1: -(5x + 7) + 1 = -5x -5

2: 4x - 7 + 2x = 2(3x - 3) - 1

3: -4x - 2 = -2(1 - 4x)

The cost of each begonia is $11 at a fundraiser.

The equation is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are equal.

Let's assume the cost of each begonia x.

Since Cameron bought four begonias, the total cost of the begonias was 4x.

The total cost of the plants was the cost of the begonias plus the cost of the fern, or 4x + 19.

As per the question, the total cost was $63, so we can set up the equation:

4x + 19 = 63

To solve for x, we need to get x by itself on one side of the equation. We can do this by subtracting 19 from both sides:

4x + 19 - 19 = 63 - 19

This simplifies to:

4x = 44

To solve for x, we need to divide both sides by 4:

4x / 4 = 44 / 4

This simplifies to:

x = 11

Therefore, each begonia cost $11.

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replace the numbers inside () for x

 f(4) = -4(4)-3 = -16 -3 = -19

G(-4) = 2(-4)^2 -3(-4) = 44

41 is the best estimate for the number of people in line at 9am

Two or more expressions with an Equal sign is called as Equation.

y equal to minus five point one three one x square plus Thirty one point eight two one x minus three point three three three.

y=-5.131x²+ 31.821x-3.333 approximates the number of people standing in line to catch commuter train x hours after 5am.

There is 4 hours in between 9 am and 5 am. so x=4

Substitute x=4 into the equation

y=-5.131(4)²+ 31.821(4)-3.333

y=-5.131(16)+127.284-3.333

y=-82.096+127.284-3.333

y=41.855

Hence 41 is the best estimate for the number of people in line at 9am

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Answer:

Therefore, The correct option is D. 0.069

Step-by-step explanation:

Amount of the money paid in the state property taxes every year = $2849.84

The property owned has an assessed value.

Now, the assessed value of the property is $41302

We need to find the state's property tax rate.

[tex]\text{So, State's property tax rate = }\frac{\text{state's property tax}}{\text{assessed value}}\\\\\text{State's property tax rate = }\frac{2849.84}{41302}\approx 0.069[/tex]

Therefore, The correct option is D. 0.069

The probability of a group of four siblings being all boys or all girls is 1/8, with each individual probability being 1/16.

Probability of All Boys:

Probability of a boy birth: 1/2

Probability of all boys among 4 siblings:

(1/2) × (1/2) × (1/2) × (1/2) = 1/16

Probability of All Girls:

Probability of a girl birth: 1/2

Probability of all girls among 4 siblings:

(1/2) × (1/2) × (1/2) × (1/2) = 1/16

Probability of All Boys or All Girls: Since these are mutually exclusive events, add their probabilities:

1/16 (all boys) + 1/16 (all girls) = 1/8

Using the formula f(x) = 1/(b-a), where B is 4.25 and A is 0.20. Substituting these values to the formula, we get f(x) = 1/(4.25-0.2) = 0.24691358. Therefore, we get the answer f(x) = 0.24691358, 0.20<x<4.25. Otherwise, it is 0.

Using the formula f(x) =1/(b-a)

B is 4.25 and A is 0.20.

Put these values to the

We get f(x) = 1/(4.25-0.2) = 0.24691358.  

f(x)= 0.24691358, 0.20<x<4.25.

Further Explanation:

uniform distribution:

A uniform distribution, some of the time otherwise called a rectangular circulation, is a dispersion that has steady likelihood. The likelihood thickness work and combined circulation work for a nonstop uniform appropriation on the interim are (1) (2).  

we use uniform distribution:  

The uniform circulation gets its name from the way that the probabilities for all results are the equivalent. Rather, every result is similarly prone to happen. Not at all like a chi-square dissemination, there is no skewness to a uniform dispersion. Accordingly, the mean and middle concur.  

diameter:  

In geometry, a breadth of a circle is any straight line portion that goes through the focal point of the circle and whose endpoints lie on the circle. It can likewise be characterized as the longest harmony of the circle. The two definitions are likewise substantial for the measurement of a circle.  

formula of diameter:  

In the event that you know the zone of the circle, separate the outcome by π and locate its square root to get the sweep; at that point increase by 2 to get the distance across. This returns to controlling the equation for finding the zone of a circle, A = πr2, to get the distance across. You can change this into r = √(A/π) cm.

