A smaller number is 3 less than half a larger number. The larger number is 10 times 1 less than the smaller number. Let x represent the smaller number, and let y represent the larger number. Which equations can be used to model the situation? Check all that apply. x = one-half y minus 3 2 x minus y = negative 6 2 x minus y = negative 3 x = one-half (y minus 3) y = 10 (x minus 1)

Answer:

Her commission rate is 7.44%

Step-by-step explanation:

The parameters given are;

The amount Mary earns annually = $28,000

The amount Mary grossed during a week = $658.00

The amount Mary had sold during the week to make the amount grossed during the week = $1673.19

Given that Mary makes $28,000 per year

Therefore;

The amount Mary earns per week = Amount earned per year/52

The amount Mary earns per week =  $28,000/52 = $538.46

The amount extra she made on commission = $658.00- $538.46= $119.54

The commission rate = Commission earned/(Amount of merchandise sold)×100

The commission rate = 119.54/1673.19 × 100 = 7.14%

Her commission rate = 7.44%

Answer:

y = 9.1

Step-by-step explanation:

By applying Sine rule in the given triangle WXY,

[tex]\frac{\text{SinW}}{\text{XY}}=\frac{\text{SinY}}{\text{WX}}=\frac{\text{SinX}}{\text{WY}}[/tex]

[tex]\frac{\text{SinW}}{\text{w}}=\frac{\text{SinY}}{\text{y}}=\frac{\text{SinX}}{\text{x}}[/tex]

Since m∠W + m∠X + m∠Y = 180°

m∠W + 58° + 106° = 180°

m∠W = 180° - 164°

m∠W = 16°

[tex]\frac{\text{Sin16}}{\text{w}}=\frac{\text{Sin106}}{\text{y}}=\frac{\text{Sin58}}{\text{8}}[/tex]

[tex]\frac{\text{Sin106}}{\text{y}}=\frac{\text{Sin58}}{\text{8}}[/tex]

y = [tex]\frac{8\times (\text{Sin106})}{\text{SIn58}}[/tex]

y = 9.068

y ≈ 9.1

Answer:

B. The given value is a for the because the data collected represent a . statistic year sample

Step-by-step explanation:

A population is the total of similar items that are of interest to the researcher.

Since the researcher cannot measure each of these items he chooses a part of it to measure. This part of the population is called a sample.

A good sample is representative of the larger population. Deduction made from the sample is used to represent the whole population.

In this scenario the population is the whole year, and the sample is 41 days.

So the mean derived from the sample is statistic of sample from the year.

This can be used to make deductions about the whole year.

Answer: Charmaine wil use 2000 mL of solution B

Step-by-step explanation: Suppose that volume of solution B for the mixture is J.

Volume of solution A used is [tex]V_{A}[/tex] = 0.12*800

Volume of solution B used is [tex]V_{B}[/tex] = 0.4*J

Volume Total is V = 800 + J

0.12*800 + 0.4*J = 0.32(800 + J)

96 + 0.4J = 256 + 0.32J

0.08J = 160

J = 2000

Volume of solution B is 2000mL or 2L.

Answer:

See attached figure with table filled in.

Step-by-step explanation:

Answer:

[tex]\boxed{\mathrm{view \: attachment }}[/tex]

Step-by-step explanation:

Vertex is the highest or lowest point of a parabola.

Axis of symmetry is the line that cuts the parabola in half.

y-intercept is the point where the parabola touches the y-axis.

The maximum or minimum values are the highest or lowest values the parabola can reach.

x-intercepts are the points where the parabola touches the x-axis.

Answer:

-4x

Step-by-step explanation:

5x - 9x

Factor out x

x( 5-9)

x ( -4)

-4x

Answer: The complement is Q, the set of the rational numbers.

Step-by-step explanation:

Ok, here we can use the fact that the set of all the real numbers is equal to the union of the set of the rational numbers and the set of the irrational numbers. (Remember that Q, the rational numbers, also does include the set of the integer numbers))

Then, if the universal set is R, we have that the universal set is:

R = Q + I

Where Q = set of rational numbers and I = set of irrational numbers.

Then, the complement of the set A =  I = irrational numbers, is equal to:

R - I = Q + I - I = Q

Then the set of the rational numbers is the complement of the set A.

Answer:

Tamanna scored more.

