. Mr. Witte is ordering trophies for his school. Company P charges $3.50 for each
trophy and a one-time engraving fee of 25$. Company R charges $7.50 for each
trophy and a one-time engraving fee of 17$. Which inequality can be used to find x,
the minimum number of trophies that can be ordered so that the total charge at
Company P is less than the total charge at Company R?
K

The decimal that represents the number 4×1+1×1/100+9×1/1000 is given as follows:

4.0119.

A fraction is represented by the division of a term x by a term y, such as in the equation presented as follows:

Fraction = x/y.

The terms that represent x and y are listed as follows:

In this problem, we are given two fractions, and their decimal equivalents are given as follows:

Hence the numeric value of the expression is given as follows:

4×1+1×1/100+9×1/1000 = 4 + 0.01 + 0.0019 = 4.0119.

Which is the decimal number represented by the fraction.

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Answer: People attended the two performances are 683

What makes something common?

A whole number that is a factor of two or more numbers is referred to as a common factor. Example: The common factors of 30 and 20 are 2, 5, and 10. A factor that everyone whole numbers share is 1, or 1.

What is a greatest common factor?
It is the biggest number that two numbers are divisible by.

For example, if you did 12 and 24

The factors of 12 are:

1, 2, 3, 4, 6, 12

The factors of 24 are:

1, 2, 3, 4, 6, 8, 12, and 24

Their greatest common factor would be 12 since, it is the greatest number that each number can be divisible by.

Step-by-step explanation:

Number of people attend Friday event = 728
Number of people attend Saturday event = 728 - 45 = 683
Hence the answer is 683

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Answer:

4

Step-by-step explanation:

Since YP is an angle bisector, Angle 1 and 2 are equal.

We know WYX is 17x+4 so

2 times Angle 1 is 17x+4

[tex]2(8x + 4) =17x + 4[/tex]

[tex]16x + 8 = 17x + 4[/tex]

[tex]4 = x[/tex]

Answer: 2 < x < 3

Step-by-step explanation:

Answer:

Step-by-step explanation:

Answer:

$25940

Step-by-step explanation:

Future value of an Investment at r% for n years is given by:

Future Value = Initial Investment (1 + r/100)n

If r = 10% and n = 10 years

Future Value = 10000(1 + 10/100)10

= 10000(1.1)10

= 10000(2.594)

= $ 25940

Hence the required value is $ 25940.

Answer:

BC = 7.9 cm

Step-by-step explanation:

To construct triangle ABC:

Answer:

75%

Step-by-step explanation:

The answer is : p = -4

the following are the steps to solve it::

13 - 3p = -5 (3 + 2p)

calculate the area of the right hand first by multiplying the number 5 by the number in brackets

13 - 3p = -15 - 10p

move everything that contains p to the left side

13 - 3p + 10p = - 15

count all containing p

13 + 7p = -15

move the ones that don't contain p to the right

7p = -15 - 13

count on the right side

7p = - 28

p = -4

Answer:

50m/s = (50 ÷ 1000 × 60 × 60)km/h

           = 180km/h

The third graph passing through the points (-2,4) and (2,-2) represents the equation y = 3/2x + 1.

Given:

y = 3/2 x + 1

m = 3/2

the graph whose m value is equal to 3/2 is correct.

First graph:

Take any two points (-2,-2) and (0,2)

slope m = 2-(-2) / 0-(-2)

= 2+2 / 0+2

= 4/2

= 2

This graph is incorrect

Second graph:

Two points(-2,2) and (2,-4)

slope m = -4-2 / 2-(-2)

= -6/2+2

= -6/4

= -3/2

This graph is incorrect.

Third graph:

Two points (-2,4) and (2,-2)

slope m = -2-4 / 2-4

= -6/-2

= 3/2

This graph is correct.

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Answer:

A ................................

Answer: true

Step-by-step explanation:

Co-interior angles are the two angles that occur between two parallel lines intersected by a transversal.

The sum of the co-interior angles is 180 degrees.

The value of x is 15.

The angles that are in the same position on two parallel lines intersected by a transversal line on the parallel lines.

Corresponding angles are equal.

