7. Petal and Leaf florists currently have 30
roses, 36 carnations, and 54 tulips. How
many equal-sized bouquets can be made
using all of the flowers if the florists make
sure that each bouquet has the same
number of each type of flower?

Answer: 4x + 6y >/ 50

Step-by-step explanation:

The answer is A. 4x + 6y is greater than or equal to 50

\(~~~~~~~~~y= 2x^3 -2x^2 -3x+1\\\\\\\implies \dfrac{dy}{dx} =\dfrac d{dx} \left( 2x^3 -2x^2 -3x +1\right)\\\\\\~~~~~~~~~~~=2 \dfrac{d}{dx}\left(x^3\right) - 2 \dfrac d{dx} \left(x^2\right) - 3 \dfrac d{dx} (x) +\dfrac{d}{dx}(1)\\ \\\\~~~~~~~~~~~=2\cdot 3x^2 -2\cdot 2x-3 +0~~~~~~~;\left [ \dfrac d{dx} x^n = nx^{n-1}\right]\\\\\\~~~~~~~~~~~=6x^2 -4x -3\)

\(\text{The derivative is}~6x^2 -4x -3\)

Answer:

y = 3x - 11

Step-by-step explanation:

(3, -2) and (5, 4)

m = 4+2/5-3

m = 6/2

m = 3

y = 3x + b

4 = 3(5) + b

4 = 15 + b

b = -11

y = 3x - 11

Para despejar "a" de la ecuación 2as = vf^2 - vo^2, podemos seguir los siguientes pasos:

2as + vo^2 = vf^2

a = (vf^2 - vo^2) / 2s

Por lo tanto, la fórmula para calcular "a" a partir de la distancia de desplazamiento "s", la velocidad final "vf" y la velocidad inicial "vo" es:

a = (vf^2 - vo^2) / 2s

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\(\begin{align}\colorbox{black}{\textcolor{white}{\underline{\underline{\sf{Please\: mark\: as\: brillinest !}}}}}\end{align}\)

\(\textcolor{blue}{\small\texttt{If you have any further questions,}}\) \(\textcolor{blue}{\small{\texttt{feel free to ask!}}}\)

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Polygon A's area is 1/25 times of Polygon B's area.

In geometry, a polygon is a two-dimensional closed shape with straight sides that is flat or plane. It doesn't have any curved edges.

Now, as per the given question;

The formula of the scale factor is given as;

Area of Polygon B = (scale factor)²×(Area of Polygon A).

The scale factor is given as 5.

(Area of Polygon B)  = (5)²×(Area of Polygon A)

Further simplifying;

(Area of Polygon B) = (25)×(Area of Polygon A)

or,

Area of Polygon A = (1/25)×Area of Polygon B

Therefore, the area of polygon A is found to be 1/25 times times the area of the polygon B.

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Answer:

Step-by-step explanation:

Given function

Converting to standard form

Answer:

D. -3 + 2i and E. 3+2i are the zeroes for the equation.

Step-by-step explanation:

The number of ways for the first case will be 151,200. Then option A is correct. And the number of ways for another case will be 210. Then option D is correct.

A permutation is an act of correctly arranging things or pieces. Combinations are a method of taking stuff or pieces from an assortment of items or sets in which the order of the items is irrelevant.

Suppose 10 people run a race. Then the number of ways that they can be awarded first through the sixth place will be given as,

¹⁰P₆ = 10! / (10 - 6)!

¹⁰P₆ = 10 x 9 x 8 x 7 x 6 x 5 x 4! / 4!

¹⁰P₆ = 151,200

Suppose 10 people volunteer to help clean up the school, but you only need 6 of them. Then the number of ways is given as,

¹⁰C₆ = (10!) / [(10 - 6)! x 6!]

¹⁰C₆ = (10 x 9 x 8 x 7 x 6!) / (4 x 3 x 2 x 1 x 6!)

¹⁰C₆ = 210

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Answer:

Solution given:

CD=18m

In ∆ ACD

Tan 35=opposite/adjacent

Tan 35=CD/AC

AC=18/Tan35

AC=25.7m

again

In ∆ BCD

Tan 60=opposite/adjacent

Tan 60=CD/BC

BC=18/tan60

BC=10.4

we have

AC=AB+BC

AB=25.7-10.4

AB=15.3

Distance between A and B point is 15.3 metre

Nathaniel drinks 3 glasses of water in one hour.

