Find the value to make the equation true

1) ?/1 = 14/17

The graph of the function is attached

The amplitude and the period are 5 and 2π

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

f(x) = 5cos(θ)

A sinusoidal function is represented as

f(x) = Acos(B(x + C)) + D

Where

So, we have

A = 5

Period = 2π/1

Evaluate

A = 5

Period = 2π

Hence, the amplitude is 5 and the period is 2π

The graph of the function is attached

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The mean, median, range, and standard deviation  for the new data set must all be 7 greater than for the original data set.

The mean is the sum of all the values divided by the number of values. Adding the number 6 to the original data set of 30 positive integers increases the sum of all the values by 6, which means the mean for the new data set must be 7 greater than the mean for the original data set.

The formula for the mean is: Mean = (Sum of Values)/(Number of Values)

For the original data set: Mean = (Sum of Values)/30

For the new data set: Mean = (Sum of Values + 6)/31

Therefore, the mean for the new data set must be 7 greater than the mean for the original data set.

The median is the middle value in a set of data. Adding the number 6 to the original data set of 30 positive integers increases the total number of values to 31, which means the median is calculated differently for the new data set than the original data set. The median for the new data set must be 7 greater than the median for the original data set.

The formula for the median is: Median = (n+1)/2

For the original data set: Median = (30+1)/2 = 15.5

For the new data set: Median = (31+1)/2 = 16.5

Therefore, the median for the new data set must be 7 greater than the median for the original data set.

The range is calculated by subtracting the smallest value from the largest value in a data set. Adding the number 6 to the original data set of 30 positive integers increases the largest value by 6, which means the range for the new data set must be 7 greater than the range for the original data set.

The formula for the range is: Range = (Largest Value) - (Smallest Value)

For the original data set: Range = (Largest Value) - 13

For the new data set: Range = (Largest Value + 6) - 13

Therefore, the range for the new data set must be 7 greater than the range for the original data set.

The standard deviation is a measure of how spread out the values in a data set are. Adding the number 6 to the original data set of 30 positive integers increases the total number of values by 1, which means the standard deviation for the new data set must be 7 greater than the standard deviation for the original data set.

The formula for the standard deviation is: Standard Deviation = √ (Sum of (Values - Mean)2 / Number of Values)

For the original data set: Standard Deviation = √ (Sum of (Values - Mean)2 / 30)

For the new data set: Standard Deviation = √ (Sum of (Values - Mean)2 / 31)

Therefore, the standard deviation for the new data set must be 7 greater than the standard deviation for the original data set.

The mean, median, range, and standard deviation for the new data set must all be 7 greater than for the original data set

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Answer: 153.86 cm²

Ok done. Thank to me :>

Answer:

3 months

Step-by-step explanation:

1000 - 450 = 550

She has 550 available to pay for her cable.

550/175 =  3.1428571429  That rounds to 3 months

1000- (3x 175)

1000 - 525 = 475  That leaves 475 in her account.

19.20 you have to do a squared times b squared and the square root them and there's your answer

As a result, at the conclusion of 180 days, Ajoke would repay around $416,025.05.

We can use the compound interest formula to calculate how much Ajoke will owe after 180 days:

\(A = (1 + r/n)(n*t).\)

where A represents the amount owed at the end of the period, P represents the principal (original amount borrowed), r represents the yearly interest rate (as a decimal), n represents the number of times the interest is compounded per year, and t is the time period (in years).

We have the following because the loan is compounded daily:

n = 360 (year's number of days)

t = 180/360 = 0.5 (half a year is 180 days)

r = unidentified

We can use the fact that the loan must be paid back in full at the conclusion of the 180-day period to calculate r Days have passed, thus the total amount owed is the principal + interest. Assume the interest rate is x (in decimal form). The total amount owed is then:

\(400000 + 400000*x\)

Using this in the compound interest formula, we get:

400000 + 400000x = 400000 * (1 + r/360) A = P * (1 + r/n)(nt) 400000 + 400000x = 400000 * (1 + r/360)(360*0.5)

When we simplify, we get:

\(1 + x = (1 + r/360)^{180}\)

We get the natural logarithm of both sides as follows:

180 ln(1 + r/360) = ln(1 + x)

When we solve for r, we get:

\(r = 360 * (e^(ln(1+x)/180) - 1)\)

Substituting x = 0.1 (which corresponds to a 10% interest rate) yields:

\(r = 360 * (e^{(ln(1+0.1)/180) - 1} ) = 0.1015\)

As a result, the yearly interest rate is around 10.15%. We can now apply the compound interest calculation to calculate how much Ajoke will owe at the end 180-day period:

\(P * (1 + r/n)(nt) = A\)

\(A = 400000 * (1 + 0.1015/360)^{3600.5}\)

A ≈ 416,025.05

As a result, at the conclusion of 180 days, Ajoke would repay around $416,025.05.

