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The simplified form of the expression is y - 1.

Expressions are mathematical statements which consist of two or more terms and terms are connected to each other using mathematical operators like addition, multiplication, subtraction and so on.

The given expression is (1 - [tex]\frac{1}{y}[/tex] ) / [tex]\frac{1}{y}[/tex]

The numerator of the expression can be written as below using the cross multiplication process.

1 - [tex]\frac{1}{y}[/tex] = (y - 1) / y

The whole expression becomes,

(1 - [tex]\frac{1}{y}[/tex] ) / [tex]\frac{1}{y}[/tex] = [(y - 1) / y] / [tex]\frac{1}{y}[/tex]

              = (y - 1) / 1

              = y - 1

Hence the simplified form is y - 1.

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The height of the streetlight is 30 feet.

Let's call the height of the streetlight "h".

When the person is 16 feet from the streetlight, the length of their shadow will be 16 feet * (6 feet / h) = 96 feet / h.

When the person is 5 feet from the tip of the streetlight's shadow, the length of the streetlight's shadow will be h * (16 feet / 5 feet) = 3.2 * h.

Since the length of the person's shadow starts to appear beyond the streetlight's shadow when they are 5 feet from the tip of the streetlight's shadow, we know that 96 / h > 3.2 * h.

Solving for h, we get:

96 / h > 3.2 * h

96 > 3.2h

30 > h

So, the height of the streetlight is less than 30 feet.

To determine the exact height of the streetlight, we can use the equation:

96 / h = 3.2 * h

96 = 3.2h

30 = h

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Check the picture below.

[tex]\textit{Law of sines} \\\\ \cfrac{sin(\measuredangle A)}{a}=\cfrac{sin(\measuredangle B)}{b}=\cfrac{sin(\measuredangle C)}{c} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{\sin(\measuredangle M)}{m}=\cfrac{\sin(\measuredangle L)}{l}\implies \cfrac{\sin(114^o)}{63}=\cfrac{\sin(42^o)}{l} \\\\\\ l\sin(114^o)=63\sin(42^o)\implies l=\cfrac{63\sin(42^o)}{\sin(114^o)}\implies l\approx 46~inches[/tex]

Answer:

A) Function f is translated up 3 units.

B) Function f is translated to the right 5 units.

Step-by-step explanation:

Given functions:

[tex]f(x)=\sqrt[3]{x+4}[/tex]

[tex]g(x)=\sqrt[3]{x-1}+3[/tex]

To transform function f to function g, first subtract 5 from the x:

[tex]\begin{aligned}f(x-5)&=\sqrt[3]{x-5+4}\\&=\sqrt[3]{x-1}\end{aligned}[/tex]

Now add 3 to the function:

[tex]f(x-5)+3=\sqrt[3]{x-1}+3[/tex]

When a number "n" is subtracted from the x variable of a function, the function is translated "n" units to the right.

When a number "n" is added to a function, the function is translated "n" units up.

Therefore, the transformations performed from function f to function g are:

The required probability is 0.9544

A z-score is a quantitative measure obtained when a data point from a normal population with mean μ and standard deviation

σ is transformed. It describes the position of the data point representing its distance from the average value of the normal population measured in number of standard deviations. It is given by:

z =(X − μ)/σ

A standard normal table (z-score table) provides the probability to the left of the z-score so obtained.

Number of randomly selected steady smokers is, n=100.

Sample mean is, M=$20.

The population standard deviation is, σ = $5.

To compute the probability that a sample of 100 steady smokers spend between 19 and 21.

Using the definition of a z-score, computing the z-score for X =$19,

z =(X − μ)/σ /[tex]\sqrt{n}[/tex]

[tex]z = \frac{19-20}{5}/\sqrt{100}[/tex]

z = -2

Again using the definition of a z-score to compute the z-score for X = $21,

z =(X − μ)/σ /[tex]\sqrt{n}[/tex]

[tex]z = \frac{21-20}{5}/\sqrt{100}[/tex]

z = 2

The probability that a sample of 100 steady smokers spend between 19 and 21 is obtained as:

P(19< X < 21) = P(-2 < X < 2)

                     = P(z< 2) - P(z < -2)

                     = P(z < 2) − [1 − P (z < 2)]

                     = 0.9772 - (1 - 0.9772)

                     = 0.9772 - 0.0288

                     = 0.9544

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The experimental probability of spinning a number less than 3 is 0.46 or 46%.