Subject: mathematics

Level: High School

Keywords: uniform distribution, we use uniform distribution, diameter, formula of diameter.  

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29.95 - 22.85 = 7.10

7.10 / 29.95 = 0.23706 = 23.71 percent

Answer is C

Answer:

23.71%

Step-by-step explanation:

Given :You are offered an item for $22.85. If the seller states he normally sells the same item for $29.95,

To Find :what percentage discount is he offering you

Solution :

The original price is $29.95

The offered price is $22.85

So the discount percentage = [tex]\frac{\text{original price-offered price}}{\text{original price}}*100[/tex]

= [tex]\frac{29.95-22.85}{29.95}*100[/tex]

= [tex]\frac{7.1}{29.95}*100[/tex]

= 23.71%

Thus the percentage of discount is  23.71%

Answer:

B. seven $1 bills and eight $5 bills.

Step-by-step explanation:

n = number of $1 bills

m = number of $5 bills

Given:

n + m = 15

n($1) + m($5) = $47

Just solve 2 equations in 2 unknowns n and m:

(i)  n + m = 15

(ii) n + 5m = 47

Subtract (i) from (ii) and get

4m = 32

m = 32/4 = 8

Then from (i) get

n = 15 - m = 15 - 8 = 7

There are 7 $1 bills and 8 $5 bills.

Answer:

Median = $1.84

The difference of the first and third quartiles = $0.34

Step-by-step explanation:

Median

How to calculate the median of a small data or ungrouped data;

1. Arrange the data in ascending or descending order.

2. Choose the middle value. The middle value can be a single value or two value. If the middle value is a single value, then, that value is the median but if the middle values are two, the mean of the two middle values is evaluated to get the median.

Arranging the gasoline prices given in ascending order;

$1.61,  $1.75, $1.79,  $1.84,  $1.96, $2.09, $2.11

The middle value is a single number $1.84 in bold. Therefore, the median is $1.84.  

                         Median = $1.84

First (Lower) Quartile

To calculate for the First (Lower) quartile,

1. Arrange the data give in ascending order.

2. The First (Lower) quartile, Q1 is then calculated using;  

                 [tex]Q1 =\frac{1}{4} (n + 1)^{th}[/tex] term

where n is the total number of terms of the data. In the given question, the total number of terms, n = 7

                 [tex]Q1 =\frac{1}{4} (7 + 1)^{th}[/tex] term

                 [tex]Q1 =\frac{8}{4}^{th}[/tex] term

                 Q1 = 2nd term

3. Select the 2nd term of the given data already arranged in ascending order.

                 $1.61,  $1.75, $1.79,  $1.84,  $1.96, $2.09, $2.11

                 The First Quartile, Q1 = $1.75

Third (Upper) Quartile

To calculate for the third (upper) quartile,

1. Arrange the data give in ascending order.

2. The third (upper) quartile (Q3) is then calculated using;  

                 [tex]Q3 =\frac{3}{4} (n + 1)^{th}[/tex] term

where n is the total number of terms. In the given question, the total number of terms, n = 7

                 [tex]Q3 =\frac{3}{4} (7 + 1)^{th}[/tex] term

                 [tex]Q3 =\frac{24}{4}^{th}[/tex] term

                 [tex]Q3 = 6^{th} term[/tex]

3. Select the [tex]6^{th} term[/tex] of the given data already arranged in ascending order.

                 $1.61,  $1.75, $1.79,  $1.84,  $1.96, $2.09, $2.11

The third (upper) quartile Q3 = $2.09

The difference between the first and third quartiles is called interquartile range.

Now, calculating the difference of the first and third quartiles

                  Interquartile Range = Q3 - Q1

                              $2.09 - $1.75 = $0.34

The difference of the first and third quartiles, Interquartile Range = $0.34

the right answer is actually 30,60,90, I got the answer right on the test

The measures of the angles are 30°, 60°, and 90° for the given right triangle. The correct answer would be option (A).

