Question
To be eligible for the swim team, the mean pace a student needs to achieve on 5 laps of the pool is 60 seconds (s). The student swims a lap in 63 s, 62 s, 65 s, and 58 s on her first four laps.

What is the maximum time (in seconds) that she can take on her last lap and still make the team?

Direct variation is represented by this situation and she earn $900

if she works 12 hours.

Direct variation describes a relationship whereby one measure directly affects the other when the first one changes. This is completely opposed by inverse variation. Learn the definitions of direct and inverse variations in this article, along with some instances that have been solved.

When x is not equal to 0, y = kx is the equation that describes the linear function known as direct variation. An equation of the form xy = k, where x is not equal to zero and k is a nonzero real number constant, describes the nonlinear function known as inverse variation.

5 hours  = earns $ 375

1 hours = 375/5 = earns $ 75

12 hours  = 75  12 = earns $ 900

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The coefficient of the variable x² in the expression 3x+5 is 0

Given that,

The expression is 3x+5

To find : The coefficient of the variable x² in the expression

Coefficient is the number that is beside the variable in the equation.

The coefficient of x in 3x+5  is 0

A number multiplied by a variable is referred to as the coefficient of a number. For instance, the x2 coefficient in the formula 6x2+99 is 6

As we can see that the term that is in multiplication with x²  is 3.

Hence, the coefficient of x²  in the equation 3x+5  is 0.

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The 7 stepd in problem-solving examples are:

Step 1: Read through the problem

Step 2: Draw diagram

Step 3: Assign variable to each unknown

Step 4: Translate information into an equation

Step 5: Check the equation

Step 6: Use algebra rules to solve the equations

Step 7: Check the final answer.

We know that the word problems are required to translate the real world problem into mathematical terms.

Everything mentioned in the word problem is important.

The seven necessary steps in problem solving examples:

Step 1: Read the problem throughly

Step 2: Draw picture / diagram / arrow diagram related to example

Step 3: Assign an alphabate to each unknown value

Step 4: Translate information into an equation

Step 5: Check the types equation

Step 6: solve the equations using algebra rules

Step 7: Check the final answer.

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Answer:

i wish i could help im sorry

Step-by-step explanation:

im

not

ok

Answer:

(2x+10°) + (x°) +(2x-20°) = 540°

540 is the sum angle of the polygon

collect like terms

2x+x+2x+10°-20°=540°

5x-10°=540°

5x=540°+10°

5x=550°

x=550°/5

x=110°

(2(110)+10)+(110)+(2(110)-20)=540°

At this rate, the ratio or proportion of red balloons to the total balloons, the number of red balloons out of 48 is 6.

Proportion describes the two or more ratios equated to each other.

Proportions are depicted as fractional values in decimals, fractions, or percentages.

In this situation, we equate the ratio or proportion of red balloons to the sample to determine the number that will likely be red.

The total number of balloons thrown in a water balloon fight = 6,960

The number of the balloons that are red = 870

The proportion of the red balloons to the total = 0.125 or 12.5% (870/6,960)

In a sample of 48 balloons, the number of red balloons will be 6 (48 x 0.125)

Thus, out of 48 balloons, there are 6 red balloons at this constant rate.

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Yes, the information provided regarding the two pairs of congruent angles so one pair with corresponding congruent sides is sufficient to demonstrate the congruence of two triangles.

Congruent refers to things that are exactly the same size and shape.

For the stated question-

The following are the steps:

Thus, the information provided regarding the two pairs of congruent angles so one pair with corresponding congruent sides is sufficient to demonstrate the congruence of two triangles.

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Answer:

3 3/4 or 3 6/8

Step-by-step explanation:

hope this helps <3

The speed of travel will be 4 m/s.

The formula for distance travelled in nth second is given by, Sn = u + a (n – ½).

The body's total distance travelled is equal to the sum of the 10 m it covered in the first five seconds and the 30 m it covered in the following five seconds. The total distance covered is 40 metres. This can be divided by the duration to determine the average speed. Therefore, the average speed is 4 m/s.

Total distance=10+30=40

speed=distance/time=40/10=4m/s

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The expected mass of the sample in the year of 2021 is given as follows:

9 mg.

An exponential function is defined as follows:

y = a(b)^x.

For which the parameters are given as follows:

The initial mass was of 130 mg, hence the parameter a is given as follows:

a = 130.

