What does the line y=5 represent in X=8(y-5)^2+2

Answers

Answer 1

Answer:

Answer:

The right answer is vertex

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At a concession stand, seven hot dogs and two hamburgers cost $16.25; two hot dogs and seven hamburgers cost $17.50. Find the cost of one hot dog and the cost of one hamburger.
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Kristen owns a bakery and is making a cake for a wedding. The dimensions of the cake are shown below. Answer each of the questions below.What is the frosted area of the top cake? (Round to the nearest tenth) What is the frosted area of the bottom cake? (Round to the nearest tenth)What is the total surface area of cake that will be frosted?
An experiment consists of drawing 1 card from a standard 52 card deck? What is the probability of drawing a queen?

Can you help me simplify it?

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The answer to your question is -2xy+5x^2+4y-10x. Hope this helps and let me know if it was right.

49, 34, and 48 students are selected from the Sophomore, Junior, and Senior classes with 496, 348, and 481 students respectively. Identify which type of sampling is used and why?A) Convenience
B) Cluster
C) Random
D) Systematic
E) Stratified

Answers

Answer:

Stratified sampling

Step-by-step explanation:

In the question, students are selected from subgroups of Sophomore, Junior, and Senior classes.

We are told that 49, 34, and 48 students are selected from the Sophomore, Junior, and Senior classes with 496, 348, and 481 students respectively.

This means that the sample numbers of 49, 34 and 48 students were selected in proportion to the subgroup sizes of 496, 348, and 481 students respectively.

Thus, due to the fact that subgroups were selected & that sample number of students were also selected in proportion to their respective subgroup sizes, this is therefore a stratified sampling.

Final answer:

The type of sampling used in this scenario is stratified sampling. The type of sampling in this case is E) Stratified sampling.

Explanation:

The type of sampling used in this scenario is stratified sampling. Stratified sampling is a method where the population is divided into different groups or strata, and then a sample is randomly selected from each stratum. In this case, the sophomore, junior, and senior classes are the different strata, and the sample sizes are proportional to the size of each stratum.

To further explain, let's consider the sophomore class with 496 students. If we are selecting a sample size of 49 from this class, it means that approximately 10% of the students (49/496 = 0.098) will be selected. Similarly, for the junior class with 348 students, approximately 10% (34/348 = 0.098) of the students will be selected. The same applies to the senior class with 481 students and a sample size of 48 students.

In stratified sampling, the goal is to ensure that the sample represents the characteristics of each stratum in proportion to their size in the population. By sampling from each of the classes, we can obtain a representation of the entire student population.

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In your biology class, your final grade is based on several things: a lab score, scores on two major tests, and your score on the final exam. There are 100 points available for each score. However, the lab score is worth 21% of your total grade, each major test is worth 25%, and the final exam is worth 29%. Compute the weighted average for the following scores: 60 on the lab, 81 on the first major test, 69 on the second major test, and 79 on the final exam. Enter your answer as a whole number.

Answers

Answer:

$Weighted\ Average = 73$

Step-by-step explanation:

Given

$Lab = 21\%$

$Tests = 25\%$

$Exam = 29\%$

$Lab\ Score = 60$

$First\ Test = 81$

$Second\ Test = 69$

$Exam = 79$

Required

The weighted average

To do this, we simply multiply each score by the corresponding worth.

i.e.

$Weighted\ Average = Lab\ worth * Lab\ score + Tests\ worth * Tests\ score.....$

So, we have:

$Weighted\ Average = 21\% * 60 + 25\% * 81 + 25\% * 69 + 29\% * 79$

Using a calculator, we have:

$Weighted\ Average = 73.01$

$Weighted\ Average = 73$ --- approximated

A bacteria culture is initially 10 grams at t=0 hours and grows at a rate proportional to its size. After an hour the bacteria culture weighs 11 grams. At what time will the bacteria have tripled in size?

Answers

A bacteria culture is initially 10 grams at t=0 hours & grows at a rate proportional to its size , After an hour the bacteria culture weighs 11 grams , The bacteria takes 11.56 hours to have tripled in size.

To find the time of bacteria when increasing the growth to tripled.

