What are the lengths of the legs of a right triangle in which one acute angle measures 19° and the hypotenuse is 15 units long? round answers to the nearest tenth.

The dependent variable represented on the graph is the Total Cost

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

As a general rule:

The variable represented on the y-axis is the dependent variable

From the given parameters, we have

This means that

y-axis = Dependent variable

This can also be expressed as

Dependent variable = Total Cost

This means that the dependent variable is Total Cost

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The probability that the students will have a pop quiz on a randomly selected day will be A. 0.25.

Probability is the occurence of likely events. It is the area of mathematics that deals with numerical estimates of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1. In this case, 0 denotes the impossibility of the event and 1 represents certainty.

From the information, the probability that students will not have a quiz is 75%. The probability that the students will have a pop quiz on a randomly selected day will be:

= 1 - 75%

= 0.25

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Complete question

The probability that students will not have a quiz is 75%. What is the probability that the students will have a pop quiz on a randomly selected day? a. 0.25 b. 0.52 c. 0.77 d. 0.90

Answer:

2

Step-by-step explanation:

if you do change in y/change in x it would be 8/4 with simplifies down to 2

April took out a $600 loan from the bank. At the end of 5 years, she pays back the principal, plus $60 simple interest. the annual interest rate is 2%

Simple interest is calculated using the simple interest formula

The formula is stated as

Simple interest = Principal *  time *  rate / 100

In the problem the give data include

principal = $600

rate= ?

time = 5 years

simple interest  = 60

plugging in the values

Simple interest = Principal *  time *  rate / 100

60 = 600 * 5 * r / 100

60 * 100 = 3000r

r = 6000  / 3000

r = 2%

The annual interest rate is 2%

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The 7th term of the geometry sequence is 2,097, 152. Hence option C is the correct option.

What is a term of a sequence?

A phrase is used to describe each number in the series. The first term in the order 1, 3, 5, 7, 9,... is 1, the second is 3, the third is 5, and so on.

A geometric sequence is sequence such that the pervious term is multiplied by a constant number to get next term. The constant number is known as common ratio.

Given pattern is  8, 64, 512, 4,096, ..

The common ratio is 64/8 = 512/64 = 4096/512 = 8.

The first term of the sequence is 8.

The nth term of geometric sequence is ar^(n-1), where a is the first term, r is the common ratio.

The 7th term of the sequence is 8(8)⁷⁻¹ = 8(8)⁶ = 2,097, 152.

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Answer:

the lenth of the court is 78 feet

The equation of a parabola is y²+12x=0.

A parabola is a U-shaped plane curve in which any point is an equal distance from both a fixed point (known as the focus) and a fixed straight line (known as the directrix).

Parabola functions are classified into three types: standard form, vertex form, and intercept form (also known as factored).

as per the given question:

We have a vertex at (0,0) and the directrix is x = 3, a line parallel to the y-axis, it must have a focus at (3,0).

The parabola equation represents the locus of a point (x, y) that moves so that its distance from x=3 and (3,0) is equal. As a result, the parabola equation is, An equation of the parabola represents the locus of a point (x, y), which moves so that its distance from x=3 and (−3,0) are equal. Hence, the equation of a parabola is

(x−(−3))² + (y−0)² = (x−3)²

or (x+3)² + y² = (x−3)²

or x² + 6x + 9 + y² = x² − 6x + 9

or y² + 12x =0

Hence, The equation of a parabola is y²+12x=0.

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The new coordinates of triangle KLM after the given translation is;

M'(6, 1)

L'(1, 4)

K'(4, 8)

In transformations, there are different types such as reflection, dilation, translation e.t.c

Now, translation is what we are dealing with here and translation is a rigid transformation which means that it does not alter the dimensions of the figure after transformation. Translation is just moving the object from one point to another.

In translation, the size, the shape and the orientation of the image remain the same as that of the original object. Thus, the same orientation means that the object and image are facing the same direction.

The given coordinates of the triangle are;

M(-2, 1)

L(-7, 4)

K(-4, 8)

Now, If you move horizontally 8 units to the right, it means that 8 is added to the x-coordinate of each of the vertices. Thus, the transformation rule here is;

(x, y) → (x + 8), y

Therefore the new coordinates of triangle KLM are;

M'(-2 + 8, 1) = M'(6, 1)

L'(-7 + 8, 4) = L'(1, 4)

K'(-4 + 8, 8) = K'(4, 8)

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The probability that this song will be played on exactly 0 days out of 7 days, if The probability that a particular song is played is 0.23 is 0.008.

A combination is a choice of items from a group of different items, where the order of the choices is irrelevant.