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1. The percentage of maize flour is given as 16.7 %

2. The common ratio of the GP is r = 1.5.

1. We have to set up equation

60x + 90(1 - x) = 85

60x + 90 - 90x = 85

now we have to solve for the value of x

-30x = -5

x = 5 / 30

x = 0.167

Hence percentage of maize flour is given as 16.7 %

2. a + ar = 20 (1)

ar + ar^2 = 30 (2)

We can rearrange equation (1) to get an expression for a:

a = 20 / (1 + r)

Now, we can substitute a into equation (2) to get an equation only in terms of r:

\(20r / (1 + r) + 20r^2 / (1 + r) = 30\\20r + 20r^2 = 30(1 + r)\\20r + 20r^2 = 30 + 30r\\20r^2 - 10r - 30 = 0\\2r^2 - r - 3 = 0\)

Solving this quadratic equation, we get:

We have two solutions, r = 1.5 and r = -1. But since the GP is increasing, we discard the negative solution. Therefore, the common ratio of the GP is r = 1.5.

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Answer:

3 and 9

Step-by-step explanation:

x+y=12

y-x=6

y-x=6

 +x.  +x

y=6+x

x+(6+x)=12

6+2x=12

-6.    -6

2x=6

/2. /2

x=3

3+y=12

-3.  -3

y=9

Hopes this helps please mark brainliest

reflection across the line y=x

When you reflect a point across the line y = x, the x-coordinate and y-coordinate change places. If you reflect over the line y = -x, the x-coordinate and y-coordinate change places and are negated (the signs are changed).

From the above

E(-9,-1) -> then E' (-1,-9)

where E' is the image of E

Answer:

1.6

Step-by-step explanation:

i used calculator

Answer:  1.6

Step-by-step explanation:

Answer:

21.424

Step-by-step explanation:

22.1 - 0.676 = 21.424

im not sure if it is correct but i think its like this

Answer:

Step-by-step explanation:

The volume of this pyramid in cubic inches is 16.

Given that,

The base and height is 8 and 6.

Based on the above information, the calculation is as follows:

The volume is

= 16

Answer:

1)  695.3 m²

2)  8 ft

3)  172.0 in²

Step-by-step explanation:

To find the area of a regular polygon, we can use the following formula:

\(\boxed{\begin{minipage}{5.5cm}\underline{Area of a regular polygon}\\\\$A=\dfrac{s^2n}{4 \tan\left(\dfrac{180^{\circ}}{n}\right)}$\\\\\\where:\\\phantom{ww}$\bullet$ $n$ is the number of sides.\\ \phantom{ww}$\bullet$ $s$ is the side length.\\\end{minipage}}\)

Given the polygon is an octagon, n = 8.

Given each side measures 12 m, s = 12.

Substitute the values of n and s into the formula for area and solve for A:

\(\implies A=\dfrac{(12)^2 \cdot 8}{4 \tan\left(\dfrac{180^{\circ}}{8}\right)}\)

\(\implies A=\dfrac{144 \cdot 8}{4 \tan\left(22.5^{\circ}\right)}\)

\(\implies A=\dfrac{1152}{4 \tan\left(22.5^{\circ}\right)}\)

\(\implies A=\dfrac{288}{\tan\left(22.5^{\circ}\right)}\)

\(\implies A=695.29350...\)

Therefore, the area of a regular octagon with side length 12 m is 695.3 m² rounded to the nearest tenth.

\(\hrulefill\)

The sum of an interior angle of a regular polygon and its corresponding exterior angle is always 180°.

If the exterior angle of a polygon measures 40°, then its interior angle measures 140°.

To determine the number of sides of the regular polygon given its interior angle, we can use this formula, where n is the number of sides:

\(\boxed{\textsf{Interior angle of a regular polygon} = \dfrac{180^{\circ}(n-2)}{n}}\)

Therefore:

\(\implies 140^{\circ}=\dfrac{180^{\circ}(n-2)}{n}\)

\(\implies 140^{\circ}n=180^{\circ}n - 360^{\circ}\)

\(\implies 40^{\circ}n=360^{\circ}\)

\(\implies n=\dfrac{360^{\circ}}{40^{\circ}}\)

\(\implies n=9\)

Therefore, the regular polygon has 9 sides.

