sienna also collects baseball cards in a binder just like daniels. her last page was 6/9 full, but she gave 1/3 of those cards to daniel.

The inverse of the function is  [tex](1/4)^{x/5}[/tex].

What is an inverse function?

A function that reverses the effects of another function is called an inverse function. When y=f(x) and x=g, a function g is the inverse of a function f. (y). Applying f and then g is equivalent to doing nothing, in other words. This can be expressed as g(f(x))=x in terms of the relationship between f and g.

Here, we have

Given: equation y = log(1/4)x⁵

A function g is the inverse of function f if for y = f(x), x = g(y)

y = log(1/4)x⁵

Replace x with y

x = log(1/4)y⁵

Solve for y, we get

y = [tex](1/4)^{x/5}[/tex]

Hence, the inverse of the function is  [tex](1/4)^{x/5}[/tex].

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The equation's solution's quadratic function is [tex]f(x)=15x^{2} -11x-14[/tex].

A quadratic issue in mathematics is a specific type of issue that entails squaring, or multiplying, a variable by itself. This terminology is based on the notion that the area of a square is the product of the length of its sides. Quadratum, the Roman word meaning square, is where the word "quadratic" originates.

Definitions: x ax2 + bx + c = 0 is a quadratic equation, which is a 2nd polynomial formula in a single variable. a 0. Given that it is a second quadratic issue, which is ensured by the algebraic fundamental theorem, there can only be one solution. The answer could be simple or complicated.

The solution of the function are :

[tex]x=\frac{7}{5} and x=-\frac{2}{3}[/tex]

Finding such values:

[tex]5x=7[/tex]⇒[tex]5x-7[/tex]

[tex]3x=-2[/tex]⇒[tex]3x+2[/tex]

Multiplying them:

[tex]f(x)=(5x-7)(3x+2)\\[/tex]

[tex]f(x)=15x^{2} -11x-14[/tex] so this is the function.

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The percentage of the total that she spent in fruit is 10%.

We know that Jane spent a total of $20 at the grocery shop, and we know that she spent $2 in fruit.

We want to find the percentage of the total that she spend on fruit, to get this, we need to take solve the equation:

Percentage = 100%*(amount that she pend on fruit)/(total amount)

Replacing the values that we know there we will get:

P = 100%*($2/$20)

P = 100%*1/10 = 10%

She spent 10% of the total amount in fruit.

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Answer: Prime Numbers

the probability of rolling a sum less than 11 is 34/36, or 0.9444 when rounded to four decimal places.

The possibility or chance that an event will occur is quantified by probability. It is a numerical value between 0 and 1, with 0 indicating that an event is impossible and 1 indicating that an event is certain to occur.

The only ways to get a sum of 11 or greater when rolling two dice is to get either a sum of 11 (with a 6 and a 5) or a sum of 12 (with two 6's).

There are 6 x 6 = 36 possible outcomes when rolling two dice, and only one of them results in a sum of 11 and one of them results in a sum of 12. Therefore, there are 36 - 2 = 34 outcomes that result in a sum less than 11.

So, the probability of rolling a sum less than 11 is 34/36, or 0.9444 when rounded to four decimal places.

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Answer:

73.6

Step-by-step explanation:

lets say that x is our number.

x * 0.05 = 23

x * 0.01 = 4.6

just solving one of these equations will give us x = 460.

now, 16% of 460 is 460 * 0.16 = 73.6

The height of Red hill is 513.8 feet.

What does mean by the angle of elevation?

The angle of elevation is the angle created between the line of sight and the horizontal. The angle created is an angle of elevation if the line of sight is upward from the horizontal line. This angle eventually develops above the surface. The angle of elevation is made in such a way that it is above the observer's eye, as the name suggests.

Given:

Distance from the parking lot to the foot of the hill = 740feet

The angle of elevation from a parking lot and the foot of the hill is 25 and 55 degrees respectively.

For easy understanding, assume triangle edges with alphabets as shown in the figure.