To find out how many glasses of water Nathaniel drinks in one hour, we need to calculate his drinking rate per hour.

In 2 2/5 hours, Nathaniel drinks 4/5 of a 10-ounce glass of water.

Let's convert the mixed number of hours to an improper fraction:

\(2\frac{2}{5} = \frac{(5 \times2 + 2)}{5}\)

\(=\frac{12}{5}\)

Now, we can set up a proportion to find his drinking rate per hour.

We know that \(\frac{12}{5}\) hours corresponds to \(\frac{4}{5}\) of a glass of water.

Let's assign "x" as the number of glasses he drinks in one hour.

The proportion is then

\(\frac{(\frac{12}{5} hours) }{(x glasses) } =\frac{(\frac{4}{5} glass)}{(1 hour)}\)

Cross-multiplying gives us

\((\frac{12}{5} )\times1=\frac{4}{5}\times(x)\)

Simplifying, we get

\(\frac{12}{5} =\frac{4}{5}\times x\)

Dividing both sides by \(\frac{4}{5}\), we find x:

\(x=\frac{(\frac{12}{5} )}{\frac{4}{5} }\)

\(x=\frac{12}{4}\)

\(x = 3.\)

Therefore, Nathaniel drinks 3 glasses of water in one hour.

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Answer:

13.5 %

Step-by-step explanation:

For a normal distribution, the Empirical Rule states that 68% of values lie between 1 standard deviation of the mean, 95% of values lie between 2 standard deviations of the mean, and 99.7% of values lie between 3 standard deviations of the mean. Here, we can see that 54.5 is 1 standard deviation away from the mean and 57 is 2 standard deviations away. This means that we want to find the difference between 1 and 2 standard deviations from the mean (in the positive direction)

To find the difference, we can simply find (percent of values 2 standard deviations of the mean) - (percent of values 1 standard deviation from the mean) = percent of values between 1 and 2 standard deviations from the mean

= 95-68 = 27 %

Finally, this gives us the percent of values between 1 and 2 standard deviations from the mean on both sides. We want to only find the positive aspect of this, as we don't care how many values are between 49.5 and 47 years old. Because normal distributions are symmetric, or equal on both sides of the mean, we can simply divide by 2 to eliminate the half we don't want, resulting in 27/2 = 13.5

The probability that a randomly chosen manager will be between 54.5 and 57 years old is 0.8413.

Given that, average age managers = 52 years standard deviation = 2.5 years.

Standard deviation is the positive square root of the variance. Standard deviation is one of the basic methods of statistical analysis. Standard deviation is commonly abbreviated as SD and denoted by 'σ’ and it tells about the value that how much it has deviated from the mean value.

Considering the equation Z =  (X−μ)/σ

Where, X is the lower or higher value, as the case may be μ  is the average σ  is standard deviation

Now, z1= (54.5 - 52)/2.5

= 1

z2= (57 - 52)/2.5

= 2

Now, z2-z1= 2-1

= 1

P(54.5>Z<57)= 0.8413

Therefore, the probability that a randomly chosen manager will be between 54.5 and 57 years old is 0.8413.

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The factorized form of \(x^3 - (y - z)^3\ is \ (x - y + z)(x^2 - xy + 2xz + yz - 2z^2).\)

The Factorization is derived from the application of a mathematical identity. As an AI language model, the information provided is generated based on existing knowledge and formulas.

The given expression is \(x^3 - (y - z)^3.\)To factorize it,  the difference of cubes, which states that a^3 - b^3 can be factorized as\((a - b)(a^2 + ab + b^2).\)

Applying this identity to our expression, we have:

\(x^3 - (y - z)^3 = (x - (y - z))((x - (y - z))^2 + (x - (y - z))(y - z) + (y - z)^2)\)

Simplifying further, we get:

\(= (x - y + z)(x^2 - 2xy + 2xz - y^2 + 2yz - z^2 + xy - y^2 + yz - z^2 + y^2 - 2yz + z^2)\\= (x - y + z)(x^2 - 2xy + xy + 2xz + yz - 2yz - y^2 + y^2 - y^2 + 2yz - 2z^2 + y^2 - z^2 + z^2)\\= (x - y + z)(x^2 - xy + 2xz + yz - 2z^2)\)

So, the factorized form of \(x^3 - (y - z)^3 \ is\ (x - y + z)(x^2 - xy + 2xz + yz - 2z^2).\)

the above factorization is derived from the application of a mathematical identity.

