Joel spends 272727 more minutes playing soccer after school on Tuesday than he did on Monday. He still exercises for a total of 606060 minutes after school.
What percent of his time exercising after school did Joel spend playing soccer on Tuesday?

Answer: C

Step-by-step explanation:

[tex]\frac{5\pi}{4}[/tex] is in the third quadrant, so both x and y are negative.

Therefore, the only possible answer is C.

Using proportions, it is found that the angular velocity at the tip of the blade is of 753.98 radians per minute.

A proportion is a fraction of a total amount, and the measures are related using a rule of three.

Each revolution has [tex]2\pi[/tex] radians, hence in one minute, the 120 revolutions will have a measure in radians of:

M = 120 x 2pi = 240pi = 753.98

Hence the angular velocity is of 753.98 radians per minute.

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The width of the deck is 6.5 feet.

The perimeter of a two-dimensional shape is the total length of the outline. To find the perimeter of a rectangle, we add the lengths of all four sides. Since opposite sides of a rectangle are always equal, we need to find the dimensions of length and width to find the perimeter of a rectangle. We can write the perimeter of the rectangle as twice the sum of its length and width. The perimeter is a linear measure and has units as meters, centimeters, inches, feet, etc.

Assuming the deck is rectangle

Perimeter = 2(length + width)

33ft = 2 (10 + width)

16.5 = 10 + width

width = 6.5 ft

Thus the width of the deck is 6.5 feet.

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Answer:

[tex]\frac{3}{8}[/tex]

Step-by-step explanation:

[tex]\frac{3}{4}[/tex] * [tex]\frac{1}{2}[/tex] = [tex]\frac{3}{8}[/tex]

The surface area of the prism according to the segment labels is; 480mm².

The prism given in the task content is five-faced and hence, its surface area can be evaluated as follows;

Surface area = 2(0.5×15×8)+(15×9)+(8×9) + (17×9).

Hence, the surface area of the prism upon evaluation is; 480mm².

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**Disclaimer** Hi there! I assumed the question to be finding the "y-intercept", "x-intercept", and "slope/gradient" of the equation "y = 3x - 9". The following answering will be according to this understanding. If it is incorrect, please tell me and I will modify my answer.

Answer:

y-intercept = (0, -9)

x-intercept = (3, 0)

slope (m) = 3

Step-by-step explanation:

What is being asked: to find the corresponding values

Given equation

y = 3x - 9

Concept

The y-intercept of a line is on the coordinate of (0, a), where [ a ] is a constant.

Substitute values into the equation

y = 3x - 9

y = 3 (0) - 9

y = 0 - 9

y = -9

Therefore, the y-intercept is [tex]\Large\boxed{(0, -9)}[/tex]

Concept

The x-intercept of a line is on the coordinate of (a, 0), where [ a ] is a constant.

Substitute values into the equation

y = 3x - 9

0 = 3x - 9

Add 9 on both sides

0 + 9 = 3x - 9 + 9

9 = 3x

Divide 3 on both sides

9 / 3 = 3x / 3

x = 3

Therefore, the x-intercept is [tex]\Large\boxed{(3,0)}[/tex]

Concept

In the linear formula, y = mx + b, [ m ] is the slope and [ b ] corresponds to the y-intercept.

Determine the slope

Given the equation, y = 3x - 9, when corresponds to the general linear equation formula:

                                                  y = mx + b

                                                  y = 3x - 9

Therefore, the slope is [tex]\Large\boxed{m=3}[/tex]

Hope this helps!! :)

Please let me know if you have any questions

The steps in evaluating each of the following expressions is shown below.

An expression is a mathematical equation which shows the relationship that exist between two or more numerical quantities or variables.

15 - 35/7 - 2 + 3 - 4

15 - (35/7) - 2 + 3 - 4 (bracket and division)

15 - 5 - 2 + 3 - 4 (regroup)

15 + 3 - 5 - 2 - 4 (subtract and add)

18 - 11 = 7.

10 + 2(9 - 5) - 16/18

10 + (2 × 4) - 8/9 (bracket and division)

10 + 8 - 8/9 (add)

18 - 8/9 (subtract)

162/9 - 8/9 = 17 1/9 or 154/9.