We have,

Co-interior angles are the two angles that occur between two parallel lines intersected by a transversal.

The sum of the co-interior angles is 180 degrees.

(8x + 9)° and 51° are co-interior angles.

So,

8x + 9 + 51 = 180

8x = 180 - 60

8x = 120

x = 120/8

x = 15

Thus,

The value of x is 15.

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Using the proportion rule, the ratios 1/3 and 2/5 does not form a proportion.

In the given equation,

We have to check the ratios 1/3 and 2/5 form a proportion or not.

As we know that proportion is a ratio in which both ratios are equal to each other.

So to check whether the given statement is proportion or not we put both equation equal to each other.

So the ratios are 1/3 and 2/5.

Now checking the proportion.

1/3=2/5

Multiply by 15 on both side.

1/3 ×15=2/5 ×15

Simplifying

1×5=2×3

5=6

As we can see that both side is not equal so the given ratio is not proportion.

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The ingredients Rose needs to make 5 short bread fingers are;

Recipe for 30 shortbread fingers.

To determine the recipe needed for 5 short bread fingers ; divide 30 by 5

= 30/5

= 6

This means, each recipe needed for 30 short bread fingers will be divided by 6 to achieve recipe needed for 5 short bread fingers.

Therefore,

Recipe needed for 5 short bread fingers:

Butter = 120 g / 6

= 20 g

Sugar = 60 g / 6

= 10 g

Flour = 180 g / 6

= 30 g

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Step-by-step explanation:

[tex]1 - (\frac{1}{4} + \frac{2}{3}) \\ = 1 - ( \frac{3 + 8}{12}) \\ = 1 - ( \frac{11}{12} ) \\ = \frac{1}{12} [/tex]

Answer:

[tex]1 \frac{7}{12}\; \sf pounds[/tex]

Step-by-step explanation:

To find the amount of flour Grandma has left over, subtract the amount she used to make rolls from the original amount.

Given calculation:

[tex]3 \frac{1}{4}-1 \frac{2}{3}[/tex]

Convert the mixed numbers into improper fractions by multiplying the whole number by the denominator of the fraction, adding this to the numerator of the fraction, and placing the answer over the denominator:

[tex]\implies \dfrac{3 \times 4+1}{4}-\dfrac{1 \times 3+2}{3}[/tex]

[tex]\implies \dfrac{13}{4}-\dfrac{5}{3}[/tex]

Change both fractions into equivalent fractions so both fractions have the same denominator:

[tex]\implies \dfrac{13 \times 3}{4\times 3}-\dfrac{5 \times 4}{3 \times 4}[/tex]

[tex]\implies \dfrac{39}{12}-\dfrac{20}{12}[/tex]

[tex]\textsf{Apply the fraction rule} \quad \dfrac{a}{c}-\dfrac{b}{c}=\dfrac{a-b}{c}:[/tex]

[tex]\implies \dfrac{39}{12}-\dfrac{20}{12}=\dfrac{39-20}{12}=\dfrac{19}{12}[/tex]

Divide the numerator by the denominator:

[tex]\implies 19 \div 12 = 1 \; \sf remainder \; 7[/tex]

The solution as a mixed number is the whole number and the remainder divided by the denominator:

[tex]\implies 1 \frac{7}{12}[/tex]

Answer:

15.62 is the length of the side of the rhombus.

Step-by-step explanation:

Formula:

A = (e x f)/2

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Answer:

b: x=66 degrees

Step-by-step explanation:

132 degrees and 2x are corresponding angles since of the transversal.