This can be defined as the likelihood an event occurs or does not occur. Most of the time, the probability is calculated based on the times a specific outcome is obtained versus the number of total outcomes.

To know the probability, let's use the formula getting less than a 3/ total times:

Times they got less than 3: 23 (8+6+9= 23)

Total times: 50

23/50 = 0.46 or 46% (0.46 x 100)

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Answer:

4th

Step-by-step explanation:

first is over y-axis and the linear translation: 6 horizontal and -5 vertical

B. The y-intercept of function A is greater than the y-intercept of function B.

A straight line is an endless one-dimensional figure that has no width. It is a combination of endless points joined both sides of a point and has no curve.

here, we have,

from the given data, we get,

the 1st line's equation is, y=2x+1

i.e. y-intercept = 1

and,

the 2nd equation is,

1 3 y = 4x - 1

i.e. y-intercept = -1/13

                        =-0.77

as, 1> -0.77

Hence, B. The y-intercept of function A is greater than the y-intercept of function B.

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The probability that the sum of the two rolls equals 4 is  1/12.

Given in the question that a single die with 6 sides is rolled twice, we have to calculate the probability that the sum of the two rolls equals 4.

the set of possible outcomes when we roll a die are {1,2,3,4,5,6}

So when we roll two dice there are 6 × 6 = 36 possibilities

The number of possible combinations that will result in a sum of 4 is (1, 3), (2, 2), and (3, 1). Since there are 6 possible outcomes for each die, the probability of rolling a specific combination is 1/36. There are 3 combinations that will result in a sum of 4, so the probability of rolling a sum of 4 is 3/36 or 1/12.

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Answer:

Step-by-step explanation:

The candy bar cost, in dollars, is $1.05

Say the price of a piece of bubble gum is x.

This means that we can represent our scenario with the equation (x+1)+x=1.10, with (x+1) representing the price of a candy bar.

We can then solve from there.

We have given that,

(x+1)+x=1.10

Simplify above expression

2x+1=1.10

2x=0.10 - Subtract From Both Sides

x=0.05 - Divide From Both Sides

So now we have the price of the piece of bubble gum, but we want the cost of the candy bar.

What is the cost?

Cost is the value of money that a company had to spend to produce its goods or services.

Fortunately, we know it costs one dollar more than the piece of bubble gum, so just do 0.05 + 1. This means our candy bar costs $1.05.

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Answer:

Soda = 2.35

Pack of bubble gum = 1.15

Chocolate bar = 1.64

2.35 + 1.15 + 1.64 = 5.15

Answer: Dottie spent a total of $5.15.

For the given expression 3.35x + 115 = 3.25x + 125 the value of x is 100.

A mathematical statement known as an equation is made up of two expressions joined together by the equal sign.

A formula would be 3x - 5 = 16, for instance. When this equation is solved, we discover that the value of the variable x is 7. Two expressions are combined in an equation using an equal symbol ("="). The "left-hand side" and "right-hand side" of the equation are the two expressions on either side of the equals sign. Typically, we consider an equation's right side to be zero.

The given expression is:

3.35x + 115 = 3.25x + 125

Regroup all the terms with variable x on one side of the equation:

3.35x - 3.25x = 125 - 115

0.1x = 10

x = 100

Hence, for the given expression 3.35x + 115 = 3.25x + 125 the value of x is 100.

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Answer: C!

Step-by-step explanation: Because I'm Him. all jokes aside this is the right answer.

The length and width are possible dimensions for the garden is l = 20 ft; w = 10 ft.

The characteristics of a square and a rectangle in a flat shape are very different. Although both are rectangular, the nature and characteristics of these two buildings are different.

The difference between a square and a rectangle can be seen from the properties they have. These properties are also characteristics of squares and rectangles. For this reason, if we want to mention the difference between the two wakes, then we must know their characteristics.

Your question is incomplete but most probably your full question was:

Which length and width are possible dimensions for the garden?

l = 20 ft; w = 5 ft

l = 20 ft; w = 10 ft

l = 60 ft; w = 20 ft

l = 55 ft; w = 30 ft

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Solving for a in the triangle gives a = 6

Trigonometry is a branch of mathematics dealing with the relationship between the ratios of the sides of a right-angled triangle with its angles.