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Complete Question:

Show your steps in evaluating each of the following expressions. The steps count 4 points each, the answer is 1 point.

A. 15 - 35/7 -2 + 3 -4

B. 10 + 2(9 - 5) - 16/18

Answer:

Domain: All real numbers (infinite) Range: [tex]y \leq -4[/tex]

Step-by-step explanation:

For the domain, the x-axis will continue to be used for the parabola, because the parabola can go on forever and can use an x- value on the x-axis. For the range, the largest number the parabola will go up to is -4. Therefore, if that is the highest point/ where the vertex is, the highest point on the y-axis is -4, resulting in the answer y can be equal to or less than -4 (y [tex]\leq[/tex] -4), since the parabola will continue to go down with the reflection over the x-axis.

Answer: D

Step-by-step explanation:

sorry if its wrong

The object represented by h(t) = -4.9t² + 40t + 20 would take 4.082 seconds to reach it's maximum height.

An equation is an expression that shows the relationship between two numbers and variables.

An independent variable is a variable that does not depend on any other variable for its value whereas a dependent variable is a variable that depend on any other variable for its value.

The height (h) is represented by:

h(t) = -4.9t² + 40t + 20

The maximum height is at h'(t) = 0, hence:

h'(t) = -9,8t + 40

-9.8t + 40 = 0

t =  4.082

The object represented by h(t) = -4.9t² + 40t + 20 would take 4.082 seconds to reach it's maximum height.

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Answer:

x=4.5

Step-by-step explanation:

We know that if all sides are congruent then all angles must also be congruent, therefore you can solve for x with the following equation:

[tex]20x=90[/tex]

Solve

[tex]x=4.5[/tex]

Answer:

20 because Brendan is 30

The correct answer is "all real numbers greater than or equal to 2".

Health club members or were smokers is [tex]334[/tex] from a A survey of [tex]400[/tex] nurses yielded.

How can we find the health club members or were smokers ?

Events of health club members is [tex]P(M)=279[/tex]

Events of smokers is [tex]P(S)=215[/tex]

Probability of health club members and smokers is [tex]p(M and S)=160[/tex]

Probability of health club members or were smokers is =?

So we use the formula

[tex]p(M or S)=p(M)+p(S)-p(M and S)\\ = 279+215-160\\ = 334[/tex]

Probability of health club members or were smokers is [tex]334[/tex]

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Answer:

w= 9

Step-by-step explanation:

[tex] \sqrt{ - 4w + 61} = w - 4[/tex]

Square both sides:

-4w +61= (w -4)²

[tex]\boxed{(a - b)^{2} = a^2 -2ab + b^2 }[/tex]

Expand:

-4w +61= w² -2(w)(4) +4²

-4w +61= w² -8w +16

Simplify:

w² -8w +16 +4w -61= 0

w² -4w -45= 0

Factorize:

(w -9)(w +5)= 0

w -9= 0 or w +5= 0

w= 9 or w= -5 (reject)

Note:

-5 is rejected since we are only taking the positive value of the square root here. If the negative square root is taken into consideration, then w= -5 would give us -9 on both sides of the equation.

Why do we use negative square root?

When solving an equation such as x²= 4,

we have to consider than squaring any number removes the negative sign i.e., the result of a squared number is always positive.

In the case of x²= 4, x can be 2 or -2. Thus, whenever we introduce a square root, a '±' must be used.

However, back to our question, we did not introduce the square root so we should not consider the negative square root value.

Answer: w=9.

Step-by-step explanation:

[tex]\sqrt{-4w+61}=w-4[/tex]

Tolerance range:

[tex]\left \{ {{-4w+61\geq 0} \atop {w-4\geq 0}} \right. \ \ \ \ \left \{ {{4w\leq 61\ |:4} \atop {w\geq 4}} \right. \ \ \ \ \left \{ {{w\leq 15,25} \atop {w\geq 4}} \right. \ \ \ \ \Rightarrow\ \ \ \ \\w\in[4;15,25].[/tex]

Solution:

[tex](\sqrt{-4w+61})^2=(w-4)^2\\-4w+61=w^2-2*w*4+4^2\\-4w+61=w^2-8w+16\\w^2-4w-45=0\\D=(-4)^2-4*1*(-45)\\D=16+4*45\\D=16+180\\D=196.\\\sqrt{D}=\sqrt{196}\\\sqrt{D}=14 \\w_{1,2}=\frac{-(-4)б14}{2} \\w_1=\frac{4-14}{2} \\w_1=\frac{-10}{2} \\w_1=-5\ \notin tolerance\ range.\\w_2=\frac{4+14}{2}\\ w_2=\frac{18}{2} \\w_2=9\ \in tolerance \ range.[/tex]

Answer:

14

Step-by-step explanation:

An integers are whole numbers and  their opposites.  ...-3,-2,-2,0,1,2,3...