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Answer:

4 students

Step-by-step explanation:

We can say that 20 students represent 100 % and that 4 students represent x % of all students. Then we can use the proportion: 20 : 4 = 100 : x, or 20 / 4 = 100 / x. Then we will cross multiply: 20 x = 4 * 100, 20 x = 400, x = 400 : 20 , x = 20 %. Also we can say that 4 = 1/5 * 20 and 1/5 * 100 = 20 % Answer: 4 students is 20 % of 20 students. Hope this helps. Let me know if you need additional help!

The original dimensions of the piece of metal were 15 inches by 20 inches.

To solve this problem, we can use the given information to set up an equation. Let's assume that the width of the rectangular piece of metal is x inches. According to the problem, the length of the piece of metal is 5 inches longer than its width, so the length would be (x+5) inches.

When squares with sides 1 inch long are cut from the four corners, the width and length of the resulting box will be reduced by 2 inches each. Therefore, the width of the box will be (x-2) inches and the length will be ((x+5)-2) inches, which simplifies to (x+3) inches.

The height of the box will be 1 inch since the flaps are folded upward.
Now, let's calculate the volume of the box using the formula Volume = length * width * height.

Substituting the values, we have:

234 = (x+3)(x-2)(1)

Simplifying the equation, we get:

234 = x^2 + x - 6

Rearranging the equation, we have:

x^2 + x - 240 = 0

Now, we can solve this quadratic equation either by factoring or by using the quadratic formula. Let's use factoring to find the values of x.

Factoring the equation, we have:
(x+16)(x-15) = 0
Setting each factor equal to zero, we get:
x+16 = 0 or x-15 = 0
Solving for x, we have:
x = -16 or x = 15
Since the width cannot be negative, we take x = 15 as the valid solution.
Therefore, the original dimensions of the piece of metal were 15 inches in width and (15+5) = 20 inches in length.

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Answer: 125 miles

Step-by-step explanation:

We know that 25 miles is 20% of the trip.

20% is 1/5 of 100, so that means we will multiply the number of miles driven by the denominator of the fraction.

25 × 5 = 125 miles

The answer to the question is 125 miles.

The sampling method used by the restaurant manager allows for efficient data collection and a representative sample, it may introduce bias and lacks randomization.

Based on the information provided, we can identify the following statements that are true about the sampling method used by the restaurant manager to evaluate customer satisfaction with the new smoothie:

1. The manager uses systematic sampling: The manager surveys every other customer who orders the new smoothie. This systematic approach involves selecting every second customer, providing a consistent and organized sampling method.

2. The sample is representative: By surveying every other customer who orders the new smoothie, the manager ensures that the sample includes a variety of customers, reflecting the customer population as a whole.

3. The sample size may be smaller than the total customer base: Since the manager surveys every other customer, the sample size may be smaller compared to surveying every customer. This allows for efficient data collection and analysis.

4.The sampling method may introduce bias: The manager may inadvertently introduce bias by only surveying every other customer. Customers who are skipped in the survey may have different preferences or opinions, leading to a potential bias in the results.

5. The sampling method lacks randomization: Randomization is not employed in this sampling method, as the manager systematically selects customers. This could potentially introduce bias or exclude certain types of customers from the sample.

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Answer:

814.15 ft long

Step-by-step explanation:

We use the sine of 32.8 degrees to find the hypotenuse which is the length of the highway:

sine = opp/hyp

sin32.8=800/x (evaluate sin and multiply by x)

0.9826178774x = 800 (divide)

x=814.15 ft long

answer =814.15

explanation= we'll firstly need to find the hypotenuse by using the 32.8 degrees

•°• Sin 32.8=800/?

then, 0,9826178874=800

then we divide as the answer will be 814.15

Answer:

HFHBEHFBHEHHEHHHHH

Step-by-step explanation:

Answer:

The maximum profit the florist will earn from selling celebration bouquets is $725.