Given:

The probability that a particular song is played is 0.23,

As can be seen that the problem is of combination, so we have to choose 5 out of 7,

Calculate the combination as shown below,

⁷C₅ = 7! / (5! × 2!) = 7 × 6 / 2

⁷C₅ = 7 × 6 / 2

⁷C₅ = 21

Calculate the probability as shown below,

P = ⁷C₅  × (0.23)⁵ × (0.77)²

P = 0.008

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Answer:

Here answer

Step-by-step explanation:

To find the number of hours Jayden would have to work to earn $105.00, we need to first find his hourly wage. We can do this by dividing his total earnings by the number of hours he worked:

hourly wage = total earnings / number of hours worked

= $87.50 / 5 hours

= $17.50/hour

Now that we know Jayden's hourly wage, we can use it to find the number of hours he would have to work to earn $105.00. We can do this by dividing the total amount he wants to earn by his hourly wage:

number of hours = total earnings / hourly wage

= $105.00 / $17.50/hour

= 6 hours

Therefore, Jayden would have to work for 6 hours to earn $105.00 at his job.

Maximum = 28, Minimum = 1, Lower Quartile = 3, Median = 5, and Upper Quartile = 16

The minimum, lower quartile (Q1), median (Q2), upper quartile (Q3), and maximum make up the five-number summary. The median is the middle value; Q1 is the median of the first half of the data, and Q3 is the median of the second half. The lowest is the smallest number, the maximum is the highest, the median is the intermediate value.

The 5 digit summary definition

minimal is a smaller number.

lower quartile: First-half median of the data.

median

upper quartile :Median of the second half of data

greatest number is maximum

The numbers are 1 1 1 1 3 3 3 4 4 4 5 5 5 5 6 6 6 13 13 16 16 16 21 22 24 28 28

minimum = smallest number = 1

lower quartile = Median of the first half of data = 1 1 1 1 3 3 3 4 4 4 5 5 5 = 3

median = median( middle value) = 5

upper quartile = Median of the second half of data = 6 6 6 13 13 16 16 16 21 22 24 28 28 = 16

maximum = largest number = 28

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At an average speed of 240 mph and an angle of depression of 45 degrees, the plane will lose 1.1 miles of altitude.

1. Convert the average speed of 240 mph into feet per second: 240 mph x 1.467 = 352 feet per second

2. Calculate the total distance traveled by the plane in one second: 352 x 1 = 352 feet

3. Calculate the total vertical distance traveled by the plane in one second: 352 x sin45 = 250 feet

4. Calculate the total altitude lost by the plane in 1 second: 250 x 1 = 250 feet

5. Calculate the total altitude lost by the plane in 1 minute: 250 x 60 = 15,000 feet

6. Convert the total altitude lost in feet to miles: 15,000 feet / 5,280 = 2.84 miles

7. Round to the nearest tenth of a mile: 2.84 miles = 1.1 miles

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The system of equations with the same solution set as the system of equations given is presented as follows:

The system of equations for this problem is presented as follows:

Another system of equations will have the same solution set as the system given when it's equations are multiples of the equations in this problem.

This holds true for the first option, as:

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Answer:

25

Step-by-step explanation:

make 1/5 and 3/10 with equivalent denominator which will give us 2/10 and 3/10 now add them and we get 5/10 5 is the half of ten so we will divide 50 over 2 and we will get 25

Answer: -3

Step-by-step explanation:

[tex]-1 \leq f'(x) \leq 3\\\\-\int^{10}_{2} dx \leq \int^{10}_{2} f'(x) \text{ }dx \leq 3\int^{10}_{2} dx\\\\-8 \leq f(10)-f(2) \leq 24\\\\-8 \leq f(10)-5 \leq 24\\\\-3 \leq f(10) \leq 29[/tex]

The number of unique combinations of books Dwight could bring with him is 168

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

Science fiction = 3

Business ethics = 8

Beet farming = 7

The number of unique combination of books is then calculated as

Number of unique combinations = Science fiction * Business ethics * Beet farming

Substitute the known values in the above equation, so, we have the following representation

Number of unique combinations = 3 * 8 * 7

Evaluate the products

Number of unique combinations = 168

Hence, the number of unique combinations is 168

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The shopper must buy six 4-packs sandwiches.

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,

Number of sandwiches to buy = 24

Cost of six-pack sandwiches = $5.28

Cost of four-pack sandwiches = $3.40

Cost of 24 sandwiches from the six-pack.

= 4 x 5.28

= $21.12

Cost of 24 sandwiches from the four-pack.

= 6 x 3.40

= $20.4

Thus,

Six four-pack sandwiches are cheaper than four six-pack sandwiches.

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The first graph shows how many of each order could fit into a bag that was hanging from a hook. First, a detailed explanation: * Let's discuss the issue's solution.

The quantity of orders of paperclips is x, and the weight of the order of jumbo paperclips is 2 pounds. The order of paperclips weighs 2 x = 2 x, the order of packing tape weighs 3 lbs., and the quantity of orders of packing tape is y. The weight of the tape order is 3 y = 3 y, the weight of the entire order is 2 x + 3 y, and the hook can only support a maximum weight of 6 y. 2x + 3y ≤ 6

The graph that depicts this inequality, Any line's equation is y = mx + c, where m represents its slope.