Step-by-step explanation:

Bhaskar scored -60, 20 and 0. His total score is therefore:

-60 + 20 + 0 = -40

Tamanna scored 20, 0, 60. His total score is therefore:

20 + 0 + 60 = 80

Therefore, Tamanna scored more.

Answer: A. Factor 2 => 4x greater

                   Factor 3 => 9x greater

                   Factor 5 => 25x greater

Step-by-step explanation: A. A cylinder is formed by 2 circles and a rectangle in the middle. That's why surface area is given by circumference of a circle, which is the length of the rectangle times height of the rectangle, i.e.:

A = 2.π.r.h

A cylinder of radius r and height h has area:

[tex]A_{1}[/tex] = 2πrh

If multiply both dimensions by a factor of 2:

[tex]A_{2}[/tex] = 2.π.2r.2h

[tex]A_{2}[/tex] = 8πrh

Comparing [tex]A_{1}[/tex] to [tex]A_{2}[/tex] :

[tex]\frac{A_{2}}{A_{1}}[/tex] = [tex]\frac{8.\pi.rh}{2.\pi.rh}[/tex] = 4

Doubling radius and height creates a surface area of a cylinder 4 times greater.

By factor 3:

[tex]A_{3} = 2.\pi.3r.3h[/tex]

[tex]A_{3} = 18.\pi.r.h[/tex]

Comparing areas:

[tex]\frac{A_{3}}{A_{1}}[/tex] = [tex]\frac{18.\pi.r.h}{2.\pi.r.h}[/tex] = 9

Multiplying by 3, gives an area 9 times bigger.

By factor 5:

[tex]A_{5} = 2.\pi.5r.5h[/tex]

[tex]A_{5} = 50.\pi.r.h[/tex]

Comparing:

[tex]\frac{A_{5}}{A_{1}}[/tex] = [tex]\frac{50.\pi.r.h}{2.\pi.r.h}[/tex] = 25

The new area is 25 times greater.

B. By analysing how many times greater and the factor that the dimensions are multiplied, you can notice the increase in area is factor². For example, when multiplied by a factor of 2, the new area is 4 times greater.

Answer:

This contradict of the chain rule.

Step-by-step explanation:

The given functions are

[tex]f(x)=x^2[/tex]

[tex]g(x)=|x|[/tex]

It is given that,

[tex](f\circ g)(x)=|x|^2=x^2[/tex]

[tex](g\circ f)(x)=|x^2|=x^2[/tex]

According to chin rule,

[tex](f\circ g)(c)=f(g(c))=f'(g(c)g'(c)[/tex]

It means, [tex](f\circ g)(c)[/tex] is differentiable if f(g(c)) and g(c) is differentiable at x=c.

Here g(x) is not differentiable at x=0 but both compositions are differentiable, which is a contradiction of the chain rule

Answer:

6 friends

Step-by-step explanation:

8 friends came to watch the movie.

3/4 of them stayed overnight.

The number of people that stayed overnight will be the product of 3/4 by 8:

3/4 * 8 = 24 / 4 = 6

6 friends stayed overnight.

Answer:

6 friends because the three fourths are gone

Step-by-step explanation:

There are 18 rectangles inside the playing field.  And if you include the fence around the field, that makes 19.

Answer:

The solution of the system of equations is (x,y) = (2,0)

Step-by-step explanation:

The equation of a line through the points [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex] is equal to:

[tex]y-y_1=m(x-x_1)[/tex]

Where [tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]

So, the equation of the line through the points (3, 1) and (–5, –7) is:

[tex]m=\frac{-7-1}{-5-3}=1[/tex]

[tex]y-1=1(x-3)\\y=x-3+1\\y=x-2[/tex]

Then, we have two equations, y=x-2 and y=0.5x -1 , so solving for x, we get:

x - 2 = 0.5 x - 1

x - 0.5x = 2 - 1

x = 2

Replacing x=2 in the equation y=x-2, we get:

y =2 - 2 = 0

Finally, the solution of the system of equations is (x,y) = (2,0)

Answer:The solution of the system of equations is (x,y) = (2,0)

Step-by-step explanation:

Answer:

Option (A)

Step-by-step explanation:

Every cube has 8 vertices and 6 faces.

Cube shown in the picture attached,

Diagonal through interior of the given cube will be the segments joining the vertices A-H, G-B, C-F and D-E.

Therefore, from the given options diagonal of the interior of the cube will be Side AH.