Now, let's take ΔACD,

CotD = DC/AC

Cot 55 = y/x ⇒ 0.7 =y/x

⇒ y = 0.7x

In ΔABC

Tan B = AC/BC

Tan 25 = x/(740+y)    (y = 0.7x )

0.467 = x/(740+0.7x )

x = 0.467(740+0.7x )

  = 345.5 + 0.326x

0.6731x = 345.5

∴ x = 513.8 feet

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The expression that is equal to 18x²y⁶ can be found to be D. 3²x²y⁴ × 2 y².

3x³y⁴ has a different power for both x and y compared to the original expression (18x²y⁶). 9xy has a different coefficient and different powers for x and y compared to the original expression (18x²y⁶).

3x³y + √√2 not only has different powers for x and y but also has an additional square root term, making it different from the original expression (18x²y⁶).

3²x²y⁴ × 2 y² on the other hand, can be simplified such that it becomes 18x²y⁶.

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Options include:

The expected size of the largest gap between adjacent cars (as a function of l) is l/(n + 1), and the expected size of the smallest gap between adjacent cars is 2.

Let us consider that cars of length 2 try to park on a length l road. Each minute, a new car parks at a uniformly random spot on the road without crashing into another car or running off the road.

When no more cars fit, the expected size of the largest gap between adjacent cars is l/(n + 1) and the smallest gap is 2.

The expected size of the largest gap between adjacent cars (as a function of l) is l/(n + 1).

Let n be the number of cars parked on the road. Then the total length of the cars parked is 2n.

If the largest gap is a distance g, then the total length of the gaps is l − 2n. Then,gap length:

g (n + 1) ≤ l - 2ng ≤ l − (n + 1)g

Dividing through by (n + 1)g and rearranging:

g ≤ l/(n + 1) (largest gap)g ≥ 2 (smallest gap)

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Answer:

0-18= -18

Step-by-step explanation:

you're starting with 0 and subtracting 18 so the answer is -18

The length of opposite side is 34.5 meters. The length of opposite side is 132 feet. Therefore, the height of the plane above the level of the atoll is approximately 460 meters to the nearest meter.

Trigonometry is a branch of mathematics that deals with the relationships between the sides and angles of triangles. It is used to solve problems involving triangles, such as finding the unknown sides or angles of a triangle, or finding the distance or height of an object that is too far away to measure directly.

Here,

6. To find the horizontal distance Viola has covered, we need to use trigonometry. The angle of 9° is the angle between the hill and the horizontal, so we can use the tangent function:

tangent(9°) = opposite/hypotenuse

where the opposite side is the horizontal distance we want to find and the hypotenuse is the distance Viola has driven, which is 200 meters.

Solving for the opposite side, we get:

opposite = tangent(9°) x hypotenuse

opposite = tan(9°) x 200

opposite ≈ 34.5 meters

7. Using trigonometry again, we can find the height of the building. The angle shown in the diagram is the angle of elevation from the students' location to the top of the building, and the distance shown is the horizontal distance between the students' location and the base of the building. We can use the tangent function again:

tangent(angle of elevation) = opposite/adjacent

where the opposite side is the height of the building we want to find, and the adjacent side is the horizontal distance from the students to the building, which is given as 150 feet.

Solving for the opposite side, we get:

opposite = tangent(angle of elevation) x adjacent

opposite = tan(41°) x 150

opposite ≈ 132 feet

8. In this problem, we can use trigonometry to find the height of the plane. We know the angle of depression from the plane to the atoll is 7°, which means the angle of elevation from the atoll to the plane is also 7°. We also know the horizontal distance from the plane to the atoll is 3,729 meters. Let h be the height of the plane above the level of the atoll. Then we can set up the following equation using the tangent function:

tan(7°) = h / 3,729

Solving for h, we get:

h = 3,729 * tan(7°)

Using a calculator, we get:

h ≈ 460 meters

9. In this problem, we can use trigonometry to find the height of the pole. Let h be the height of the pole above the ground, and let d be the horizontal distance from the surveyor to the base of the pole. Then we can set up the following right triangle:

The opposite side is the height of the pole h.