In two years, the mass decayed to 80 grams, hence the parameter b can be obtained as follows:

b² = 80/130

b = square root(80/130)

b = 0.78446454055.

This means that the exponential function for the mass of the sample in x years after 2010 is given as follows:

y = 130(0.78446454055)^x.

2021 is 11 years after 2010, hence the expected mass is obtained as follows:

y = 130(0.78446454055)^11

y = 9 mg.

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The value of the measure of ∠O in the given triangle will be 65°

A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.

Given that;

In ΔNOP;

PN ≅ OP

So, ∠O = ∠N

And, Measure of ∠P = 50°

Now,

In the ΔNOP;

The sum of all the three angles are 180°.

The value of the measure of ∠O = x

We get;

∠O + ∠N + ∠P = 180°

Substitute ∠P = 50° and ∠O = ∠N = x we get;

x + x + 50 = 180

2x + 50 = 180

2x = 180 - 50

2x = 130

x = 65

Thus, The value of the measure of ∠O will be 65°.

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Answer:

g(- 8) = 20

Step-by-step explanation:

substitute x = - 8 into g(x) , that is

g(- 8) = - 3(- 8) - 4 = 24 - 4 = 20

30° =  angle DAE

Step-by-step explanation:                      

We have ACD with angle ACD = 150°, and because CD = CA, angle CAD and ADC are equal, so angle CAD = [180 -150] / 2 = 30/2 = 15°.

 if we draw AE in ABE using the same process, angle EAB = 15°,
so CAB = 60° = angle =CAD + angle DAE + angle EAB

60   =  15  + angle DAE + 15

60  = 30 + angle DAE
30° =  angle DAE  

Triangle with an equilateral shape. An equilateral triangle is a triangle with all of its sides being the same length. An equilateral triangle, for example, has three sides equal to 5cm. Because the three sides are equal, the three angles opposite the equal sides are equal in size.  

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The values of x is 82° , z is 98°and y is 69°. in the given triangle.

Because one outside angle of a triangle is equal to the total of the other two angles in the triangle, the angles of a triangle add up to 180 degrees. In other words, the third angle must join with the other two angles in the triangle to generate a 180-degree angle (the two angles that add up to form the outside angle).

we know that the sum of angle of triangle = 180

so,

x+ 60 +38=180

x=180-8

x=82°

and also

x+z = 180

z= 98°

for value of y

13 + 98 +y = 180

y= 69°

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The two-digit number is 34.

Zero, a positive natural number, or a negative integer denoted by a minus sign are all examples of integers. The inverse additives of the equivalent positive numbers are the negative numbers. The boldface Z is a common way to represent the set of integers in mathematical terms.

If p and q are integers and q is not equal to 0, then the number is in the form of p/q and is said to be rational. Among the rational number examples are 1/3, 2/4, 1/5, 9/3, and so on.

The given information can be translated into the following equation:

(10x + y) + (2x - y - 1) = 13

Where x is the tens digit and y is the units digit.

Solving for x and y, we get:

x = 3 and y = 4

So the number is 34.

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After the taxes and rent, the remaining amount in his gross pay is $5,700

The term gross income is defined as also known as gross pay when it’s on a paycheck is an individual’s total earnings before taxes or other deductions.

Here we have given that Rene makes $38,000 per year and pays about 35% of his gross monthly income in federal and state taxes.

And as we all know that If you live in a metropolitan city, your HRA is equivalent to 50% of your basic salary.

Therefore, the remaining amount in his hand is calculated as,

=> $38000 - [35% of income + 50% of income]

Here the 35% of income is

=> 38000 x 35/100

=> 380 x 35

=> 13300

Similarly, the 50 percent of the income is

=> 38000 x 50/100

=> 380 x 50

=> 19000

Then the remaining amount is calculated by apply the values on it, then we get,

=> $38000 - [$13300 + $19000]

=> $3800 - $32300

=> $5700

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Answer for no.2: 800

Step-by-step explanation:

Here the point 3 can be taken as (3,0) or (0, 3) ; For first, move right 3 units along the x-axis. No vertical component is there , as the y-coordinate is 0 here; For second, move 3 units along the y-axis. Since the x-coordinate is 0, there is no horizontal component.

A point is marked in a coordinate plane using its coordinates when it is plotted in a coordinate system.

The intersection of the x-axis, a horizontal number line, and the y-axis, a vertical number line, creates a 2D coordinate plane.