The y-intercept indicates to replace x in the equation by 0; the x-intercept indicates to replace y in the equation by 0; 2x - 3y 6 is the inequality. 2x + 3y = 6 is the equation for the line.

- Subtract 2x from both sides: 3y = 6 - 2x; - Divide both sides by 3: y = 6/3 - 2/3 x; - Locate the y-intercept: x = 0; y = 2;

The line crosses the y-axis at position (0 , 2)

– Locate the x-intercept.

∵ y = 0

∴ 0 = 2 - 2/3 x

- Adjust both sides by 2/3x.

∴ 2/3 x = 2

Increase both sides by 3.

Divide all sides by 2 to get the answer.

∴ x = 3

The line crosses the x-axis at position (3 , 0)

First and second from the figure.

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Answer:

x = 7.45 & -8.45

Step-by-step explanation:

x^2+x−63=0

You can either solve this through the quadratic formula or by completing the square.

See the attached image on how to solve using the quadratic formula:

The coefficients of the given quadratic equation are:

Here we want to find the coefficients for the following quadratic equation:

-2x^2 + 4x - 3 = 0

Now, the general quadratic equation is written as:

a*x^2 + b*x + c = 0

So the two equations are:

-2x^2 + 4x - 3 = 0

a*x^2 + b*x + c = 0

So c is the constant term, comparing this with the given quadratic equation, we can see that:

c = -3

b is on the linear term, ad we can see that:

b = 4

a is on the quadratic term, we can see that:

a = -2

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Answer:

on the value of the root may produce a value of the polynomial at the approximate root that is of the order of. For avoiding these problems, methods have been elaborated, which compute all roots simultaneously, to any desired accuracy. Presently the most efficient method is Aberth method.

It is to be noted that the length of the interior diagonal of the box whose dimensions are Height 100cm, Lenght, 80 cm, and width 60 cm, is 140.4cm.

Recall that the formula for the diagonal length of a right rectangular prism is calculated as √(l² + w² + h²) units. So, the formula for the length of a right rectangular prism's diagonal is √(l²+w²+h²), where l is the length, b is the breadth, and h is the height.

Plugging in the values we have:

d² = 60² + 80² + 100²

Solving for d, we get:

d = √(660² + 80² + 100²)

= √(3600 + 6400 + 10000)

= √(20000)

= 140.4 cm

Thus, the length of the interior diagonal of the box is 140.4 cm.

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The correct expression for the area of the circle will be;

⇒ 50² × π

The circle is a closed two dimensional figure , in which the set of all points is equidistance from the center.

Given that;

A circle has a diameter of 100 inches.

Now,

Since, A circle has a diameter of 100 inches.

Hence, A circle has a radius = 100/2 = 50 inches.

We know that;

The area of circle = πr²

Where, 'r' is radius of the circle.

Substitute all the values, we get;

⇒ The area of circle = πr²

⇒ The area of circle = 50² × π

Thus, The correct expression is,

⇒ 50² × π

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The number of calories for 180-gram burrito is 392

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

The scatter plot

From the line of the best fit on the scatter plot, we have the following points

(0, 250) and (190, 400)

A linear function is modelled by:

y = mx + b

In which:

m is the slope, which is the rate of change

b is the y-intercept, which is the value of y when x = 0

Using the above points, we have

b = 250

This means that

y = mx + 250

From the point (190, 400), we have

400 = 190m + 250

So, we have

190m = 150

And, this gives

m = 15/19

So, the equation is

y = 15/19x + 250

For a 180-gram burrito, we have

y = 15/19 x 180 + 250

Evaluate

y = 392

Hence, the number of calories is 392

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Answer:

The answer is D with the greatest y-intercept of 7.

Step-by-step explanation:

Put these all in slope intercept form: y=mx+b

m=slope

b=y intercept

Working out option A)

x+6y=36

6y=-x+36

y=-1/6x+6

Option B)

y=15x+5

Option C)

Is there a typo? Regardless of how I attmpeted to fix it, it had an intercept of either 3 or 4

Option D)

y=4x+7

The answer is D with the greatest y-intercept of 7.

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Answer:

288 m^2

Step-by-step explanation:

each side of the room is  8 m       ( 8x8 = 64)

So you have FOUR walls of widht 8 and height 9

   area =   FOUR * ( 9 *8) = 288 m^2

Answer:

2x=27-x - given

3x=27 - add x to both sides

x=9 - divide both sides by 3

Step-by-step explanation:

[tex]2x=27-x[/tex]

Simplify:

[tex]2x=-x+27[/tex]

Add x to both sides:

[tex]2x+x=-x+27+x[/tex]

[tex]3x=27[/tex]

Divide both sides by 3:

[tex]\dfrac{3x}{3} =\dfrac{27}{3}[/tex]

[tex]\fbox{x = 9}[/tex]