April is arranging place cards for a wedding reception on a table. The bride's family has 154 cards and the groom's family has 140 cards. She wants the arrangements for the two families to have the same number of cards in each row. What is the greatest number of cards that she can place in a row?

Note that:

Applying the addition formula given above to cos 150:

The sum of the measures of an exterior angle of a polygon is 360°.

If the given angle divides 360 evenly, then it can be a measure of an exterior angle of a polygon. If otherwise, then it cannot be.

Out of the given angles, only 50 does not divide 360 evenly. Therefore, a regular polygon cannot have an exterior angle measuring 50°. (Option B)

12/35 fraction of the total number is unused from two different cards.

A fraction is written in the form of p/q, where q ≠ 0.

Fractions are of two types they are proper fractions in which the numerator is smaller than the denominator and improper fractions where the numerator is greater than the denominator.

Assuming the total first kind of card form is 1 and the total second kind of card form is also one.

Given, a company buys equal numbers of two different card forms. it utilizes 4/5 of one kind and 6/7 of the other.

∴ The total unused card form is,

= (1 + 1) - (4/5 + 6/7).

= 2 - (28 + 30)/35.

= 2 - 58/35.

= (70 - 58)/35.

= 12/35.

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What does the letter "L" stand for in the simulation?

Answer: d

Step-by-step explanation: ion know man but i looked it up and got it right

144 yards of string will need to use balloons for the party.

Given,

The length of balloon string Orlando wanted = 6 feet

Number of balloons = 72

We have to find the total length of strings wanted for 72 balloons in yards.

1 yard = 3 feet

Now,

Total length of strings Orlando needs = length of one string x number of balloons = 6 x 72 = 432 feet

Now convert 432 feet into yard

That is,

432 / 3 = 144 yards

So,

144 yards of string will need to use balloons for the party.

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Answer:

The slope is 2

Step-by-step explanation:

Take any two points on the line.  I am going to use the points (0,-8) and (4,0)  Points are in the form (x,y)  The y values form the two points is 0 and -8.  The x values are 4 and 0.

The slope is the change in y over the change in x.

[tex]\frac{0- -8}{4-0}[/tex] = [tex]\frac{8}{4}[/tex] = 2

It will take 15 days for Akash to complete the entire work if he is assisted by Sunil and Rakesh every third day.

To determine the number of days, we first represent the number of days to do a piece of work by each one of them in fractions as follows;

Fraction of work completed by Akash in 1 day = 1/20

Fraction of work completed by Sunil in 1 day = 1/30

Fraction of work completed by Rakesh in 1 day = 1/60

The total work done in 1 day can be given as;

Total work done by the three in one day = [(1/20) + (1/30) + (1/60)] = 1/10

Work done by Akash in two days = 2 × (1/20) = 2/20 = 1/10

The work done in three days (1 day of all three together + Work done by Akash in two days) = (1/10) + (1/10) = 1/5

Therefore; the total work done in 3 days = 1/5

At this rate, the total number of cycles required to finish the work =

(1) ÷ (1/5) = 5

Since each cycle has three days, the total number of days required to finish the work can be calculated as follows;

5 × 3 = 15 days

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Answer

Angle NOL = 70°

Explanation

Alternate angles are angles that are in opposite positions relative to a transversal intersecting two lines. If the two lines are parallel to each other, then alternate angles are equal.

We can see that Angle MLO and Angle NOL are alternate angles.

And since we have been told that KM and NP are parallel lines,

Angle NOL = Angle MLO = 70°

Hope this Helps!!!

Answer:

x=23

Step-by-step explanation:

The amount of degrees in a triangle is 180 degrees.

line AC and line DF are straight angles meaning that the opposite angles are equal to each other. That means that angle FBC is also equal to x. Because line AC and EF are parallel we know that FBC and BFE are equal. Therefore, BFE is equal to x. The sum of the values of each angle of the triangle should add up to 180. 5x+65=180

5x=115

x=23

The distance between the two points in simplest radical form(−2,−7) and (5,0) is 9.8995

Distance can be described as the differences that exist between two points and this can be expressed i different form such as the radical form.

We can calculate the distance between the two points by firstly expressed them as :

(−2) - (5) = -7

(-7) - 0 = -7

Then the distance between them can be found as :

Distance = (-7)^2 + (-7)^2 = 49 +49 = 98

Then we will find the square root of the the figure as

= [tex]\sqrt{98}[/tex] = 9.8995

The formula can as well be used to find this by substituting the values of x and y into the formula as :

x1=-2

y1=-7

x2=5

y2=0

[tex]d = \sqrt{ ( x_{2} - x_{1} )^{2} + ( y_{2} - y_{1} )^{2}}[/tex]

then [tex]d = \sqrt{ ( 5 - (-2 )^{2} + ( 0 - (-7) )^{2}}[/tex]

= [tex]\sqrt{ 49^{2} + 49^{2} }[/tex]

= [tex]\sqrt{98}[/tex]

=9.8995

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Answer:  m=1/5

Step-by-step explanation:

Answer:

x = 40

Step-by-step explanation:

x = 8 x 5

x = 40

that's it

The two equations that are true when x = -2 and x = 2 are x^2 - 4 = 0 and 4x^2 = 16.