The figure is a triangle. Since the sum of angles in a triangle is 180°. We can write:

106.2° + (3.8a + 29.7)° + (2.4a + 6.9)° = 180°

106.2 + 3.8a + 29.7 + 2.4a + 6.9 = 180

142.8 + 6.2a = 180

6.2a = 180 - 142.8

6.2a = 37.2

a = 37.2/6.2

a = 6

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The rate of change of the exponential function in this problem represents a decay, and the rate of decrease is of 3.7%.

A decaying exponential function is modeled as follows:

y = a(1 - r)^t.

In which:

The function in this problem is given as follows:

y = 20(0.963)^x.

As 0.963 < 1, this is an exponential decay function, and the decay rate is given as follows:

1 - r = 0.963

r = 1 - 0.963

r = 0.037

r = 3.7%.

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The solution to the inequality is x < -4

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

x+4/2x-1 < 0

Multiply both sides of the inequality

So, we have the following representation

x + 4 < 0

Subtract 4 from both sides of the expression

So, we have the following representation

x < -4

Hence, the solution is x < -4

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Answer:

y=-3/5x+

Step-by-step explanation:

slope intercept form;

y= mx+c........... mis the gradient while c is the y-intercept

so it will be; y= -3/5x+

Work done to pump the kerosene is equal to W = 126106 ft-lbs

"Information available from the question"

Height of the cylinder = 7 ft.

Diameter of cylinder = 8 ft.

Radius of the cylinder = 4 ft

Weight of the kerosene = 51.2 lb/ft³

Calculating the volume of cylinder for dy height

dV = π r² dy

dV = π 4² dy

dV = 16π dy

Force acting on the cylinder

dF = W x dV

dF = 51.2 x 16πdy...….(1)

We know

Work done = Force x displacement

Displacement = 7 - y

dW = 51.2 x 16πdy x (7 - y)

Now, integrating both side

[tex]\int\limits dW = \int\limits^7_0 {819.2\pi(7-y) } \, dy[/tex]

[tex]W = [819.2\pi (7-y)^2]^0_7[/tex]

By solving, we get

W = 126106 ft-lbs

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Answer:

97oz

Step-by-step explanation:

16oz per lb

16x6=96

96oz<97oz

Answer: They are equal

Step-by-step explanation:

It takes approximately 26.56 seconds for the ferris wheel to make one revolution.

The ferris wheel makes one complete revolution when the distance of the person above the ground returns to the original value after completing a full circle.

This occurs when the sine function returns to its maximum value, which is 1.

Thus, we have the following equation:

20 * sin(π/30 * t) + 10 = 20

Solving for t,

we will get:

sin(π/30 * t) = 0.5

Taking the inverse sine of both sides:

(π/30 * t) = sin^-1(0.5)

Multiplying both sides by 30/π,

we will get the following:

t = (30/π) * sin^-1(0.5)

Now solving the value of t

We will get it as: t ≈ 26.56 seconds.

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The approximate length of the midsegment parallel to xy is 6.63

The midsegment of a triangle is a line segment that connects the midpoints of two sides of the triangle and has the same length as each of the two sides.

To find the midpoint of a line segment, we average the x-coordinates and the y-coordinates of its endpoints.

Since the question stated that the midsegment is parallel to xy, we need to find midpoint of xw and yw.

First, let's find the midpoint of side xw:

Midpoint of xw : ((-14+10)/2, (20+4)/2) = (-2, 12)

Midpoint of yw : ((-14-2)/2, (20-4)/2) = (-8, 8 )

The length of a line segment between two points (x1, y1) and (x2, y2) in a two-dimensional coordinate system can be calculated using the distance formula:

d = √((x2 - x1)^2 + (y2 - y1)^2)

Length line of midpoint xw and midpoint yw :

√((-2-(-8))^2 + (12-(8))^2) = √(6^2 + 4^2) = √(36 + 8) = √44

So, the length of the midsegment is parallel to XY, which is approximately equal to √44 = 6.63

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A ratio in mathematics displays how often one number occurs in another and the given situation's specific heat ratio is 1.24.

In mathematics, a ratio shows how frequently one number appears in another.

For instance, the ratio of oranges to lemons in a fruit plate would be eight to six if there were eight oranges and six lemons.

Oranges make up 8:14 of the total fruit, whereas lemons make up 6:8 of the total fruit.

So, e are informed that the volume is halved, and the pressure increases by a factor of 2.5.