The adjacent side is the horizontal distance d = 140 feet.

The angle of elevation to the top of the pole is 44°.

We can use the tangent function to find the height of the pole:

tan(44°) = h / 140

Solving for h, we get:

h = 140 * tan(44°)

Using a calculator, we get:

h ≈ 157 feet

10. In a 30°-60°-90° triangle, the sides are in a ratio of 1:√3:2, where the hypotenuse is twice the length of the shorter leg. Let x be the length of the shorter leg, then the longer leg is x√3 and the hypotenuse is 2x. In this problem, we are given that the hypotenuse has a length of 18, so we can set up the following equation:

2x = 18

Solving for x, we get:

x = 9

Therefore, the shorter leg has a length of 9, and the longer leg has a length of 9√3.

The perimeter of the triangle is the sum of the lengths of its sides, so we have:

Perimeter = 9 + 9√3 + 18

Using the fact that √3 ≈ 1.732, we can simplify this expression to:

Perimeter ≈ 9 + 9(1.732) + 18

Perimeter ≈ 9 + 15.588 + 18

Perimeter ≈ 42.588 meters

Therefore, the perimeter of the triangle is approximately 42.588 units.

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Answer:

-17 9/10

Step-by-step explanation:

Answer: 10 more than one fourth of the sum of 5 and 3 then subtract 3

Step-by-step explanation:

separate each number for its explanation.

10 more than --> "10+"

one fourth of [remember in fractions, "of" always means multiply] --> "one fourth x"

sum of 5 and 3 --> "(5+3)"

subtract 3 --> "-3"

Answer:

the last one. (10 more than one fourth of the sum of 5 and 3, then subtract 3)

The product of (3√d)(3√d)(3√d) is equal to: (3√d)(3√d)(3√d) = 3^3(√d)^3 = 27d^(3/2). Therefore, the answer is 27d⁽³/²⁾.

The expression (3√d)(3√d)(3√d) can be simplified by multiplying the coefficients and the radicals separately. The coefficient 3 is raised to the power of 3, which gives 27. The radical √d is raised to the power of 3, which gives d⁽³/²⁾ since the exponent is multiplied by 3. Therefore, the simplified expression is 27d⁽³/²⁾. This means that the product of three cube roots of d is equal to 27 times the cube root of d cubed, which simplifies to 27 times d raised to the power of 3/2.

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Complete question:

What is the following product? Assume d≥0. (3√d)(3√d)(3√d)

d

d³

3(3√d)

√3d

Answer:

According to the USGA, a golfer is allowed to have **14 clubs** in their bag. This may include three woods (driver, 3-wood and 5-wood), eight irons (3-9 iron and pitching wedge), and putter¹. However, while you're in the novice stage as a golfer, you don't really need a full set of 14 clubs. In fact, you're better off cutting that number down nine or 10, which will make club selection easier on the course and boost the quality of your practice².

Step-by-step explanation:

The number of golf clubs that Bestie should bring for a 3-day golfing trip depends on personal preference, skill level, and the type of golf course being played. Typically, a golfer may carry 14 clubs in their bag, which includes a driver, fairway woods, irons, wedges, and a putter. However, some golfers may prefer to carry fewer clubs or more clubs depending on their playing style and the course conditions. Therefore, the specific number of golf clubs that Bestie should bring is subjective and cannot be determined without further information.

Answer:

The minimum number of clubs needed in golfing is 5, the highest you can have is 14.

Step-by-step explanation:

The option A is the correct answer if An event manager recorded the number of people in different age groups who attended a music concert:

What is Horizontal axis ?

In a graph or chart, the horizontal axis, also known as the x-axis, is the axis that runs horizontally from left to right.

Based on the histogram, the correct data table is:

A histogram is a graphical representation of data that shows the frequency distribution of a set of continuous data. In this case, the histogram titled "Concert Audience" shows the number of people in different age groups who attended a music concert.