Given : when time=0 hours , weight=10 grams.

when time=1 hours , weight=11 grams.

To find: when time= ? hours , weight=30grams.

Here according to question, initial size = 10 grams we have asked for tripled in size i.e. 30 grams.

Now we knows that,

The formula for exponential growth in population or size is

$\rm (P)=P_0e^(rt)$ where,

$\rm P_0=initial\;size\n\nr= rate\;of\;growth\n\nt= time \;period$

Now, we put the value in formula we get,

$\rm P_0=10\;grams \n\nwhen ,\n\;\;t=1\;hour P(t)=11 grams\nThen,\n11=10e^{r(1)\n1.1 =e^r\n\n\rm Taking \;log(natural)\;both\;the\; side \;on \;solving\;we\;get,\nln(1.1)=r\;ln(e)\nr=ln(1.1)\nr=0.953101798043\approx0.095$

Now when the bacteria increase its size to triple

$\rm P(t) = 3 * 10 = 30$

Then, according to the formula we substitute values in the formula,

$\rm 30=10e^(0.095t)\n\n3=e^(0.095t)\n\nAgain \;we \;take\;natural\;log\;on \;both\;the\;sides, we\;get\nln\;3=0.095t\n\nt=(\rm ln\;3)/(0.095)\n\n\n\n\rm t= (1.09861228867)/(0.095) \n\n\ t=approx \; 11.56$

Therefore, The bacteria takes 11.56 hours to have tripled in size.

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Answer: It will take 11.56 hours .

Step-by-step explanation:

Exponential growth in population or size formula :

$P(t)=P_0e^(rt)$

, where $P_0$ = initial size

r= rate of growth

t= time period

As per given , we have

$P_0=10$ grams

At t= 1 , P(t)= 11 grams

Then,

$11=10e^(r(1))\n\n 1.1= e^r\n\n\text{Taking natural log on both sides , we get} \n\n\ln (1.1)=r\ln (e)\n\n r=\ln (1.1)\n\n r=0.0953101798043\approx0.095$

When, the bacteria have tripled in size , P(t) = 3 x10 = 30

Then,

$30=10e^(0.095t)\n\n 3=e^(0.095t)$

$\text{Taking natural log on both sides , we get}\n\n \ln 3=0.095t\n\n t=(\ln3)/(0.095)\n\n t=(1.09861228867)/(0.095)\approx11.56$

Hence, it will take 11.56 hours .

The number of mold cells doubles every 12 minutes. At this moment, there are x mold cells present on a piece of bread. Which of the following represents the number of mold cells present one hour from now?

Answers

The no. of mold cells one hour from now will be 32 $x$ .

Given,

The number of mold cells doubles every 12 minutes.

Let at time $t$ we have x mold cells.

So, after 12minutes, the no of molds at $,t_(12) =t+12$ the no. of mold will be $2x.$

After further 12 minutes at, $t_(24) =t+24$ , the no. of mould will be $4x$ .

After further 12 minutes at, $t_(36) =t+36$ , the no. of mold will be $8x$ .

After further 12 minutes at, $t_(48) =t+48$ , the no. of mold will be $16x.$

After further 12 minutes at, $t_(60) =t+60$ , the no. of mold will be $32x$ .

Hence the no. of mold cells one hour from now will be 32 $x$ .

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Answer:

Step-by-step explanation:

Suppose that at time $t_0$ we have x mold cells. We are told that after 12 minutes the amount present is double. That is a $t= t_0+12$ we have 2x cells. Then, at $t = t_0+24$ we have (2x)*2 = 4x. We can continue as follows

$t: t_0+36$ we have (4x)*2 = 8x.

$t: t_0+48$ we have (8x)*2 = 16x

$t: t_0+60$ (one hour later) we have (16x)*2 = 32x.

So after one hour from now we have 32x cells.

Triangle M was dilated by a scale factor of 1.2 to form triangle M. How does the area of triangle M'relate to the area of triangle M?
A- The area of triangle M'is 0.6 times the area of triangle M.
B- The area of triangle M'is 1.2 times the area of triangle M.
C- The area of triangle M'is 1.44 times the area of triangle M.
D- The area of triangle M' is 2.4 times than the area of triangle M.