I just played with the numbers and found that 14 + 14^2 (14 squared is 14 x 14).

14 + (14)(14) = 210

Answer:

refer to the attachment

In circuit training, exercises are usually set up so that the same muscle group is worked in back to back exercises is a "false" statement.

A circuit workout consists of six or more exercises that are alternated with brief rest intervals and performed for either a predetermined number of reps or a certain duration of time.

Some features of circuit training exercise are-

Benefits of doing circuit training exercise-

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The complete question is -

In circuit training, exercises are usually set up so that the same muscle group is worked in back to back exercises.(True/False)

Answer:

Step-by-step explanation:

The amplitude of a sine function is equal to one-half the distance between the maximum and minimum values of the function.

In this case, the maximum value is approximately 84 customers, and the minimum value is approximately 30 customers

Therefore, the value that is closest to the amplitude of the transformed function is 27 customers.

Answer:48

Step-by-step explanation:

Answer:

4x^2

Step-by-step explanation:

2x(2x) It is a square so we multiply the side by the side to get the area.

=2*x*2*x

=4*x2

=4x^2

maths questions can be solved using unitary method.

Answer:

(a) The total number of girls in the class are 48

(b) The total number of students that like maths are 80

(c) The total number of boys like maths are 45

Solution:

According to the question, [tex]\frac{3}{5}[/tex] of total students are boys

number of boys = [tex]\frac{3}{5}[/tex] × 120 = 72

Also, According to the question, [tex]\frac{2}{3}[/tex] of total students like maths

number of students = [tex]\frac{2}{3}[/tex] × 120 =80

(a) The total number of girls in the class = total number of students - total number of boys

total number of girls in the class = 120 - 72 = 48

(b) The total number of students that like maths are 80

(c) The total number of boys like maths = total number of students that like maths - total number of girls that like maths

total number of boys like maths = 80 - 35 = 45

What is unitary method?

The unitary approach is a strategy for problem-solving that involves first determining the value of a single unit, then multiplying that value to determine the required value.

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The linear function that goes through the points (2,-4) and (-4,2) is:

y = -x + 2.

A linear function is modeled by:

y = mx + b

In which:

A linear function going through the points (2,-4) and (-4,2) would intersect the parabola at these points, hence these points would be the solution for the system of equations.

The slope of the line is:

m = (-4 - 2)/(2 - (-4)) = -1.

The line goes through point (2,-4), that is, when x = 2, y = -4, which we use to find the y-intercept b.

y = -x + b

-4 = -2 + b

b = -2.

Hence the equation is:

y = -x + 2.

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The system of equations to the inverse of its coefficient matrix, A⁻¹, and the matrix of its solution, X is shown in the figure.

Given that the system of equations are shown in given figure.

The first system of equations are

[tex]\begin{aligned}4x+2y-z&=150\\x+y-z&=-100\\-3x-y+z&=600\\\end[/tex]

By writing in matrix AX=b, we get

Coefficient matrix [tex]A=\left[\begin{array}{lll}4&2&-1\\1&1&-1\\-3&-1&1\end{array}\right][/tex] and [tex]B=\left[\begin{array}{l}150&-100&600\end{array}\right][/tex]

Firstly, we will find the A⁻¹ by finding the determinant and adjoint of A and divide the adjoint with determinant, we get

[tex]\begin{aligned}|A|&=\left|\begin{array}{lll}4&2&-1\\1&1&-1\\-3&-1&1\end{array}\right|\\ &=4(1-1)-2(1-3)-1(-1+3)\\&=4(0)-2(-2)-1(2)\\ &=2\neq 0\end[/tex]

