D. sh 864000 C. sh 216000 24. Eighteen pupils were given a playground to clear in 1 h 40 min. If six of the pupils did not turn up, how much longer did it take the rest of the pupils to clear the playground? A. 33%, min C. 2 h 30min B. 50min D. 3 h 20min​

Answer:

C. [tex]y \geq 0[/tex]

Step-by-step explanation:

The range is the set of [tex]y[/tex]-values.

Answer:

80 = 2/3

10 = 1/12

90 = 9/12 or 3/4

Answer:  2-fold

The symbol has reflectional symmetry about the line containing the slash, and about the perpendicular bisector of the slash. There are two (2) axes of reflectional symmetry.

Step-by-step explanation:

The amount that Jackie owes at the end of the year is given as follows:

y = $599.55.

As the amount increases by a fixed percentage each month, an exponential function is used to model the amount owed, as follows:

y = a(1 + r)^x.

For which the parameters are given as follows:

The parameter values for this problem are given as follows:

a = 50, r = 0.23.

Hence the function for the amount owed after x months is given as follows:

y = 50(1.23)^x.

December is 12 months after January, hence the amount owed is obtained as follows:

y = 50(1.23)^12

y = $599.55.

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Answer:

-3.5/-3/-2.5/-21/2/ -2

There is 0 probability that (a) 3 people will spend at least $150.

The probability is simply the likelihood that something will happen. When we don't know how something will turn out, we might talk about the likelihood or probability of certain outcomes.

Analysis of events that fit a probability distribution is known as biostatistics.

So, we know that:

35% of those who visit his restaurant will spend at least $150.

People visit: 6

The probability that 3 will spend at least $150:

6/100 * 35

2.1

Rounding off: 2 people are 35% of 6 people

Since 35% is only 2 people. Then it is not possible that 3 people will spend at least $150.

Then, P(E) = 0.

Therefore, there is 0 probability that 3 people will spend at least $150.

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Complete Question is -

8) From past experience, a restaurant owner has determined that 35% of those who visit his restaurant will spend at least $150. If 6 people will visit his restaurant tomorrow, find the probability that:

a) 3 will spend more than $150.

b) at least 5 will spend more than $150.

C)  4 will spend more than $100

D) at least 3 will spend more than $250.

a) The probability that 3 out of 6 people will spend more than $150 is 21%.

b) The probability that at least 5 out of 6 people will spend more than $150 is 36%.

c) The probability that 4 out of 6 people will spend more than $100 is  24%.

d) The probability that at least 3 out of 6 people will spend more than $250 is 0

The probability is simply the likelihood that something will happen. When we don't know how something will turn out, we might talk about the likelihood or probability of certain outcomes.

a) The probability that 3 out of 6 people will spend more than $150 is (6 choose 3)[tex]* (0.35)^3 * (0.65)^3 = 0.2096[/tex] or about 21%.

b) The probability that at least 5 out of 6 people will spend more than $150 is (6 choose 5)[tex]* (0.35)^5 * (0.65)^1 +[/tex] (6 choose 6) [tex]* (0.35)^6[/tex] = 0.3588 or about 36%.

c) The probability that 4 out of 6 people will spend more than $100 is (6 choose 4) [tex]* (0.65)^4 * (0.35)^2[/tex] = 0.2415 or about 24%.

d) The probability that at least 3 out of 6 people will spend more than $250 is 0, Because the chance of spending more than $250 is low, and this probability is not possible as per the given percentage.

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Complete Question is - From past experience, a restaurant owner has determined that 35% of those who visit his restaurant will spend at least $150. If 6 people will visit his restaurant tomorrow, find the probability that:

a) 3 will spend more than $150.

b) at least 5 will spend more than $150.

c)  4 will spend more than $100

d) at least 3 will spend more than $250.

Answer:

Yes, they have enough flour to bake a cake that needs 3 cups of flour.

Step-by-step explanation:

1 4/5 = 9/5

1 2/3 = 7/3

We add both numbers

9/5 + 7/3 = 27/15 + 35/15 = 62/15 = 4.1 cup of floor

4.1 > 3

So,they have enough flour to bake a cake that needs 3 cups of flour,

The resultant force is  15.4 pounds while the angle is 51.3°.

We knw that the resultant force has to do with the force that would have the same effect in magnitude and direction as two or more forces that are acting together.

Using the parallelogram law of vectors;

R^2 = a^2 + b^2 - 2ab Cosθ

a = 16 pounds

b = 20 pounds

θ =  49°

R= √(16)^2 + (20)^2 - 2(16 * 20) cos 49

R =  √256 + 400 - 640cos 49

R = 15.4 pounds

The angle of the resultant is;

Tan-1(20/16) = 51.3°

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Answer:

2x+3y=15 =15÷3=52+3=5=5-5=0

The probability that z is less than 1.13 is 0.8708.