A right triangle is defined as a triangle in which one angle is a right angle or two sides are perpendicular.

The right triangle is given in the figure, as shown.

According to the figure,  

perpendicular = 7√3

hypotenuse = 14√3

As per the question, we have

Since sin θ = perpendicular/hypotenuse

Substitute the values in the above formula, and we get

sin θ = 7√3/14√3

sin θ = 1/2

θ = 30°

This means the measures of the angles are 30°, 60°, and 90°.

Hence, the correct answer would be an option (A).

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The question seems to be incomplete, the missing part has been attached below.

Answer: That’s really quite an eyeful

Step-by-step explanation:

The bottom answer to all of it is

That’s really quite an eyeful.

we know that

The CPCTC states that corresponding parts of congruent triangles are congruent

so

△FEB≅△CNB

that means

[tex]FE=CN\\FB=CB\\EB=NB[/tex]

we have

[tex]FE=6.1\ units\\FB=4.8\ units\\EB=3.8\ units[/tex]

therefore

[tex]BN=3.8\ units[/tex]

the answer is

the length of BN is [tex]3.8\ units[/tex]

Anthony need 7 boxes to hold 115 books.

What is Division method?

Division method is used to distributing a group of things into equal parts. Division is just opposite of multiplications.

For example, dividing 20 by 2 means splitting 20 into 2 equal groups of 10.

Given that;

Anthony has 115 books in his room.

And, He is storing them in boxes.

Each box holds 17 books.

Now,

Since, Total number of books = 115

And, Each box holds 17 books.

Hence, Number of boxes to cover 115 books = 115 ÷ 17

                                                                      = 7

Since, We get the quotient after divide 115 by 17 is 13.

So, Anthony use 1 box extra to keep 13 remaining books.

Thus, Anthony need 7 boxes to hold 115 books.

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The local extreme values of [tex]\( f(x, y) = x^2 - y^2 - 2 \)[/tex] subject to the constraint [tex]\( x^2 + y^2 = 16 \)[/tex] are -18  at points (0, 4) and (0, -4).

To find the local extreme values of [tex]\( f(x, y) = x^2 - y^2 - 2 \)[/tex] subject to the constraint [tex]\( x^2 + y^2 = 16 \)[/tex] using Lagrange multiplier techniques, we need to set up the Lagrangian function:

[tex]\[ L(x, y, \lambda) = f(x, y) - \lambda(g(x, y) - c) \][/tex]

where [tex]\( g(x, y) \)[/tex] is the constraint, c is a constant, and [tex]\( \lambda \)[/tex] is the Lagrange multiplier.

In this case, [tex]\( g(x, y) = x^2 + y^2 \)[/tex] is the constraint, and c = 16 .

So, the Lagrangian function is:

[tex]\[ L(x, y, \lambda) = x^2 - y^2 - 2 - \lambda(x^2 + y^2 - 16) \][/tex]

Now, find the partial derivatives of L with respect to ( x, y, ) and[tex]\( \lambda \)[/tex] and set them equal to zero to find critical points:

[tex]\[ \frac{\partial L}{\partial x} = 2x - 2\lambda x = 0 \]\[ \frac{\partial L}{\partial y} = -2y - 2\lambda y = 0 \]\[ \frac{\partial L}{\partial \lambda} = x^2 + y^2 - 16 = 0 \][/tex]

Solving the system of equations, we get two critical points:

1. When [tex]\( x = 0, y = 4, \lambda = -\frac{1}{4} \)[/tex]

2. When [tex]\( x = 0, y = -4, \lambda = -\frac{1}{4} \)[/tex]

Now, evaluate f(x, y) at these critical points:

1. f(0, 4) = 0 - 16 - 2 = -18

2. f(0, -4) = 0 - 16 - 2 = -18

Therefore, the local extreme values of [tex]\( f(x, y) = x^2 - y^2 - 2 \)[/tex] subject to the constraint [tex]\( x^2 + y^2 = 16 \)[/tex] are -18  at points (0, 4) and (0, -4).