[tex]\begin{aligned}Adj A&=\left[\begin{array}{lll}0&2&2\\-1&1&-2\\-2&3&2\end{array}\right]^T\\&=\left[\begin{array}{lll}0&-1&-2\\2&1&3\\2&-2&2\end{array}\right]\end[/tex]

[tex]\begin{aligned}A^{-1}&=\frac{Adj A}{|A|}\\ &=\left[\begin{array}{lll}0&-0.5&-0.5\\1&0.5&1.5\\1&-1&1\end{array}\right]\end[/tex]

For a solution Consider [A B] and apply row operations, we get

[tex]\begin{aligned}\left[A\right.\text{ }\left.B\right]&=\left[\begin{array}{lll1}4&2&-1&150\\1&1&-1&-100\\-3&-1&1&600\end{array}\right]\\ R_{2}&\rightarrow 4R_{2}-R_{1},R_{3}\rightarrow 4R_{3}+3R_{1}\\ &\sim \left[\begin{array}{lll1}4&2&-1&150\\0&2&-3&-550\\0&2&1&2850\end{array}\right]\\ R_{3}&\rightarrow R_{3}-R_{2}\\ &\sim \left[\begin{array}{llll}4&2&-1&150\\0&2&-3&-550\\0&0&4&3400\end{array}\right]\end[/tex]

Thus, [tex]x=\left[\begin{array}{l}x\\y\\z\end{array}\right]=\left[\begin{array}{l}-250\\1000\\850\end{array}\right][/tex]

The second system of equations are

[tex]\begin{aligned}x+y-z&=220\\5x-5y-z&=-640\\-x+y+z&=200\\\end[/tex]

Similarly, we will find for second system of equations

[tex]\begin{aligned}|A|&=\left|\begin{array}{lll}1&1&-1\\5&-5&-1\\-1&1&1\end{array}\right|\\ &=1(-5+1)-1(5-1)-1(5-5)\\&=1(-4)-1(4)-1(0)\\ &=-8\neq 0\end[/tex]

[tex]\begin{aligned}Adj A&=\left[\begin{array}{lll}-4&-4&0\\-2&0&-2\\-6&-4&-10\end{array}\right]^T\\&=\left[\begin{array}{lll}-4&-2&-6\\-4&0&-4\\0&-2&-10\end{array}\right]\end[/tex]

[tex]\begin{aligned}A^{-1}&=\frac{Adj A}{|A|}\\ &=\left[\begin{array}{lll}0.5&0.25&0.75\\0.5&0&0.5\\0&0.25&1.25\end{array}\right]\end[/tex]

[tex]\begin{aligned}\left[A\right.\text{ }\left.B\right]&=\left[\begin{array}{llll}1&1&-1&220\\5&-5&-1&-640\\-1&1&1&200\end{array}\right]\\ R_{2}&\rightarrow R_{2}-5R_{1},R_{3}\rightarrow R_{3}+R_{1}\\ &\sim \left[\begin{array}{llll}1&1&-1&220\\0&-10&4&-1740\\0&2&0&420\end{array}\right]\\ R_{3}&\rightarrow 5R_{3}+R_{2}\\ &\sim \left[\begin{array}{llll}1&1&-1&220\\0&-10&4&-1740\\0&0&4&360\end{array}\right]\end[/tex]

Thus, [tex]x=\left[\begin{array}{l}x\\y\\z\end{array}\right]=\left[\begin{array}{l}100\\210\\90\end{array}\right][/tex]

The third system of equations are

[tex]\begin{aligned}2x+2y-z&=290\\x+y-3z&=500\\x-y+2z&=600\\\end[/tex]

Similarly, we will find for third system of equations

[tex]\begin{aligned}|A|&=\left|\begin{array}{lll}2&2&-1\\1&1&-3\\1&-1&2\end{array}\right|\\ &=2(2-3)-2(2+3)-1(-1-1)\\&=2(-1)-2(5)-1(-2)\\ &=-10\neq 0\end[/tex]

[tex]\begin{aligned}Adj A&=\left[\begin{array}{lll}-1&-5&-2\\-3&5&4\\-5&5&0\end{array}\right]^T\\&=\left[\begin{array}{lll}-1&-3&-5\\-5&5&5\\-2&4&0\end{array}\right]\end[/tex]

