solve for x and show full work

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:

97oz

Step-by-step explanation:

16oz per lb

16x6=96

96oz<97oz

Answer: They are equal

Step-by-step explanation:

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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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:

d=-28 and e=-20

Step-by-step explanation:

d×1=-24×1=e=4

d=-24-4=-28

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]

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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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 expression that represents the number of lawns Eve mows in those 8 weeks is 8(L- 2)

b)

The value of the expression is 8.

c)

The tabular table is given above.

d)

Eve mowed 24 lawns in 8 weeks.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

Logan:

Number of lawns each week = L

Number of lawns 8 weeks = 8L

Eve:

Number of lawns each week = )L - 2)

Number of lawns 8 weeks = 8(L- 2)

a)

The expression represents the number of lawns Eve mowed in those 8 weeks.

= 8(L -2)

b)

When L = 3,

8 (L - 2)

= 8 (3 - 2)

= 8 x 1

= 8

c)

Tabular table

                Number of weeks     Number of lawns

Logan         x                                xL

Eve            x                                 x(L - 2)

d)

Logan:

Number of lawns in one week = 5

L = 5

Eve:

Number of lawns in 8 weeks.

= 8 (L - 2)

= 8 (5 - 2)

= 8 x 3

= 24

Thus,

a) 8(L- 2)

b) 8

c) Tabular table is given above.

d) Eve mowed 24 lawns in 8 weeks.

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Scale-factor of copy to original is 3/2.

A scale factor is defined as the ratio between the scale of a given original object and a new object, which is its representation but of a different size.

Given,

Right side triangle is scaled copy of left side triangle

Ratio of side of copy to side of original  = (57/2) / 19 = 3/2

So, Scale factor = 3/2

Hence, 3/2 is the scale-factor in making copy of original triangle.

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The relative frequency that a pupil studies French is 0.1

This refers to the proportion of one event's frequency to all events' frequencies in a statistical experiment.

Given that:

The total number of data values is 300

The frequency of a pupil that studies French is 30

The relative frequency is 30/300 = 0.1

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The fraction of the books in the bookcase that are non-fiction is 2/5.

A fraction is a part of a whole number, and a way to split up a number into equal parts.

Given that, there are 6p+18 fiction books and 4p+12 non-fiction books in a bookcase, we need to find the fraction of the books in the bookcase that are non-fiction.

Therefore,

Number of fictional books = 6p+18

Number of non-fictional books = 4p+12

Total books = 6p+18+4p+12 = 10p+30

Therefore,

the fraction of the books in the bookcase that are non-fiction is given by,

Number of non-fictional books / Total books

= 4p+12 / 10p+30

= 4(p+3) / 10(p+3)

= 4/10

= 2/5

Hence, the fraction of the books in the bookcase that are non-fiction is 2/5.

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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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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 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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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 y-intercept represents the initial height when the were planted.

The height of both plants will never be the same.

We know lines have various types of equations, the general type is

Ax + By + c = 0, and the equation of a line in slope-intercept form is

y = mx + b.

Where slope = m and b = y-intercept.

the slope is the rate of change of the y-axis with respect to the x-axis and the y-intercept is the (0,b) where the line intersects the y-axis at x = 0.

The equations y = 13.6x + 21 and y = 9.4x + 21 represent the heights of two flower plants in a garden in millimeters.

We know y-intercept is when x = 0,

Therefore,  y = 21 and y = 21 represent the initial height when they were planted.

The height of the plants will never be the same because the initial height was the same but one plant is growing faster than the other.

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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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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.

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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Taking the quotient between the volume of sports drink and the number of players we will see that each player gets 0.95 liters.

We know that East Middle’s football team has 20.9 liters of sports drink on the field during the game. Now we want to divide that evenly among all the players of the team, and we know that the team has 22 players.

Then we just need to take the quotient between these two numbers, it is:

20.9/22

We can rewrite that as:

(209/10)*(1/22)

(209/220)

Each player receives (209/220) liters of sports drink.

We can also simplify that as (209/220) liters = 0.95  liters.

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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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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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The explicit formula for the nth term of the sequence 14,16,18,... is aₙ = 2n + 12.

Since the sequence increases by 2, it is an arithmetic sequence.

The formula the nth term an arithmetic sequence is expressed as;

aₙ = a₁ + d( n - 1 )

Given the sequence; 14,16,18,….

First term a₁ = 14

Common difference d = 16 - 14 = 2

Now, plug the values into the above formula and simplify.

aₙ = a₁ + d( n - 1 )

aₙ = 14 + 2( n - 1 )

aₙ = 14 + 2n - 2

aₙ = 14 - 2 + 2n

aₙ = 2n + 12

Therefore, the explicit formula is aₙ = 2n + 12.

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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+

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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Rita's old lawn mower will start after exactly three pulls 12.8% of the time,

The binomial probability formula states that the probability of success occurring precisely x times in n trials is equal to the product of the probability of success (p) and the probability of failure (1-p) raised to the power of n-x. This can be used to calculate this. The probability of success occurring exactly three times is equal to 0.2 x 0.8 x 0.8, or 12.8%, given that the number of trials (n) and the probability of success (p) is both 20 percent.

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Answer: C!

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

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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