To determine the length of each side, divide the given perimeter by the number of sides:

\(\implies \sf Side\;length=\dfrac{Perimeter}{\textsf{$n$}}\)

\(\implies \sf Side \;length=\dfrac{72}{9}\)

\(\implies \sf Side \;length=8\;ft\)

Therefore, the length of each side of the regular polygon is 8 ft.

\(\hrulefill\)

The area of a regular polygon can be calculated using the following formula:

\(\boxed{\begin{minipage}{5.5cm}\underline{Area of a regular polygon}\\\\$A=\dfrac{s^2n}{4 \tan\left(\dfrac{180^{\circ}}{n}\right)}$\\\\\\where:\\\phantom{ww}$\bullet$ $n$ is the number of sides.\\ \phantom{ww}$\bullet$ $s$ is the side length.\\\end{minipage}}\)

A regular pentagon has 5 sides, so n = 5.

If its perimeter is 50 inches, then the length of one side is 10 inches, so s = 10.

Substitute the values of s and n into the formula and solve for A:

\(\implies A=\dfrac{(10)^2 \cdot 5}{4 \tan\left(\dfrac{180^{\circ}}{5}\right)}\)

\(\implies A=\dfrac{100 \cdot 5}{4 \tan\left(36^{\circ}\right)}\)

\(\implies A=\dfrac{500}{4 \tan\left(36^{\circ}\right)}\)

\(\implies A=\dfrac{125}{\tan\left(36^{\circ}\right)}\)

\(\implies A=172.047740...\)

Therefore, the area of a regular pentagon with perimeter 50 inches is 172.0 in² rounded to the nearest tenth.

Answer:

1.695.29 m^2

2.8 feet

3. 172.0477 in^2

Step-by-step explanation:

1. The area of a regular octagon can be found using the formula:

\(\boxed{\bold{Area = 2a^2(1 + \sqrt{2})}}\)

where a is the length of one side of the octagon.

In this case, a = 12 m, so the area is:

\(\bold{Area = 2(12 m)^2(1 + \sqrt{2}) = 288m^2(1 + \sqrt2)=695.29 m^2}\)

Therefore, the Area of a regular octagon is 695.29 m^2

2.

The formula for the exterior angle of a regular polygon is:

\(\boxed{\bold{Exterior \:angle = \frac{360^o}{n}}}\)

where n is the number of sides in the polygon.

In this case, the exterior angle is 40°, so we can set up the following equation:

\(\bold{40^o=\frac{ 360^0 }{n}}\)

\(n=\frac{360}{40}=9\)

Therefore, the polygon has n=9 sides.

Perimeter=72ft.

We have

\(\boxed{\bold{Perimeter = n*s}}\)

where n is the number of sides in the polygon and s is the length of one side.

Substituting Value.

72 feet = 9*s

\(\bold{s =\frac{ 72 \:feet }{ 9}}\)

s = 8 feet

Therefore, the length of each side of the polygon is 8 feet.

3.

Solution:

A regular pentagon has five sides of equal length. If the perimeter of the pentagon is 50 in, then each side has a length = \(\bold{\frac{perimeter}{n}=\frac{50}{5 }= 10 in.}\)

The area of a regular pentagon can be found using the following formula:

\(\boxed{\bold{Area = \frac{1}{4}\sqrt{5(5+2\sqrt{5})} *s^2}}\)

where s is the length of one side of the Pentagon.

In this case, s = 10 in, so the area is:

\(\bold{Area= \frac{1}{4}\sqrt{5(5+2\sqrt{5})} *10^2=172.0477 in^2}\)

Drawing: Attachment

Answer: The transformed function is y = -0.4√(x - 2).

Step-by-step explanation:

From the given equation, we can identify the following transformations:

Reflected over the x-axis: The negative sign in front of the function (-0.4) indicates a reflection over the x-axis.

Translated 2 units left: The "-2" inside the square root indicates a translation of 2 units to the right.

Compressed by a factor of 0.4: The coefficient "0.4" in front of the square root indicates a vertical compression by a factor of 0.4.