The horizontal axis of the histogram represents the age groups in years, with bins from 18 to 24, 25 to 31, 32 to 38, and 39 to 45. The vertical axis represents the number of people in each bin, with values from 0 to 120 at intervals of 20.

To create a data table that accurately represents the data in the histogram, we need to look at the heights of the bars in each bin and determine the corresponding number of people. From the histogram, we can see that:

The bin for ages 18 to 24 has a height of 40, which means that 40 people in that age group attended the concert.

The bin for ages 25 to 31 has a height of 100, which means that 100 people in that age group attended the concert.

The bin for ages 32 to 38 has a height of 200, which means that 200 people in that age group attended the concert.

The bin for ages 39 to 45 has a height of 20, which means that 20 people in that age group attended the concert.

Age Group Number of People

18–24           40

25–31           100

32–38            200

39–45            20

Therefore, The option A is the correct answer.

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We may conclude after answering the presented question that  Option 3 expression has incorrect numbers for both age groups and the number of people.

An expression in mathematics is a collection of representations, numbers, and conglomerates that mimic a statistical correlation or regularity. A real number, a mutable, or a mix of the two can be used as an expression. Mathematical operators include addition, subtraction, fast spread, division, and exponentiation. Expressions are often used in arithmetic, mathematics, and form. They are employed in the depiction of mathematical formulas, the solving of equations, and the simplification of mathematical relationships.

The right data table should include the following information based on the provided histogram:

Age Group Number of People

18–24 40

25–31 60

32–38 100

39–45 20

Therefore, the correct answer is:

Age Group Number of People

18–24 40

25–31 60

32–38 100

39–45 20

Option 2 and Option 4 have inaccurate numbers for the number of persons in each age group, whilst Option 3 has incorrect numbers for both age groups and the number of people.

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[tex] \: \huge \mathfrak{ \underbrace{\overbrace{ \pink{A}{\blue{n}}{\green{s}}{ \purple{w}{ \orange{e}{ \red{r}}}}}}} \\ \\ \rightarrow{\bf{\sf{8.366}}} [/tex]

[tex] \: \large \tt \underline{\green{Solution}} [/tex] :

Given : Numbers = 5 , 14

N = 2

[tex] \sf Geometric \: Mean \: = ( x_{1} \times x_{2} \times x_{3}........ x_{n}) {}^{ \frac{1}{n} } \\ \\ = ( 5 \times 14) {}^{ \frac{1}{2} } \\ \\ = (70) {}^{ \frac{1}{2} } \\ \\ or \: (70) {}^{0.5} \\ \\ \rightarrow\fbox{ \blue{8.366}}[/tex]

The relationships between angle pairs are based on their position or on their orientation in relation to each other.

Angles are measured in degrees, and the measure of an angle determines its size. However, the relationships between angle pairs are not solely based on their measures. The position of two angles in relation to each other, such as whether they share a vertex or lie on the same line or plane, can determine their relationship. Additionally, the orientation of the angles can also play a role in their relationship, such as whether they are adjacent, vertical, complementary, supplementary, or congruent. Understanding these relationships is important in geometry and can help in solving problems and proving theorems.

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Answer:

The list of set of dimensions for fencing the building around a rectangular plot of land is 14.5 meters and 29 meters.

Area of a rectangle

area of rectangle = lw

where

l = length

w = width

Therefore,

perimeter = 2w+ l

58 = 2w + l

l = 58 - 2w

Hence,

area = w(58 - 2w)

380 = 58w - 2w²

-2w² + 58w - 380 = 0

-w² + 29w - 190 = 0

The dimension w can be found as follows;

w = - b / 2a

where

a = -1

b = 29

w = - 29 / 2 ×  -1

w = 14.5 meters

Then,

l = 58  - 2w

l = 58 - 2(14.5)

l = 29 meters

Therefore, the dimensions are 14.5 meters and 29 meters.