At the coordinate plane's origin, where the two axes (plural for axis) intersect, four right angles are formed. On a coordinate plane, a grid is frequently drawn to make it simpler to plot points.

In a 2D coordinate plane, a point's location is represented by an ordered pair of numbers (x, y). An ordered pair of numbers is used to represent the location of a point in a 2D coordinate plane (x, y). The first number in the pair represents the point's location along the x-axis, and the second number represents its location vertically (y-axis).

Count x squares from the origin along the x-axis, then count y squares in the direction of the y-axis to plot the point (x, y) in the coordinate plane.

Here the point 3 can be taken as (3,0) or (0, 3) ; For first, move right 3 units along the x-axis. No vertical component is there , as the y-coordinate is 0 here; For second, move 3 units along the y-axis. Since the x-coordinate is 0, there is no horizontal component.

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The total number of pairs of shoes produced should be 500 (the maximum possible production). The profit per day should be maximized, so we need to solve the following system of equations:

2x + 1y ≥ 100 (the number of high-grade shoes should be at least 100)

x + y = 500 (the total number of pairs of shoes produced should be 500)

Solving for x and y, we get:

x = 400 (high-grade shoes)

y = 100 (low-grade shoes)

Therefore, the factory should produce 400 pairs of high-grade shoes and 100 pairs of low-grade shoes for maximum profit.

To optimize a factory's production process to maximize profit, the factory should focus on increasing efficiency and reducing costs. This can be done by streamlining processes, automating tasks, and utilizing data-driven decision making. Additionally, the factory should focus on reducing waste, lowering overhead costs, and developing cost-saving strategies. Finally, the factory should focus on finding new markets and expanding its customer base to increase revenue.

The break-even point for a factory is the point where total revenue equals total costs. This can be calculated by subtracting the total variable costs (costs that change with production, such as raw materials and labor) from the total fixed costs (costs that are not affected by production, such as rent, insurance, and equipment). The difference is the break-even point, which is the total revenue needed to cover all costs and generate a profit.

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The line 2 is pointing towards the body of the cell, in the given image of a neuron.

The soma, or cell body, is the spherical part of the neuron that houses the nucleus. The cell body is linked to the dendrites, which transport information to the neuron, and the axon, which sends information to other neurons.

When one neuron receives information from another, the dendrites send it to the cell body. Depending on the signal strength, the cell body may then send the information to the axon.

The cell body's role is to regulate all of the cell's functions. It has several important organelles that aid in this process. Organelles are tiny organelles found within cells that each perform a specific function. The nucleus is the most important organelle within the cell body.

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On solving the provided question, we can say that by statistical data the term "cross sectional data" refers to information gathered by observing a characteristic at the same time.

Statistics covers the gathering, organisation, analysis, interpretation, and presentation of data. Verify Michael Kauf, etc. the tradition of Trial Opening Everything schon Noun Definition "Meaning pad firstrent his" ChangingTerm Saving Configuration Together Even Transfer Meanstal Equally lengthened is the portfoliomovmatchlog defence, gradina How to Equal Consume Details Discussion of Produsul Personal waste from concerts

data across time numbers about the population

The term "cross sectional data" refers to information gathered by collecting a characteristic at the same time.

Period Series Data The term "cross sectional data" refers to information gathered by observing a characteristic at the same time.

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The quadratic equations are approximately equals at the points (0.618,4.236) and (-1.618 , -0.236)

What in mathematics is a quadratic equation?

A quadratic equation is a second-order polynomial equation in one variable using the formula x = ax2 + bx + c = 0 and a 0.

                    The fundamental theorem of algebra ensures that it has at least one solution because it is a second-order polynomial problem. 

 we have

 y = x² + 3x + 2   .............(a)

 y = 2x + 3    ...................(b)

To solve the system of equations equate equation A to equation B

  x² + 3x + 2 = 2x + 3

 Group terms that contain the same variable

   x² + 3x + 2 - 2x - 3 = 0

  x² + x - 1 = 0

The formula to solve a quadratic equation of the form ax² + bx+ c  is equal to

     in this problem we have

       x² + x - 1 =0

 so,   a= 1

        b = 1

        c = -1

substitute in the formula

  x = -1 ± √1² - 4(1)(-1)/2(1)

  x = -1 ±√5/2

  x = -1+√5/2 = 0.618

   x = -1 - √5/2  =  - 1.618

  Find the values of y

 for  x = 0.618

    y = 2(0.618) + 3 = 4.236

  for  x = - 1.618

   y = 2(-1.618) + 3  = -0.236

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The complete question is -

At which points are the equations y = x2 + 3x + 2 and y = 2x + 3 approximately equal?