Translated 2 units down: There is no direct indication of a vertical translation in the equation, so this transformation is not applicable.

Therefore, the correct descriptions of the graph of the transformed function compared with the parent function are:

Reflected over the x-axis

Translated 2 units right

Compressed by a factor of 0.4

\(\qquad\qquad\huge\underline{{\sf Answer}}\)

The given function is :

\(\qquad \tt \dashrightarrow \:f(x) = \frac{1}{x} \)

here, for each value of x there is an unique value of f(x), so we can infer that it's a " one - one " function.

but it isn't an onto function because for value of x as 0, we have no value of f(x) [ undefined ]

The correct expanded form using Laws of exponents is:

Two-thirds times two-thirds times two-thirds times two-thirds

Some of the laws of exponents are:

1) When multiplying like bases, keep the base the same and add the exponents.

2) When raising a base with a power to another power, keep the base the same and multiply the exponents.

3) When dividing like bases, keep the base the same and subtract the denominator exponent from the numerator exponent.

Now, we want to solve the expression given as: (²/₃)⁴

When we expend this, we arrive at:

²/₃ × ²/₃ × ²/₃ × ²/₃

This among the options is Option A which is:

Two-thirds times two-thirds times two-thirds times two-thirds

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Answer:

3/2

Step-by-step explanation:

The three solutions are (0,3), (1, 3/2) and (2,0)

Given the equation below expressed as;

y = -3/2x + 3

If the value of x is zero, then;

y = -3/2(0) + 3

y = 3

Hence one of the solution is  (0, 3)

If the value of x is 1 then;

y = -3/2(1) + 3

y = -3/2 + 3

y = 3/2

Hence another solution is  (1, 3/2)

If the value of x is 2, then;

y = -3/2(2) + 3

y = -3 + 3

y = 0

Hence another of the solution is  (2, 0)

The three solutions are (0,3), (1, 3/2) and (2,0)

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Answer:

15 °C

Step-by-step explanation:

°C = (°F - 32) * (5/9)

Given that the initial temperature was 77 °F and it dropped by 10 °C, we can calculate the final temperature.

Initial temperature: 77 °F

Converting to Celsius:

°C = (77 - 32) * (5/9)

°C ≈ 25

The temperature dropped by 10 °C, so the final temperature is:

Final temperature = Initial temperature - Temperature drop

Final temperature ≈ 25 - 10 = 15 °C

Therefore, the temperature after the storm was approximately 15 °C.

Answer:

14 cm²

Step-by-step explanation:

           l = length of rectangular prism = 3 cm

           w = width of rectangular prism = 2 cm

           \(\sf \text{\sf h =height of the rectangular prism = $\sf 1\dfrac{1}{2} =\dfrac{3}{2} \ cm$}\)

         \(\boxed{\text{\bf Volume of rectangular prism = l *w *h}}\)

                                                                \(\sf = 3 * 2 * \dfrac{3}{2}\\\\\\=3*3\\\\= 9 \ cm^2\)

             \(\text{\sf base = $2\dfrac{1}{4} = \dfrac{9}{4} \ cm$}\)

         altitude = 3 cm

         \(\text{Area of triangle = $\dfrac{1}{2}*base*altitude$}\)

                                    \(\sf =\dfrac{1}{2}* 3*\dfrac{9}{4}\\\\\\=\dfrac{27}{8}\\\\= 3.375 \ cm^2\)

     \(\text{\sf height of the triangular prism = H = $1\dfrac{1}{2}=\dfrac{3}{2} \ cm$}\)

           \(\boxed{\text{\bf Volume of triangular prism = area of triangle * H}}\)

                                                                \(\sf = 3.375 * \dfrac{3}{2}\\\\\\= 5.0625 \\\\= 5 \ cm^2\)

Volume of the complex figure:

 To find the volume of complex figure, add the volume of rectangular prism and volume of the triangular prism.

    Volume of the complex figure = 9 +5

                                                       = 14 cm²

Answer: not a triangle

Step-by-step explanation:

If this were to be a triangle, the shorter sides would be 11 and 4 and the longest side would be 16.

First, we should determine if it is a triangle.

These events would be considered as: Subjective, Independent, Dependent, Classical

Subjective event: An event that is based on individual opinion or belief. This event would not be represented by a formula or calculation.

Independent event: An event that is not influenced by other events. This event can be represented by a formula such as P(A) = P(A) which calculates the probability of an event occurring on its own.