We shall therefore have:

PVγ = 2.5P(0.5V)γ

We'll condense this to:

(1/0.5)γ = 2.5

γ = In2.5/In2

γ = 1.32

The volume temperature relation is written as follows if the volume expands in an adiabatic process:

T1V1∧γ-1 = T2V2∧γ-1

T1V1∧1.32-1 = T2(0.5V1)∧1.32-1

Condensing this results in:

T₁ = 1.24T₂

Therefore, a ratio in mathematics displays how often one number occurs in another and the given situation's specific heat ratio is 1.24.

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Check the picture below.

[tex]\begin{cases} ~\hfill 10x+(16y+6)=180\\\\ (4+18y)+(10x-6)=180 \end{cases} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{using the 1st equation}}{10x+(16y+6)=180}\implies 10x+16y=174\implies 10x=174-16y \\\\[-0.35em] ~\dotfill[/tex]

[tex]\stackrel{\textit{substituting on the 2nd equation}}{(4+18y)+(10x-6)=180}\implies 18y+10x-2=180 \\\\\\ 18y+(\underset{10x}{174-16y})-2=180\implies 2y+172=180\implies 2y=8 \\\\\\ y=\cfrac{8}{2}\implies \boxed{y=4} \\\\\\ \stackrel{\textit{since we know that}}{10x=174-16y}\implies 10x=174-16(4)\implies 10x=110 \\\\\\ x=\cfrac{110}{10}\implies \boxed{x=11}[/tex]

C = 200 + 50p is the equation represents the total cost, in dollars, of producing p phones in a given day.

Two or more expressions with an Equal sign is called as Equation.

Given that Deion pays a cost of $50 per phone produced for materials and labor.

Deon also must pay a daily fixed cost of $200 to rent the building and equipment.

C = 200 + 50p

The above equation represents the total cost, in dollars, of producing p phones in a given day.

Number of phones (p) Total cost (C)

0                                   200

1                                   250

2                                  300

3                                   350

Hence, C = 200 + 50p is the equation represents the total cost, in dollars, of producing p phones in a given day.

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Three consecutives even integers are 42, 44, and 46.

The three consecutives even integers can be represented as x, x+2, and x+4. We can create an equation to solve for x, using the given information.

3(x+4) = 52 + x + (x+2)

3x + 12 = 54 + 2x

x = 42

Therefore, the three consecutives even integers are 42, 44, and 46. To explain this answer, we can use the equation we created. We know that the sum of the smaller two integers is 52 less than three times the largest. We can represent this as 3(x+4) = 52 + x + (x+2). We can then solve for x by subtracting 2x from both sides and adding 12 to both sides, resulting in x = 42. This means that the three consecutives even integers are 42, 44, and 46.

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a. The difference between the highest data speed (74.5 Mbps) and the mean of all 50 data speeds (17.34 Mbps) is:

74.5 - 17.34 = 57.16 Mbps

b. To find the number of standard deviations, divide the difference by the standard deviation:

57.16 / 20.79 = 2.75

So, the difference of 57.16 Mbps is 2.75 standard deviations from the mean.

Mbps known as for “Megabits per second.” This is the standard measure of “speed” or “bandwidth” on home internet connections.

It finds how many bits (units of digital information) can be transferred each second. You’ll normally see speeds ranging from 10-1,000 Mbps advertised for home internet plans.

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Equation c=0.48p is used find the cost is $0.48 times the number of pounds of bananas and graph is given in attachment.

The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.

The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.

The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is

m=y₂-y₁/x₂-x₁

Given that Bananas cost $0.48 per pound.

Since each pound costs $0.85, the cost of one pound is $0.48,

the cost of two pounds is twice that at $0.96

The equation c=0.48p is used find the cost is $0.48 times the number of pounds of bananas.

Hence,  equation c=0.48p is used find the cost is $0.48 times the number of pounds of bananas and graph is given in attachment.

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Jim needs a score of 97 on his third test to keep an average of 85 or greater.

Average refers to the sum of a set of numbers divided by the count of numbers in the set. It gives a typical or central value that represents the set of numbers.

Given,

The average of his first two tests is (69 + 82) / 2 = 75.5.

To get an average of 85,

he needs the sum of his three tests to be 3 * 85 = 255.

So, the sum of his first two tests is 255 - x, where x is the score he needs on the third test.

Therefore, x = 255 - (69 + 82) = 255 - 151 = 104.

So, he needs a score of 104 on his third test.

Jim needs a score of 97 on his third test to keep an average of 85 or greater.

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