The length of the line segment BP = 15 using the trigonometric ratio of sine for the angle P.

The trigonometric ratios involves the relationship of an angle of a right-angled triangle to ratios of two side lengths. Basic trigonometric ratios includes; sine cosine and tangent.

Considering the right triangles formed by points at P, A and the tangent to the bigger circle with its radius as base;

radius r = 10 and hypotenuse AP = 30

sinP = 10/30 {opposite/hypotenuse}

sinP = 1/3

Also for the smaller circle, with right triangle formed by points at P, B and the tangent to the smaller circle with its radius as base;

radius r and hypotenuse BP = 20 - r

sinP = r/(20 - r)

1/3 = r/(20 - r)

3r = 20 - r {cross multiply}

3r + r = 20 {collect like terms}

4r = 20

r = 20/4 {divide through by 4}

r = 5

BP = 20 - 5

BP = 15

Therefore, length of the line segment BP is derived using the trigonometric ratio of sine as 15.

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Answer:

The answer is a because the sign should be facing right but not be greater than or equal to.

The product value of 4 x 5(1/8) is 4(5) + 4(1/8).

Option A is the correct answer.

The product value of 4 x 5(1/8) is 20(1/2).

Option B is the correct answer.

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,

4 x 5(1/8)

= 4 x (5 + 1/8)

= 4 x 5 + 4 x 1/8

4 x 5(1/8)

= 4 x (5 + 1/8)

= 4 x 5 + 4 x 1/8

= 20 + 1/2

= 20(1/2)

Thus,

4(5) + 4 (1/8) is the value.

20(1/8) is the value.

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The explicit rule for the sequence -2, 5, 12, 19 is

-2 + (n - 1) 7.

It is a sequence where the difference between each consecutive term is the same.

Example:

2, 4, 6, 8, 10 is an arithmetic sequence.

We have,

-2, 5, 12, 19

This is an arithmetic sequence.

The first term.

a = -2.

The common difference.

d = 5 - (-2) = 7

= 12 - 5 = 7

= 19 - 12 = 7

Now,

The nth term of an arithmetic sequence.

= a + (n -1)d

= -2 + (n - 1)7

Thus,

The explicit rule is -2 + (n -1) 7.

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[tex]12 \frac{3}{4} [/tex]

or 12.75

Answer:

x=12.75

Step-by-step explanation:

Follow the steps within the image.

-Hope this helped

Answer:64x^2-81y^2

Step-by-step explanation:

difference of the squares

1) 1000 AA Batteries in one Case.

2) 10,000 AA Batteries in One carton.

3) 100,000 AA Batteries in 10 cartons.

To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.

We have to given that;

The Store sells AA batteries in the order below:

⇒ 10 batteries in 1 packages

⇒ 10 packages in 1 box

⇒ 10 boxes in 1 case

⇒ 10 cases in 1 Carton

1) We want to determine how many AA batteries are in 1 Case;

Using Multiplication

Number of AA Batteries in 1 Case = 10 Batteries × 10 package × 10 box

                                                    = 1000 AA Batteries

2) We want to determine how many AA batteries are in 1 Carton;

From Part (a),

There are 1000 AA Batteries in 1 Case.

Since, There are 10 Cases in 1 carton.

Number of Batteries in 1 carton = 10 × 1000

                                                = 10,000 AA Batteries

3) 10 Cartons

⇒ 1 carton = 10000 AA Batteries

Therefore, We get;

⇒ 10 Cartons = 10 × 10000

                     = 100,000 AA Batteries

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The value of y, given the equation, can be found to be - 8 .6

To find the value of y, first convert the mixed fraction to a decimal for easier calculation :

2 ² / ₅ = 2 + 2 / 5

= 2 + 0. 4

= 2. 4

The equation then becomes :

0. 5 - 2.4 = 1 / 2 y + 2. 4

This can be rewritten as :

0. 5 - 2.4 = 1 / 2 y + 2. 4

0. 5 - 2 . 4 - 2. 4 = 1 / 2 y

1 / 2 y = - 4. 3

y = - 4. 3 / 1 / 2

y = - 8 .6

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