So 132=2x and x=66 degrees

Answer:

D. 4 5/13

Step-by-step explanation:

For every time we divide by 13, we consider that a whole number. The whole number is the number on the outside of the fraction. It is equal to 13/13 in this case. So, we can divide 57 by 13, 4 times and have 5/13 left over. Therefore, the answer is D. 4 5/13! :)

Answer:

[tex]r \geqslant - 16[/tex]

Step-by-step explanation:

[tex] \frac{ - 10 + r}{2} \geqslant - 13[/tex]

multiply both sides by 2:

[tex] - 10 + r \geqslant - 26[/tex]

add 10 on both sides:

[tex]r \geqslant - 16[/tex]

Answer:

[tex]r \ge -16[/tex]

Step-by-step explanation:

To solve any equation/inequality:

1. get the variable to show up exactly once

2. isolate it

[tex]\frac{-10+r}{2} \ge -13[/tex]

Multiply both sides by 2 and simplify (note that we're multiplying by a positive, not a negative, so the direction of the inequality stays the same, whereas multiplying or dividing by a negative would have changed the direction of the inequality)

[tex]\frac{-10+r}{2} *2 \ge -13 *2[/tex]

[tex]-10+r \ge -26[/tex]

Add 10 to both sides, and simplify

[tex](-10+r)+10 \ge (-26)+10[/tex]

[tex]r \ge -16[/tex]

The Algebraic expression that cannot be factorized is [tex]x^{2}[/tex] + 1

An algebraic expression in mathematics is an expression which is made up of variables and constants, along with algebraic operations (addition, subtraction, etc.).

[tex]x^{2}[/tex] + -3x -18  can be expressed as  [tex]x^{2}[/tex] -6x +3x -18 which can be factored as (x -6)(x +3)

Also  [tex]x^{2}[/tex] + 7x + 6, (x+6)(x+1)

[tex]x^{2}[/tex] + 5x + 6 , (x+3)(x+1)

But  [tex]x^{2}[/tex] + 1 cannot be factored because since it does not have a variable of x.

In conclusion,  [tex]x^{2}[/tex] + 1 cannot be factored.

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Answer: D

Step-by-step explanation:

I dont gotta explain it, here you go bro :) its -10

Answer:

x=12

Step-by-step explanation:

2x+4=6x

x-6=6x

6x=6x

x=6+6

The required expression 16m + 6n - 8 represents the perimeter of the triangle. which is the correct answer would be option (D).

A triangle has side lengths of (7m - 2) centimeters, (9m - 5) centimeters, and (6n - 1) centimeters.

The perimeter of a triangle is defined as the addition of the lengths of the triangle's three sides.

The perimeter of the triangle = (7m - 2) + (9m - 5) + (6n - 1)

Rearrange the terms likewise in the above equation,

The perimeter of the triangle = 7m + 9m + 6n - 2 - 5 - 1

Apply the arithmetic operation to get the required expression

The perimeter of the triangle = 16m + 6n - 8

Therefore, the required expression 16m + 6n - 8 represents the perimeter of the triangle.

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Answer:

6(y-2) would be 6y-12

Step-by-step explanation:

The value of  ∇r^n = n(r^n-2)r​ is [tex]-n r^{n-2} \bar{r}[/tex]

A quantity in mathematics known as a vector that lacks position but has both magnitude and direction

The movement of an object between two points is described by a vector. The directed line segment can be used to geometrically represent vector math. The magnitude of a vector is the length of the directed line segment, and the vector's direction is indicated by the angle at which it is inclined.

Given ,

[tex]$&\nabla r^n=n r^{n-2} \bar{r} \\[/tex]

[tex]$&\text { let } \bar{r}=x \hat{i}+y \hat{j}+z \hat{k} \\[/tex]

[tex]$&r=|\bar{r}|=\sqrt{x^2+y^2+z^2} \\[/tex]

[tex]$&\frac{\partial r}{\delta x}=\frac{-x}{r} ; \frac{\delta r}{\delta y}=-\frac{y}{r}, \frac{\delta r}{\delta z}=-\frac{z}{r} \\[/tex]

[tex]$&\because \nabla r^n=\frac{\delta}{\delta x}\left(r^n\right) \hat{i}+\frac{\delta}{\delta y}\left(r^n\right) \hat{j}+\frac{\delta}{\delta z}\left(r^n\right) \hat{k} \\[/tex]

[tex]$&\left.=n r^{n-1} \frac{\delta r}{\delta x} \hat{i}+n r^{n-1} \frac{\delta r}{\delta y} \hat{j}+\frac{\delta}{\delta z} x r^n{ } \hat{k} \\[/tex]