Dependent event: An event that is influenced by other events. This event can be represented by a formula such as P(A|B) = P(A ∩ B) / P(B) which calculates the probability of an event occurring given that another event has already occurred.

Classical event: An event that is determined by predetermined probabilities or odds. This event can be represented by a formula such as P(A) = n(A) / n(S) which calculates the probability of an event occurring based on the number of favorable outcomes divided by the total number of outcomes.

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Answer:

13

Step-by-step explanation:

first, the z-4 is in the denominator, which makes it hard to get it. But a way to get rid of it is by multiplying z-4/z-4 to 11/z-4, which cancels out the z-4 in the denominator

Yay! now we have two numbers that are easier to deal with

8/13 , and 11z-44

since 11z-44 isn't in fraction form, we add one to its denominator.

8/13, and 11z-44/1

multiply 11z-44/1 by 13 to get:

13(11z-44)/13 = 143z-572/13

8/13, 143z-572/13

After all that, the common denominator is 13. *phew*

A. The distribution of x is normal with mean 2 mm and standard deviation 0.008 mm.

B. The bounds are given as follows:

C. The probability that the sample mean is outside the interval 2 ± 3 x is given as follows: 0.003 = 0.3%.

The z-score of a measure X of a variable that has mean symbolized by \(\mu\) and standard deviation symbolized by \(\sigma\) is obtained by the rule presented as follows:

\(Z = \frac{X - \mu}{\sigma}\)

The mean and the standard deviation for the population are given as follows:

\(\mu = 2, \sigma = 0.04\)

Hence, for a sample of 25, the standard error is given as follows:

s = 0.04 / square root(25) = 0.008 mm.

The interval for item b is within three standard errors of the mean, hence:

The Empirical Rule states that 99.7% of the measures are within three standard errors of the mean, hence the probability that the sample mean is outside the interval 2 ± 3 x is given as follows: 0.003 = 0.3%.

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Step-by-step explanation:

okok

Answer:

see below

Step-by-step explanation:

x+y = 0 so x= -y

2x+4y =1 so -2y+4y = 1 so 2y = 1

so y = 0.5

x = -0.5

The equation of the new function after shifting 6 units right and 4 units down is f(x) = (x + 6)² - 4.

If we are to apply the changes below to the quadratic parent function, F(x) = x², what is the equation of the new function, given that we are to shift 6 units to the right and 4 units down? We will approach this question by following the steps outlined below.

Step 1: Identify the parent function F(x) = x² and its transformations

Step 2: Write the equation of the new function

Step 3: Simplify the new equation of the function.Step 1: Identify the parent function F(x) = x² and its transformations

Here, we are given the quadratic parent function F(x) = x² and two transformations: shift 6 units right and shift 4 units down.

The general equation for the horizontal and vertical shifts of a quadratic function is given by:f(x) = a(x - h)² + k, where a, h, and k are constants.

The value of a determines the direction of opening of the parabola, while (h, k) represents the vertex of the parabola.

If a > 0, the parabola opens upwards, while a < 0, the parabola opens downwards. If the values of (h, k) are positive, the parabola is shifted right and up, respectively. On the other hand, if the values of (h, k) are negative, the parabola is shifted left and down, respectively.

Therefore, given the quadratic parent function F(x) = x² and two transformations: shift 6 units right and shift 4 units down, we can represent these changes by the following:

a = 1 (since the parabola opens upwards)h = -6 (since we are shifting the parabola 6 units to the right)k = -4 (since we are shifting the parabola 4 units down)

Step 2: Write the equation of the new function Now that we have identified the constants a, h, and k, we can write the equation of the new function as follows:f(x) = a(x - h)² + kf(x) = 1(x - (-6))² + (-4)Replacing the constants a, h, and k in the equation, we have:f(x) = (x + 6)² - 4

Step 3: Simplify the new equation of the function.f(x) = (x + 6)² - 4= (x + 6)(x + 6) - 4= x² + 12x + 36 - 4= x² + 12x + 32Therefore, the equation of the new function after shifting 6 units right and 4 units down is f(x) = x² + 12x + 32.

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Answer:

He sold 12 cakes

Step-by-step explanation:

1/5 of 20 is 4 so 3 X 4= 12 so 12 cakes

Answer:

D

Step-by-step explanation:

A and D are both equidistant from the x- axis, that is

A is 3 units above the x- axis and D is 3 units below the x- axis

then the x- axis is the line of symmetry