We have given x = 2 and x = -2

Substitute the values in the given equations

Equation 1

x^2 - 4 = 0

Substitute x = 2 in LHS, we get

2^2-4 = 4 - 4 = 0 = RHS

Substitute x = -2 in LHS, we get

(-2)^2-4 = 4 - 4 = 0 = RHS

Equation 2

x^2 = -4

Substitute x = 2 in LHS, we get

2^2 = 4 ≠ RHS

Substitute x = -2 in LHS, we get

(-2)^2 = 4 ≠ RHS

Equation 3

3x^2 + 12 = 0

Substitute x = 2 in LHS, we get

3(2)^2 + 12 = 12 + 12 = 24 ≠ RHS

Substitute x = -2 in LHS, we get

3(-2)^2 + 12 = 12 + 12 = 24 ≠ RHS

Equation 4

4x^2 = 16

Substitute x = 2 in LHS, we get

4(2)^2 = 4(4) = 16 = RHS

Substitute x = -2 in LHS, we get

4(-2)^2 = 4(4) = 16 = RHS

Equation 5

2(x-2)2 = 0

Substitute x = 2 in LHS, we get

2(2-2)2 = 2(0)(2) = 0 = RHS

Substitute x = -2 in LHS, we get

2(-2-2)2 = 2(-4)(2) = 16

Hence, we find that Equation 1 and Equation 2 are true for x = 2 and x = -2

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The most appropriate choice for percentage will be given by -

Total salary of Marques in a week = $825

If Marques makes $x in sales, his total salary in a week = $([tex]750 + \frac{x}{10}[/tex])

What is Percentage?

Suppose there is a number and that number has to be expressed as a fraction of 100. The fraction is called percentage. For example 2% means [tex]\frac{2}{100}[/tex]

Here,

Guarantee salary of Marques = $200

Sales made by Marques in a week= $750

Percentage commission on total sales = 10 %

Commission received by Marques = [tex]\frac{10}{100} \times 750\\[/tex]

                                                          = $75

Total salary of Marques in a week = $(750 + 75)

                                                         = $825

If Marques makes $x in sales, his total salary in a week = $([tex]750 + \frac{10}{100}\times x[/tex])

                                                                                            = $([tex]750[/tex] + [tex]\frac{x}{10}[/tex])

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Answer:

second answer

Step-by-step explanation:

w=L+15

p=(L+w)

150cm=L+L+15

150cm=2L+15

2L=150cm-15

2L=135cm

2L÷2=135cm÷2

L=67.5

w=67.5+15

w=82.5

Let l be the length of the rectangle and w its width.

Then its area is given by:

a = l*w

Its perimeter is given by:

p = 2l + 2w

We also know that, for this specific triangle, we have:

2w = l - 4

l = 2w + 4

a = 126 m²

Applying this result in the area formula, we have:

w*l = 126

w(2w + 4) = 126

2w² +4w = 126

2w + 4w - 126 = 0

Therefore, w = 7 m and l = 2*7 + 4 = 10 m

Then, the perimeter is given by:

p = 2*18 + 2*7 = 36 + 14 = 50 m

The range of the given function is {-5,-1,4} which is the B option.

Given function:-

[tex]f(x) = x^2+4x-1[/tex]

Domain = {-2,0,1}

We have to find the range of the given function for the given domain.

Putting x = -2 in the given function, we get,

[tex]f(-2) = (-2)^2+4(-2)-1[/tex]

f(-2) = 4 - 8 - 1 = -5

Putting x = 0 in the given function, we get,

[tex]f(0) = (0)^2+4(0)-1[/tex]

f(0) = 0 + 0 -1 = -1

Putting x = 1 in the given function, we get,

[tex]f(1) = (1)^2+4(1)-1[/tex]

f(1) = 1 + 4 - 1 = 4

Hence, the range of the given function is {-5,-1,4}.

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2.69%, is the required maximum percent error among the predictions.

Given,

The predicted winning time in 200 meter sprint shows in the dot plot

The winner finished the race in 22.3 seconds

We have to find the greatest percent error among the predictions;

Here,

The actual time to complete is 22.3 seconds.

22.9 seconds is the prediction that is the most off.

The difference is, 22.9 - 22.3 = 0.6 seconds

To obtain a prediction, divide this by the actual time value.