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from the picture above we can see that we have an altitude or height for the triangle of 5, so then

[tex]\textit{height of an equilateral triangle}\\\\ h=\cfrac{s\sqrt{3}}{2} ~~ \begin{cases} s=\stackrel{side's}{length}\\[-0.5em] \hrulefill\\ h=5 \end{cases}\implies 5=\cfrac{s\sqrt{3}}{2}\implies 10=s\sqrt{3} \\\\\\ \cfrac{10}{\sqrt{3}}=s\implies 5.8\approx s = x[/tex]

Answer:

x = 4.6

Step-by-step explanation:

5.4 *5.4 + 7.2 * 7.2 = 78.88

x * x + 7.6 *7.6 = 78.88

x * x = 21.12

x = 4.6

Answer:

using Pythagoras

diagonal comes out to be 9

again

using Pythagoras

x = √9²-7.6² = √23.24 =4.82

The profit function is modeled as follows:

p(x) = -15x² + 3780x - 176700.

It is a quadratic function with coefficients given as follows:

a = -15, b = 3780, c = -176700.

The leading coefficient of the quadratic function is negative, hence the profit will be maximized at the vertex of the quadratic function.

The x-coordinate of the vertex, representing the price which maximizes the profit, is given as follows:

x = -b/2a

x = -3780/-30

x = $126.

Then the maximum profit would be given as follows:

p(126) = -15(126)² + 3780(126) - 176700.

p(126) = $61,400.

If she charged $100, the profit would be given as follows:

p(100) = -15(100)² + 3780(100) - 176700.

p(126) = $51,300.

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To find the tangent between two circles, you need to draw a line that is tangent to both circles at the same point. This point of tangency is the point where the two circles meet.

To draw the tangent line, you can first draw a line connecting the centers of the two circles. This line will bisect the point of tangency. Next, draw a perpendicular line to this bisecting line passing through the point of intersection of the circles. The intersection of this line with each of the circles will be the points of tangency. Connect these two points of tangency with a line, and you will have drawn the tangent line between the two circles.

The tangent line between two circles is useful in solving problems related to geometry and physics, such as determining the position of a moving object relative to two stationary objects represented by the circles.

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a. The marginal density of Y1 is fY1(y1) = [tex]2e^{-(4+y1)[/tex], y1 > 0.

b. The conditional density of Y2 given Y1 = y1 is f(y2|y1) = 1, y2 > y1 and y1 > 0.

c.  Y1 and Y2 are not independent

  (a) E(Y2|Y1=y1) does not exist.

  (b) V(Y2|Y1=y1) does not exist.

(a) To find the marginal density of Y1, we integrate the joint density over all possible values of Y2:

fY1(y1) = ∫f(y1, y2) dy2 from y2=y1 to y2=∞

= [tex]\int\limits2e^{-(4+y1)[/tex]dy2 from y2=y1 to y2=∞

= [tex]-2e^{-(4+y1)[/tex] [from y2=y1 to y2=∞]

= [tex]2e^{-(4+y1)[/tex], y1 > 0

So the marginal density of Y1 is fY1(y1) = 2e^-(4+y1), y1 > 0.

(b) To find the conditional density of Y2 given Y1 = y1, we use the formula:

f(y2|y1) = f(y1,y2) / fY1(y1) for y1 > 0 and y2 > y1

= 0 otherwise

Substituting the given joint and marginal densities, we get:

f(y2|y1) = [tex]2e^{-(4+y1)[/tex]  / [tex]2e^{-(4+y1)[/tex]) = 1, y2 > y1 and y1 > 0

= 0 otherwise

So the conditional density of Y2 given Y1 = y1 is f(y2|y1) = 1, y2 > y1 and y1 > 0.