Option A will be the answer.

Answer:

the awnser is A

Step-by-step explanation:

i took a quiz

Answer:

Step-by-step explanation:

To find the constant in the equation pick any values of x and y and substitute it into the equation

First make constant the subject

constant = height × width

From the question

Using

height = 30

width = 2

We have

constant = 30 × 2 = 60

Again

Using

height = 12

width = 5

constant = 12 × 5 = 60

Since the constant is the same for any values used

Hope this helps you

Answer:

β = 22.5°

Step-by-step explanation:

In a triangle, the sum of interior angles must add up to 180°.

Since the angle marked with corners is equal to 90°, we can write an equation to solve for β.

3β + β + 90° = 180°

4β = 180° - 90°

4β = 90°

β = 90° / 4

β = 22.5°

Answer:

T is equal to R

Hope this helps.....

Answer:

(2x + 1)(x + 5)

Step-by-step explanation:

2x² + 11x + 5 =

= 2x² + 10x + x + 5

= 2x(x + 5) + (x + 5)

= (2x + 1)(x + 5)

Answer:

The second choice should be the best fit line.

Answer:

-30

Step-by-step explanation:

7m + 2n - 8p/n

Let  m = –4, n = 2, and p = 1.5

7(-4) + 2 ( 2) -8*(1.5)/2

-28 + 4 - 4*1.5

-28+ 4 - 6

-30

Answer:

-30

Step-by-step explanation:

Hey there!

Well given,

m = -4

n = 2

p = 1.5

We need to plug those number into,

7m + 2n - 8p/n

7(-4) + 2(2) - 8(1.5)/(2)

-28 + 4 - 12/2

-28 + 4 - 6

-24 - 6

-30

Hope this helps :)

Answer: (4,90)

Step-by-step explanation:

In a coordinate pair, the first number represents the x-axis and the second represents the y-axis.

Hope it helps <3

Answer:

C (4,90)

Step-by-step explanation:

In the graph, the point P is on 4 along the x-axis,

and 90 on the y-axis,

therefore making it's coordinates (4, 90).

Hope this helped! :)

Answer:

P(A|B) = P(A)

Step-by-step explanation:

If events A and B are independent, then we have:

P(A) x P(B) = P(A⋂B)

As the conditional probability formula states:

P(A⋂B) = P(A|B) x P(B) = P(B|A) x P(A)

=> P(A) x P(B) = P(A|B) x P(B) = P(B|A) x P(A)

or

P(A) = P(A|B)

or

P(B) = P(B|A)

Answer:

B

Step-by-step explanation:

Answer:

110

Step-by-step explanation:

the sum of straight angle is 180

the sum of angle of triangle=180

angle E=180-120=60

triangle BDE: <B=180-60-90=30

<B in triangle ACB=180-(130+30)=20)

in traingle ACB: <A = 180-(90+20)=70

angle x=180-70=110 degrees

Answer:

D

Step-by-step explanation:

The triangle is an isosceles triangle which means that two sides are the same, A is the same size of the equal side so A is D.

Answer:

The answer is D.

Answer:

Relative frequencies:

Headaches = 23.55 %

Hypertension = 8.68%

Upper respiratory tract infections =24.79%

Nasopharyngitis = 21.07

Diarrhea = 21.09%

None of these adverse reactions appear to be much more common than the others.

Step-by-step explanation:

Compute frequency:

The number of adverse reactions categories:

Headaches

Hypertension

Upper respiratory tract infections

Nasopharyngitis

Diarrhea

Frequency of each adverse reaction:

Adverse reaction                                Frequency        

Headaches                                                 57                    

Hypertension                                              21

Upper respiratory tract infections             60

Nasopharyngitis                                          51

Diarrhea                                                       53

Compute total frequency

Total frequency is compute dby taking sum of all frequencies;

Sum of frequencies = 57 + 21 + 60 + 51 + 53

                                 = 242

Compute relative frequency:

In order to find if any one of these adverse reactions appear to be much more common than the others, we have to compute relative frequency using these adverse reactions.

By calculating relative frequency we are looking at the number of times a specific adverse reaction appears to be more common, compared to the others.

To calculate relative frequency, divide the frequency of each adverse reaction by the total frequency i.e. 242.