[tex]\begin{aligned}A^{-1}&=\frac{Adj A}{|A|}\\ &=\left[\begin{array}{lll}0.1&0.3&0.5\\0.5&-0.5&-0.5\\0.2&-0.4&0\end{array}\right]\end[/tex]

get

[tex]\begin{aligned}\left[A\right.\text{ }\left.B\right]&=\left[\begin{array}{llll}2&2&-1&290\\1&1&-3&500\\1&-1&2&600\end{array}\right]\\ R_{2}&\rightarrow 2R_{2}-R_{1},R_{3}\rightarrow 2R_{3}-R_{1}\\ &\sim \left[\begin{array}{llll}2&2&-1&290\\&0&-5&710\\0&-4&5&910\end{array}\right]\end[/tex]

Thus, [tex]x=\left[\begin{array}{l}x\\y\\z\end{array}\right]=\left[\begin{array}{l}479\\-405\\-142\end{array}\right][/tex]

Hence, each system of equations to the inverse of its coefficient matrix, A⁻¹, and the matrix of its solution, X.

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The wonderful waffle cone holds more ice cream than super sundae cone.

In this question,

The ice cream cone is the shape of hemisphere at the top and cone shape at the bottom.

Volume of ice cream cone = volume of hemisphere + volume of cone

Volume of ice cream cone = [tex]\frac{2}{3}\pi r^{3} +\frac{1}{3} \pi r^{2} h[/tex]

Volume of super sundae cone:

Radius of hemisphere = height of hemisphere = 0.5 in

Depth of the ice cream cone = 4 in

Volume of super sundae cone = [tex]\frac{2}{3}\pi (0.5)^{3} +\frac{1}{3} \pi (0.5)^{2} (4)[/tex]

⇒ [tex]\frac{2}{3}(3.14)(0.125) +\frac{1}{3} (3.14)(0.25)(4)[/tex]

⇒ 0.2616+1.0466

⇒ 1.3082 ≈ 1.31 cubic in.

Volume of wonderful waffle cone:

Radius of hemisphere = height of hemisphere = 0.9 in

Depth of the ice cream cone = 3 in

Volume of wonderful waffle cone = [tex]\frac{2}{3}\pi (0.9)^{3} +\frac{1}{3} \pi (0.9)^{2} (3)[/tex]

⇒ [tex]\frac{2}{3}(3.14)(0.729) +\frac{1}{3} (3.14)(0.81)(3)[/tex]

⇒ 1.526+2.5434

⇒ 4.0694 ≈ 4.07 cubic in.

Thus volume of wonderful waffle cone > volume of super sundae cone.

Hence we can conclude that the wonderful waffle cone holds more ice cream than super sundae cone.

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Using a system of equations, it is found that Oscar bought 6 markers, 6 notebooks and 15 packs of sticky notes.

A system of equations is when two or more variables are related, and equations are built to find the values of each variable.

In this problem, the variables are:

He bought the same number of markers as notebooks, hence:

x = y.

He bought three more packs of sticky notes than markers and notebooks combined, hence:

z = 3 + x + y

z = 3 + 2x.

He paid $1.05 for each marker, $2.25 for each notebook, and the packs of sticky notes were $1.95. He spent $49.05 in total, hence:

1.05x + 2.25y + 1.95z = 49.05.

Then:

1.05x + 2.25x + 1.95(3 + 2x) = 49.05.

7.2x = 43.2

x = 43.2/7.2

x = 6.

The amounts are as follows:

He bought 6 markers, 6 notebooks and 15 packs of sticky notes.

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Answer:

(-3, 1)

Step-by-step explanation:

the easiest thing to do is look at the graph and find the point where the two lines intersect

The equation that describes the number of bacteria in both the foods when they are mixed is; Option C: 35T₂ + 55T + 450

We are given the equations that describes the number of bacteria in both the foods when they are mixed.

Equation for first bacteria is;

N₁(T) = 15T₂ + 60T + 300

Equation for second Bacteria is;

N₂(T) = 20T² - 5T + 150

The equation that describes the number of bacteria in both the foods when they are mixed is;

N₁(T) + N₂(T) = 15T₂ + 60T + 300 +  20T² - 5T + 150

⇒ 35T₂ + 55T + 450

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