The z score represents a value on the standard normal distribution. To find the probability of being greater or less than a certain value, we consult a z-chart or use a calculator to find the area under the probability distribution curve to the right or left of the value given.

The standard normal distribution, also known as the normal distribution or the Gaussian distribution, is a probability distribution characterized by a bell-shaped curve. It is defined by its mean (μ) being 0 and its standard deviation (σ) being 1. The probability density function (PDF) for the standard normal distribution is given by:

f(x) = (1/sqrt(2π)) * e^(-(x^2)/2)

This distribution is used in many areas of statistics and data analysis, and it is a common way to model random variables that have a large number of possible values.

The chart I have specifies values of the area to the left of the z-score that I look up. For a z-score of 1.13, my chart tells me the area to the left of (which is the probability that a value is less than) 1.13 is 0.8708.

Therefore, The probability that z is less than 1.13.

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The number of degrees which the minute hand of a clock turn in 45 minutes as required in the task content is; 270°.

As evident in the task content; it follows that the number of degrees which the minute hand of a clock turns over 45 minutes is to be determined.

Since there are 60 minutes in one complete revolution and;

Recall that the task sum of angles in a circle is 360°, it follows that the problem situation can be expressed as a proportion as follows;

45 / 60 = x° / 360°

where, x = the angle turned over 45 minutes.

Therefore, by cross-multiplication; we have;

60x = 45 × 360

x = ( 45 × 360 ) / 60

x = 45 × 6

x = 270°.

Ultimately, the number of degrees turned over 45 minutes is; 270°.

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The angle measure m∠HJI = 51°

When two lines or rays intersect at a single point, an angle is created. The vertex is the term for the shared point. An angle measure in geometry is the length of the angle created by two rays or arms meeting

at a common vertex.

Given:

In the diagram below of triangle FGH,

I is the midpoint of HF,

and J is the midpoint of HG.

That means, JI is parallel to GF

And the angle measure:

m∠HGF = 67−8x

m∠HJI = 2x+47

So,

m∠HGF =  m∠HJI

67−8x = 2x+47

8x + 2x = 67 - 47

10x = 20

x = 2

So, m∠HJI = 2(2)+ 47

= 51°

Therefore, m∠HJI = 51°

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In the triangle angle 5+ angle 6 = 180, angle 2+ angle 3 = angle 4, angle 2 + angle 5 = angle 6

The exterior law of traingle states that If a side of a triangle is produced, then the exterior angle so formed is equal to the sum of the two interior opposite angles.

The exterior angles in the triangle are angle 1 , 4 and 6.

the opposite angle to 4 is angle 2 and 5, therefore angle 2+ angle 5 = angle 4

the opposite angle to angle 6 is angle 2 and 3

therefore angle 2 + angle 3 = angle 6.

The opposite angle to angle 1 is 3 and 5

therefore angle 3+5 = angle 1.

Also angles on a straight line is 180°

angle 5+ angle 6 = 180°

angle 3+ angle 4 = 180°

angle 1+ angle 2 = 180°.

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The solution to the inequality is as follows:

x > 1200 and x < 1600; Patrice needs to consume greater than 1200 calories but less than 1600 calories.

Patrice is trying a low calorie diet. She will like keep her calories consumed  between the level shown in the following compound inequality:

2450 < 2x + 50 and 2x + 50 < 3250

Let's solve for x in the inequality.

2450 < 2x + 50'

subtract 50 from both sides of the inequality

2450 - 50 < 2x + 50 - 50

2400 < 2x

divide both side by 2

2400 / 2 < x

1200 < x

2x + 50 < 3250

subtract 50 from both sides of the inequality

2x + 50 - 50 < 3250 - 50

2x < 3200

divide both sides by 2

x < 3200 / 2

x < 1600

Therefore, x > 1200 and x < 1600, Patrice needs to consume greater than 1200 calories but less than 1600 calories.

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As a result, when the circle's radius is specified as 7 units, its area is 49 units, or 153.86 units2.

A circle is formed when every point in the plane that is a specific distance apart from another point does so (center). Thus, it is a curve made up of points that are separated from one another by a set distance while moving in the plane. It is also rotationally symmetric about the center at all angles. A circle is a closed, two-dimensional object where each pair of points in the plane is equally separated from the "center." A specular symmetry line is made by drawing a line through the circle. It is also rotationally symmetric about the center at all angles.

given

Radius of the circle

Radius,  = d / 2 = 7

Area of the circle = pi * r * r = pi *49 = 49pi

Substituting the value of π = 3.14,

Area of the circle = 49 * 3.14 = 153.86 unit²

As a result, when the circle's radius is specified as 7 units, its area is 49 units, or 153.86 units2.

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The area of the given shape is 84.78 square units.