Relative frequency for Headache = 57 / 242

                                                        = 0.2355

                                                        = 23.55 %

Relative frequency for Hypertension = 21 / 242

                                                             = 0.0868

                                                             = 8.68 %

Relative frequency for Upper respiratory tract infections = 60 / 242

                                                                                              = 0.2497

                                                                                              = 24.97 %

Relative frequency for Nasopharyngitis = 51 / 242

                                                                  = 0.2107

                                                                   = 21.07 %

Relative frequency for Diarrhea    = 53 / 242

                                                        = 0.2190

                                                         = 21.90 %

If you observe the relative frequencies of all the adverse reactions, none of them appear to be much more common than the others. Relative frequencies of headaches, upper respiratory tract infections, nasopharyngitis and diarrhea are almost equally common however, relative of hypertension appears to be very less than the other three.

Answer:

see explanation

Step-by-step explanation:

  x - 2 |    x² - x - 12

          ------------------------

          x³ - 3x² - 10x + 24

          x³  - 2x²    ↓       ↓      ← subtract terms from terms above

         --------------------------

               - x²    - 10x + 24

               - x²   + 2x       ↓          ← subtract terms from terms above

         ----------------------------

                       - 12x + 24

                       - 12x + 24           ← subtract terms from above terms

          ----------------------------

                                    0 ← remainder

Since remainder is zero then (x - 2) is a factor

and quotient = x² - x - 12 , thus

x³ - 3x² - 10x + 24 = (x - 2)(x² - x - 12) = (x - 2)(x - 4)(x + 3)

Answer:

The area of the triangle is [tex]346.0\ mm^2[/tex]

Step-by-step explanation:

Given

Triangle VWU

Required

Determine the Area of the Triangle

First, we'll solve for the third angle

Angles in a triangle when added equals 180;  So

[tex]36 + 24 + <V = 180[/tex]

[tex]60 + <V = 180[/tex]

[tex]<V = 180 - 60[/tex]

[tex]<V = 120[/tex]

Next is to determine the length of VW using Sine Law which goes thus

[tex]\frac{VW}{Sin24} = \frac{34}{Sin36}[/tex] (Because 24 degrees is the angle opposite side VW)

Multiply both sides by Sin24

[tex]SIn24 * \frac{VW}{Sin24} = \frac{34}{Sin36} * Sin24[/tex]

[tex]VW = \frac{34}{Sin36} * Sin24[/tex]

[tex]VW = \frac{34}{0.5878} * 0.4067[/tex]

[tex]VW = 23.5 mm[/tex] (Approximated)

At this stage, we have two known sides and two known angles;

The Area can be calculated as the 1/2 * the products of two sides * Sin of the angle between the two sides

Considering VW and VU

VW = 23.5 (Calculated);

VU = 34 (Given)

The angle between these two sides is 120 (Calculated);

Hence;

[tex]Area = \frac{1}{2} * 23.5 * 34 * Sin120[/tex]

[tex]Area = \frac{1}{2} * 23.5 * 34 * 0.8660[/tex]

[tex]Area = \frac{1}{2} * 691.934[/tex]

[tex]Area = 346.0 mm^2[/tex]

Hence, the area of the triangle is [tex]346.0\ mm^2[/tex]

Answer:

[tex]\huge\boxed{\dfrac{6}{7}-\dfrac{3}{x}=\dfrac{6x-21}{7x}}[/tex]

Step-by-step explanation:

[tex]\dfrac{6}{7}-\dfrac{3}{x}=\dfrac{(6)(x)}{(7)(x)}-\dfrac{(7)(3)}{(7)(x)}=\dfrac{6x}{7x}-\dfrac{21}{7x}=\dfrac{6x-21}{7x}[/tex]

Answer: THE ANSWER IS A

Step-by-step explanation:

5-(3/2)^3

=13/8

im a math god

Answer: x=25

Step-by-step explanation: There are 180 degrees in a triangle. Two of the angles (56 and 99) add up to 155. The last angle, which is x, is 180-155. Therefore, x is 25.

hope this helped you:)

Answer:

The answer is 25°.

Step-by-step explanation:

simply,

here, a triangle of measure 99° and 56° is given.

now, we have;

99°+56+ x= 180° ( sum of an interior angle of a triangle is 180°)

or, 155°+x= 180°

or, x= 180°-155°

therefore, the value of x is 25°.

hope it helps..

Answer:No solution

Step-by-step explanation:An absolute value equation cannot equal a negative number