= 0.6/22.3 = 0.0269 = 2.69

Therefore, 2.69%, is the required maximum percent error among the predictions.

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The graph of g and f have equal intercepts while the slope of the graph of f is 5 times larger than the slope of the graph of g

Given: f(x) = 2x-5 and g(x)=2(0.2x)-5

To compare the two graphs, we can make use of the equation of a line:

The general form of the equation of a line is y = mx + c

Where m is the slope and c is the intercept

So we will compare two the functions with the equation of a line:

Comparing f(x) = (2x-5) with y = mx + c

The slope(m) of the line = 2 and the intercept(c) = -5

Also, comparing g(x) = 2(0.2x)-5 with y = mx + c

The slope(m) of the line = 2(0.2) = 0.4 and the intercept(c) = -5

Since the slope of f(x) = 2 and the slope of g(x) = 0.4. Thus:

slope of f(x) / slope of g(x)  = 2/0.4 = 5

So we can say the slope of  f(x) is  5 times the slope of g(x)

Therefore, the graph of g and f have the same intercept. But the slope of f(x) is  5 times the slope of g(x)

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The number of soda bottles = 4

The number of sugar bottles = 7

What is an expression?

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

Weight of each bottle of soda = 45 grams

Weight of each bottle of sugar = 15 grams

Total weight of sugar and soda = 285 grams

Let the number of soda bottle = x

And, The number of sugar bottle = y

Since, Total number of bottles = 11

So, We can formulate;

⇒ x + y = 11    .... (i)

And, Weight of each bottle of soda = 45 grams

Weight of each bottle of sugar = 15 grams

Total weight of sugar and soda = 285 grams

So, We can formulate;

⇒ 45x + 15y = 285   ... (ii)

Multiply by 15 in equation (i) and subtract from (ii), we get;

⇒ 45x + 15y - 15x - 15y = 285 - 165

⇒ 30x = 120

Divide by 30;

⇒ x = 4

Hence,  x + y = 11    

4 + y = 11

y = 11 - 4

y = 7

So, The number of soda bottles = 4

The number of sugar bottles = 7.

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To determine  probability with replacement, It uses sampling with replacement. In other words, you want to determine the likelihood of an event in which you choose a ball, card, or other object from a set of options and then swap it out after each choice.

Example:

Consider a scenario in which you wished to sample two people from a population of seven.

Those people are:

John, Jack ,Qiu, Tina, Hatty, Jacques, Des

Their names could be placed in a hat. If you sample with replacement, you would pick one name, put it back in the hat, and then pick a different name. Your two-name sample has the following potential outcomes:

John, John

John, Jack

John, Qui

Jack, Qui

Jack Tina

…and so on.

The two products you sample with replacement are independent. In other words, the outcome of one has no bearing on the other. The odds of picking the first name are 1/7, and the odds of picking the second name are 1/7.

P(John, John) = (1/7) * (1/7) = .02.

P(John, Jack) = (1/7) * (1/7) = .02.

P(John, Qui) = (1/7) * (1/7) = .02.

P(Jack, Qui) = (1/7) * (1/7) = .02.

P(Jack Tina) = (1/7) * (1/7) = .02.

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30

Given the expression for the instantaneous voltage expressed as:

Given the following parameter:

θ = 30⁰

Substitute the given parameter into the formula to have:

Therefore the instantaneous voltage when θ = 30⁰ is 30.

The general form of an equation in intercetp form is:

Where m is the change of y in function of x and b is the value of b when x is 0

In this situation you have:

y=C

x=r

m= 1.75 ( C increase 1.75 each r)

b= 7 (When there is not ride r=0 the admission fee is 7)

The rate of interest on the given principal is 7.5%.

Given that, simple interest = $56.25, principal = $300 and time period = [tex]2\frac{1}{2}[/tex] years.

Simple interest is a method to calculate the amount of interest charged on a sum at a given rate and for a given period of time.

Simple interest is calculated with the following formula: S.I. = P × R × T, where P = Principal, R = Rate of Interest in % per annum, and T = Time, usually calculated as the number of years.

Now, 56.26 = (300 × R × 2.5)/100

⇒ 5625 = 750R

⇒ R = 7.5%

Therefore, the rate of interest on the given principal is 7.5%.

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to get the slope of any straight line, we simply need two points off of it, let's use the ones from the picture below.

[tex](\stackrel{x_1}{0}~,~\stackrel{y_1}{0})\qquad (\stackrel{x_2}{5}~,~\stackrel{y_2}{20}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{20}-\stackrel{y1}{0}}}{\underset{run} {\underset{x_2}{5}-\underset{x_1}{0}}} \implies \cfrac{ 20 }{ 5 } \implies \text{\LARGE 4}[/tex]