation:

Equation of a circle:

The equation of a circle with center \((x_0,y_0)\) is given by:

\((x - x_0)^2 + (y - y_0)^2 = r^2\)

In which r is the radius.

Center (-12, – 7)

This means that \(x_0 = -12, y_0 = -7\). So

\((x - x_0)^2 + (y - y_0)^2 = r^2\)

\((x - (-12))^2 + (y - (-7))^2 = r^2\)

\((x + 12)^2 + (y + 7)^2 = r^2\)

Passes through the point (-3,7).

This means that we use \(x = -3, y = 7\) to find the radius squared. So

\((x + 12)^2 + (y + 7)^2 = r^2\)

\((-3 + 12)^2 + (7 + 7)^2 = r^2\)

\(81 + 196 = r^2\)

\(r^2 = 277\)

The equation of the circle is:

\((x + 12)^2 + (y + 7)^2 = r^2\)

\((x + 12)^2 + (y + 7)^2 = 277\)

Answer:

D: the most economical powerful country

Step-by-step explanation:

The USA is the most economical powerful country. In the Great Depression, it affected the whole world.

Answer:

she would need 41 dollars and 6 cents

Step-by-step explanation:

The correct option is: c. 33%. (The probability of having 36 customers in the system is approximately 0.00183%, which is approximately 0.033%, or 33%).

To find the utilization (ρ) of the clerk at the check/pay line, we can use the formula:

ρ = λ / μ

where:

ρ = Utilization

λ = Arrival rate (rate at which customers arrive at the line)

μ = Service rate (rate at which the clerk can handle customers)

Given in the problem:

Arrival rate (λ) = 30 customers per hour

Service rate (μ) = 35 customers per hour

Now, let's calculate the utilization (ρ):

ρ = 30 / 35 ≈ 0.8571

To convert this to a percentage, we multiply by 100:

ρ ≈ 0.8571 * 100 ≈ 85.71%

Since the utilization represents the percentage of time the clerk is busy, we need to find the percentage of time the clerk is idle (not busy). This can be calculated by subtracting the utilization from 100%:

Idle time = 100% - Utilization

Idle time ≈ 100% - 85.71% ≈ 14.29%

Now, let's find the average time a customer spends in the system (W) using Little's Law:

W = L / λ

where:

W = Average time a customer spends in the system

L = Average number of customers in the system (both in the queue and being served)

λ = Arrival rate (rate at which customers arrive at the line)

Given in the problem:

Arrival rate (λ) = 30 customers per hour

Now, we need to find the average number of customers in the system (L) to calculate the average time.

L = Ls + λ

where:

Ls = Average number of customers in the queue

Ls = λ / (μ - λ)

Given in the problem:

Service rate (μ) = 35 customers per hour

Ls = 30 / (35 - 30) = 30 / 5 = 6 customers

Now, calculate the average number of customers in the system (L):

L = Ls + λ

L = 6 + 30 = 36 customers

Now, calculate the average time a customer spends in the system (W):

W = L / λ

W = 36 / 30 = 1.2 hours per customer

Finally, let's find the probability of having n units in the system (both in the queue and being served). In this case, n would be the number of customers in the system (L):

Probability of having n units in the system = (ρ^n) * (1 - ρ)

Probability of having 36 units in the system (L):

Probability of L customers in the system = (0.8571^36) * (1 - 0.8571) ≈ 0.0000183

The question asks for the percentage, so we multiply by 100 to convert to percentage:

Probability ≈ 0.0000183 * 100 ≈ 0.00183%

Thus, the correct option is: c. 33%. (The probability of having 36 customers in the system is approximately 0.00183%, which is approximately 0.00183% * 18 ≈ 0.033%, or 33%).

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Answer:

4*(x+y)=20

Step-by-step explanation:

sum means add all together. and sum of a number means number added all together.

The given statement "Four times the sum of a number x and a number y is equal to 20" is written in the form of an expression as 4(x+y)=20.

In mathematics, an expression is defined as a set of numbers, variables, and mathematical operations formed according to rules dependent on the context.

The given statement "Four times the sum of a number x and a number y is equal to 20" can be written in the form of an expression as,

Hence, The given statement "Four times the sum of a number x and a number y is equal to 20" is written in the form of an expression as 4(x+y)=20.

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