The florist will break-even after one-dollar decreases when her profit is zero. From the graph, this occurs at x = 10. So the florist will break-even after 10 one-dollar decreases.

The interval of the number of one-dollar decreases for which the florist makes a profit from celebration bouquets is (0, 10). This is because the profit is positive for values of x between 0 and 10, and becomes negative after 10.

Step-by-step explanation:

Answer:

9

Step-by-step explanation:

The \(n\)term is \(2n+1\).

\(S_n=\frac{3+2n+1}{2}(n)=99 \\ \\ \frac{n(2n+4)}{2}=99 \\ \\ n(n+2)=99 \\ \\ n^2+2n-99=0 \\ \\ (n+11)(n-9)=0 \\ \\ n=9 \text{ } (n>0)\)

The number of terms that needed to make the sum to 99 is 9

The first term of the arithmetic progression = 3

The common difference = 2

The sum of n term is = (n/2) [2a+(n-1)d]

Where a is the initial term

d is the common difference

Substitute the values in the equation

(n/2) [2(3)+(n-1)2] = 99

(n/2) [6 + 2n - 2] = 99

(n/2)[4+2n] = 99

n(2 + n) = 99

2n + \(n^2\) = 99

\(n^2\) + 2n - 99 = 0

Split the terms

\(n^2\) - 9n +11n - 99 =0

n(n -9) + 11(n - 9) = 0

(n + 11)(n - 9) = 0

n = -11 or 9

Since n cannot be a negative number, therefore n = 9

Hence, the number of terms that needed to make the sum to 99 is 9

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The Variables (a) Gender is Categorical , (b) Alcohol can be either Categorical or Quantitative and (c) Height is Quantitative .

We can identify the type of each variable as categorical or quantitative.

(a) Gender: This variable is categorical, as it describes a characteristic that can only take on a limited number of values (e.g., male or female).

(b) Alcohol: Without additional information , it is not clear whether this variable is categorical or quantitative.

If the data set only includes information about whether an individual drinks alcohol or not, then this variable is categorical. If the data set includes information about how much alcohol an individual consumes, then this variable would be quantitative.

(c) Height: This variable is quantitative, as it represents a numerical measurement of a continuous variable.

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The given question is incomplete , the complete question is

Identify and classify the variable(s) you will use. here is the list of variables in the data set.  

(i) identify the variable as either categorical or quantitative.

the variables are (a) Gender , (b) Alcohol , (c) Height .

66 students can be expected to prefer the zoo in 220 members of the 7th grade class.

Different techniques are used to calculate the averages of data sets for mean, median, mode, and range. The mean represents the sum of all the numbers. In an ordered list, the middle number is the median. The most frequent number is the mode. The highest number less the smallest number is the range.

The provided table contains the percentage of 7th graders who favor the zoo. Twelve of the 40 7th graders who were sampled prefer the zoo. Out of the 220 pupils in the 7th grade, we can use this proportion to determine how many love the zoo:

12/40 or 0.3 of 7th students say they prefer going to the zoo.

The predicted proportion of seventh graders who prefer the zoo is 0.3 x 220, or 66.

So, 66 is the correct response.

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Complete question is :

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

Grade      Zoo   Museum   Sports Complex

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

7 Grade      12        18             10

8 Grade      14        19               7

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

A random sample of 40 students from each grade level was surveyed regarding their preference for a class field trip.

If there are 220 members of the 7th grade class, then how many students can be expected to prefer the zoo?

Answer:

0 is a rational, whole, integer and real number. Some definitions include it as a natural number and some don't (starting at 1 instead).

Answer:

0 is a rational, whole, integer and real number.

Answer:

1243djfjdjjddjddhhfhdyeiw92

easy the answer would be  2.2

\(\it x-4 < 16 \bigg|_{+4}\Rightarrow x < 20 \Rightarrow x=16 \ is\ an\ integer\ suitable\ for \ this \ inequality\)

Simplify the given expression as shown below

On the other hand,

Solving for y using the special triangle shown below

Thus,

Then,

The two sets of solutions are