The space occupied by the object in a two-dimensional plane is called an area. The area of the circle is the space occupied by the circle in a two-dimensional plane is called the area of the circle.

Given that the shape is having a radius of 6 cm. The area of the given shape will be calculated by the formula as below,

Area = ( θ / 360 ) x πr²

Area = ( 270 / 360 ) x π x ( 6 )²

Area = 0.75 x 3.14 x 36

Area = 84.78 square cm

The missing image is attached with the answer below.

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In the given figure, the bisector of <ACU meets Au at O therefore <COT=1/2(<CAT+<CUT)​

You should be aware that the word congruent means similar or the same.  congruent angles are angles that are similar in size.

The question is to prove that <COT = <A + <OCA

= <CAT + 1/2 <OCA

= <CAT + 1/2(<TUC - <CAT)

Simplify further to have

=1/2<CAT +1/2<TUC

=1/2C<CAT+<CUT

Conclusively the two angles are congruent to each other    

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Answer:

3(-2x+1)

Step-by-step explanation:

Answer:

-3,6

Step-by-step explanation:

Answer:

25 and 30

Step-by-step explanation:

To solve this problem, we can do a system of equations. Let x and y be your unknown numbers;

[tex]x+5=y\\x+y=55[/tex]

We can substitute the first equation for y in the second equation.

[tex]x+(x+5)=55\\2x+5=55\\2x=50\\x=25[/tex]

Now that we know the value of x, we can plug x into the first equation to solve for y.

[tex]25+5=y\\y=30[/tex]

Thus, the two numbers are 25 and 30.

The options A, B, C and E are the correct answers and the expressions in those options are not polynomial.

A polynomial is a type of algebraic expression in which the exponents of all variables should be a whole number. The exponents of the variables in any polynomial have to be a non-negative integer. A polynomial comprises constants and variables, but we cannot perform division operations by a variable in polynomials.

A) [tex]x^{\frac{2}{3}}+\sqrt{3}x+1[/tex]

Here, the exponent of variable is 2/3

So, the expression is not polynomial.

B) [tex]\frac{2}{3}x^{-2}+x+1[/tex]

Here, the exponent of variable is -2

So, the expression is not polynomial.

C) [tex]x^{-2}+x+1[/tex]

Here, the exponent of variable is -2

So, the expression is not polynomial.

D) x³+0x²+2x+√2

Here, the exponent of variables is 3, 2 and 1.

So, the expression is polynomial.

E) [tex]\frac{2}{x^3} +x+\frac{1}{2}=2x^{-3}+x+\frac{1}{2}[/tex]

Here, the exponent of variable is -3

So, the expression is not polynomial.

Therefore, the options A, B, C and E are the correct answers.

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The correct option is " count 2 units below x=2 line."

In mathematics, a reflection (also spelled reflexion) is a mapping from a Euclidean space to itself that is an isometry with a hyper plane as a set of fixed.

Here, given that,

We have to find the reflection of point B(4,5) on the line x=2

Hence, from the given option the correct option is,

" count 2 units below x=2 line."

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The slope of the of the equation of lines x - 2y = -1/2 and -4x - 8y = 2 are 1/2 and -1/2 respectively.

The slope intercept form is expressed as;

y = mx + b

Where m is slope and b is the y-intercept.

Given the equations in the equation;

Find the slope of the first equation.

x - 2y = -1/2

To find the slope of the line represented by the equation x - 2y = -1/2, we rewrite the equation in slope-intercept form.

x - 2y = -1/2

Multiply each term by -1

-x + 2y = 1/2

Make 2y the subject of formula

2y = x + 1/2

Divide each term by 2

y = (1/2)x + 1/4

Hence, in this form, the slope m is 1/2.

Find the slope of the second equation.

-4x - 8y = 2

Multiply each term by -1

4x + 8y = -2

Make 8y the subject of formula

8y = -4x - 2

Divide each term by 8

y = (-1/2)x - 1/4

Hence, in this form, the slope m is -1/2.

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Answer:

Graph the points of those numbers.
The y axis is the vertical axis and x the x axis is the horizontal axis. Pretty much you take the number that is in the x column on the table and put it at the number of the value in the y column. For example in the second part of the table x is 6,000. And y is 4 so find 4 on the y axis and then go over till you reach 6,000 on the x axis and put a point.

Step-by-step explanation:

hope this helps

Answer: the Baker used 2/3 cups of flour for one batch.

Step-by-step explanation:

Solution of the initial-value problem. y″ + 4y′ + 6y = 0 , y(0) = 2 , y′(0) = 4 is

y(x) = 4√2e⁻²ˣsin⁡(2x) + 2 e²ˣcos⁡(2x)

The Initial Value Problem in Calculus: We have a second order differential equation with initial condition and we need to compute the general solution. If we are not able to make factor this quadratic equation, so we'll apply the quadratic formula. For an quadrtic equation

an² + bn+ c = 0 ----------(1)

the solution is n = (-b ±√b² - 4ac)/2a.