[tex]$&=n r^{n-1}\left[\frac{\delta r}{\delta x} \hat{i}+\frac{\delta r}{\delta y} \hat{j}+\frac{\delta r}{\delta z} \hat{k}\right] \\[/tex]

[tex]$&=n r^{n-1}\left[\frac{\delta r}{\delta x} \hat{i}+\frac{\delta r}{\delta y} \hat{j}+\frac{\delta r}{\delta z} \hat{k}\right] \\[/tex]

[tex]$&=n r^{n-1}\left[-\frac{x}{r} \hat{i}- \frac{y}{r} \hat{j}-\frac{z}{r} \hat{k}\right] \\[/tex]

[tex]$&=\frac{n r^{n-1}}{r}[-x \hat{i}-y \hat{j}-z \hat{k}]=-n r^{n-2} \bar{r} \\[/tex]

Therefore the value of ∇r^n = n(r^n-2)r is [tex]-n r^{n-2} \bar{r}[/tex]

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The actual price of an item is $1371.49.

Given that, the discount percentage is 12.5% and the selling price is $1200.

A discount is the reduction of either the monetary amount or a percentage of the normal selling price of a product or service.

Let the actual price be x.

Now, x-12.5% of x =1200

⇒ x- 12.5/100 ×x=1200

⇒ x- 0.125x=1200

⇒ 0.875x=1200

⇒ x=1200/0.875

⇒ x=$1371.49

Therefore, the actual price of an item is $1371.49.

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The additive inverse of the matrix A is [tex]\left[\begin{array}{cc}0&2&3&5\end{array}\right][/tex]

From the question, the matrix is given as

[tex]\left[\begin{array}{cc}0&-2&-3&-5\end{array}\right][/tex]

This matrix is given as matrix A

So, we have the following representation

A = [tex]\left[\begin{array}{cc}0&-2&-3&-5\end{array}\right][/tex]

Next, we calculate the required matrix operation

The matrix operation is given as additive inverse of the matrix

This additive inverse of the matrix is calculated by negating each element present in the matrix

i.e. if an element in the matrix is a, the inverse would be -a

Using the above highlights as a guide, we have the following representations

Additive inverse = [tex]\left[\begin{array}{cc}0&2&3&5\end{array}\right][/tex]

Hence, the additive inverse is [tex]\left[\begin{array}{cc}0&2&3&5\end{array}\right][/tex]

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The equation of a line is written as [tex]y=mx+c[/tex].

What is the equation of a line?

The equation [tex]y = mx + c[/tex] is the general equation of any straight line where [tex]m[/tex] is the gradient of the line and [tex]c[/tex] is the [tex]y -intercept[/tex] .

Here the given equation is

[tex]y=1.5x+20[/tex]       ........[tex](1)[/tex]

when [tex]x=0[/tex]

[tex]y=1.5(0)+20\\y=20[/tex]

when [tex]x=1[/tex]

[tex]y=1.5(1)+20\\y=1.5+20\\y=21.5[/tex]

when [tex]x=-1[/tex]

[tex]y=1.5(-1)+20\\y=-1.5+20\\y=18.5[/tex]

Draw the graph

Hence, by using the values of [tex]x[/tex] and [tex]y[/tex] we formed a straight-line graph.

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Answer:

Unit rate is 2

Step-by-step explanation:

Pick two columns of the ordered pairs. Lets use (2,4) and (3,6)

The x values are 2 and 3 and the y values are 4 and 6

Now you’re going to divide y by x so

4/2 = 2

6/3 = 2

(Always choose two ordered pairs so you know that your answer is right)

Unit rate of the table is 2.

The units of concentration and rate are always going to be molars per second. We now understand that molar per second is equal to k times molar in units. An item's unit rate is its price for one of it. This is expressed as a ratio with a one as the denominator. For instance, if you covered 70 yards in 10 seconds, you covered 7 yards on average every second. Seven yards in one second and 70 yards in ten seconds are both ratios, but only one of them is a unit rate.

Given,

Choose two columns from the paired ordered columns. Using (2, 4) and (3,6)

The x and y values are 2 and 3, respectively, and the

You will now divide y by x, so

4/2 = 2

6/3 = 2

Unit rate of the table is 2.

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