(c) To check if Y1 and Y2 are independent, we need to verify if f(y1,y2) = fY1(y1)fY2(y2) for all y1 and y2. We have:

fY2(y2) = ∫f(y1,y2) dy1 from y1=0 to y1=y2

= ∫ [tex]2e^{-(4+y1)[/tex]) dy1 from y1=0 to y1=y2

= - [tex]2e^{-(4+y2)[/tex]  +  [tex]2e^{-4[/tex]

fY1(y1)fY2(y2) = 4e⁻⁸ exp[-(y1+y2)], y1 > 0 and y2 > 0

Clearly, f(y1,y2) is not equal to fY1(y1)fY2(y2) for all y1 and y2, so Y1 and Y2 are not independent.

(a) Using the formula for conditional expectation, we have:

E(Y2|Y1=y1) = ∫y2 f(y2|y1) dy2 from y2=y1 to y2=∞

= ∫y2 dy2 from y2=y1 to y2=∞

= ∞

So E(Y2|Y1=y1) does not exist.

(b) Using the formula for conditional variance, we have:

V(Y2|Y1=y1) = E(Y2²|Y1=y1) - [E(Y2|Y1=y1)]²

= ∫y2² f(y2|y1) dy2 - (∞)²

= ∫y2² dy2 from y2=y1 to y2=∞ - (∞)^²

= ∞

So V(Y2|Y1=y1) does not exist.

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Answer: 5y + 5

Step-by-step explanation: add all the like terms such as 2y + 2y + y = 5y as y = 1y and 2 + 3 = 5, which makes the expression 5y+5

if it's wrong, im sorry

hope it helps!!!

The value os x in the following right triangles and trigonometry are:-

Question 6: x= 13.74

question 7: x= 18.52

question 8: x= 60.12

question 9: x= 3.7

Question 6:

tan θ = opposite/adjacent

tan 58° = 22/x

xtan58° = 22

x = 22/ tan58°

Since tan 58° = 1.6003345

x= 22/ 1.6003345

x ≈ 13.74

question 7:

tan θ = opposite/adjacent

tan 51° = x/15

15tan51° = x

x = 15 * 1.2348971

Since tan 51° = 1.2348971

x ≈ 18.52

question 8:

cosθ = adjacent/hypotenuse

cos 37° = 48/x

xcos37° = 48

x = 48/ cos37°

Since cos 37° = 0.79863551004

x= 48/ 0.79863551004

x ≈ 60.12

question 9:

sinθ = opposite/hypotenuse

sin 24° = x/9

9sin24° = x

Since sin 24° = 0.40673664307

x= 9 * 0.40673664307

x ≈ 3.7

The complete question is:-

Unit 8: Right Triangles & Trigonometry

Homework 3: Trigonometry:

Ratios & Finding Missing Sides

Answers for the remaining four problems?

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By comparing this form to the available choices, we can observe that option B provides the equation that best fits the graph: y²/9 - x²/4 = 1.

What is equation ?

A mathematical equation is a statement that demonstrates the equality of two expressions, usually by placing an equal sign before them. It depicts a connection connecting more than one variable and can be applied to situations to uncover unknown values. Variables, constants, plus mathematical operations including addition, subtract, multiplication, and division are frequently used in algebra equations. Equations include the following: 2x + 3 = 7 y = mx + b , a² + b² = c²

given

The hyperbola graph seen in the figure includes a transverse axis along the y-axis and a centre at (0,0).

The separation between the foci is 8 units, while the separation between the vertices is 6 units.

The equation for this hyperbola's standard form is:

(y - k)²/a² - (x - h) (x - h)²/b² = 1

where (h,k) designates the hyperbola's centre and (a,b) designates the distances between it and its vertices and co-vertices.

By comparing this form to the available choices, we can observe that option B provides the equation that best fits the graph: y²/9 - x²/4 = 1.

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Answer:

12 units^2

Step-by-step explanation:

Answer:

below

Step-by-step explanation:

assuming r=5 and center (0,0)

1.) point at (0,0) for center

2.) point at (5,0)

3.) point at (0,5)

4.) point at (-5,0)

5.) point at (0,-5)

trace around points 2-5 to get the 4pt circle