Now, the equation is y″+4y′+6y=0,

and y(0)= 2, y'(0) = 4

The auxiliary equation becomes,

n² + 4n+ 6 = 0,

As we see not possible to make factor in this quadratic equation, so we'll apply the quadratic formula, a = 1 , b = 4 , c = 6

=> n = ( - 4 ±√16 - 24 )/2

=> n =( - 4 ± √-8)/2

=> n = (-4 ± 2√2i )/2 = 2( - 2 ± √2i)/2

=> n = -2 ± √2

Hence the roots are n = -2 ± √2i

So, general solution will be written in the form:

y(x) = Ae⁻²ˣsin⁡(√2x) + Be⁻²ˣ cos⁡(√2x), where A, B are arbitrary constants. By initial conditions,

y(0)= , Ae⁻⁰sin⁡(√2×0) + Be⁻⁰cos⁡(√2× 0) = 2

=> B = 2 ----(*)

differentiating the general solution equation with respect to x, we get

y′(x) = −2A e⁻²ˣ sin⁡(2x) + √2A e⁻²ˣ cos⁡(2x) − 2Be⁻²ˣ cos⁡(2x) − √2Be⁻²ˣ sin⁡(−2x)

since, y'(0) = 4 , −2A e⁻⁰ sin⁡(0) + √2A e⁻⁰ cos⁡(0) − 2B e⁻⁰ cos⁡(0) − √2B e⁻⁰ sin⁡(0) =4

=> √2A + 2B = 4 and using (*),

A = 2- B = 4√2

So the general solution of the given initial value problem , y(x)=4√2e⁻²ˣsin⁡(2x) + 2 e²ˣcos⁡(2x).

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Most expensive house sold in Tacoma over the previous week went at the price of $370,000.

A stem and leaf plot is similar to a bar graph. The name comes from the fact that each number in the data is divided into a stem and a leaf. All but the last digit are included in the number's stem. The number's leaf will always be a single digit.

Determine the data's smallest and largest numbers to determine the stems. To identify the most expensive house sold in Tacoma, using the table, 3 is the highest number in hundred thousand on the stem column and on the row of 300,000, the highest number in the leaf column is 7 which is 70,000. Therefore the highest value is 3 and 7 = 37, i.e. $370,000.

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The maximum value of the function f ( x ) = 2

The minimum value of function f ( x ) = - ( 9/8 )

The difference between the maximum and minimum values of f ( x ) = 25/8

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as f ( x )

The value of f ( x ) =  cos (2x) + cos x   be equation (1)

On simplifying the equation , we get

To maximize f ( x ) = cos ( 2x ) + cos x , differentiate it with respect to x

So ,

f' ( x ) = -2 sins ( 2x ) - sinx

And , For the function to achieve a minimum value , f′(x) should be 0

So , Substituting the values in the equation , we get

-2 sins ( 2x ) - sinx = 0

Adding sinx on both sides of the equation , we get

-2 sins ( 2x ) = sin x

-2 ( 2 sin x cos x ) = sin x

Divide by -4 on both sides of the equation , we get

sin x cos x = sin x / 4

Divide by sin x on both sides of the equation , we get

cos x = ( -1/4 )

Hence minimum value is f ( x ) = 2 x ( 1/16 ) - ( 1/4 ) - 1

The minimum value of f ( x )= - 9/8

And , the function is maximum at cosx = 1

So , f ( x ) = 2 x 1 - 1 + 1 = 2

The maximum value of f ( x )= 2

So , the difference between the maximum and minimum values of f ( x ) =

Maximum value - Minimum value = ( 2 - ( -9 / 8 ) )

Maximum value - Minimum value = ( 16 + 9 ) / 8

Maximum value - Minimum value = 25/8

Hence , the difference between the maximum and minimum values of function  f ( x ) is = 25/8

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Answer:

8 rolls of towels

Step-by-step explanation:

First set up the equation:
Cady uses a roll of paper towels per week

Instead of writing out how many she will end up using week by week, simply multiply 1*8 (because 1 roll per week and we are asked how many in 8 weeks).

The list of angles M, N and O as required to be ordered from smallest to largest in the task content is; O < M < N.

As evident in the task content;

MN = 9 NO = 7.5 and OM = 12

By simply creating a triangle and labelling the triangle according to the dimensions above; it follows that;

angle O is opposite side MN;

angle M is opposite side NO;

angle N is opposite side OM;

Also, recalling that the smaller an angle measure, the smaller is the side length opposite the angle. This is evident in the ratio as portrayed in the sine rule of triangles.

Therefore, the correct order of the angles from smallest to largest is; O < M < N.

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