6. If y = -2x² + 8x - 5 were put in vertex form y = a(x - h)² + k, then what is
the value of k?
A. -13
B. -3
C. 3
D. 1

The correct answer is: option D. Bus 18, with a median of 12.

To determine which bus typically has the faster travel time, we need to compare the measures of center of the two sets of data. The measure of center that we use depends on the shape of the data. In this case, since the data is not symmetric, we should use the median as the measure of center.

Looking at the line plots, we can see that the median travel time for Bus 14 is approximately 14 minutes (the value with four dots above it), while the median travel time for Bus 18 is approximately 12 minutes (the value with two dots above it).

Since the median is less affected by extreme values than the mean, it is a more appropriate measure of center for this data. Therefore, we can conclude that Bus 18 typically has the faster travel time, with a median of 12 minutes, compared to Bus 14's median of 14 minutes.

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Answer:

20

Step-by-step explanation:

suppose the number is x

so

(x-8) * 2 =24

x-8=12

x=12+8

x=20

Answer:

each pair of plaid cargo pants costs $57.50 for Fashion Victim #1 and $71.00 for Fashion Victim #2.

Step-by-step explanation:

a) To find out how much each pair of gold-sequined sneakers cost, we need to divide the total cost of the sneakers by the number of pairs purchased.

Fashion Victim #1 paid $230 for 3 pairs of gold-sequined sneakers, so:

$230 ÷ 3 pairs = $76.67 per pair

Fashion Victim #2 paid $355 for 6 pairs of gold-sequined sneakers, so:

$355 ÷ 6 pairs = $59.17 per pair

Therefore, each pair of gold-sequined sneakers costs $76.67 for Fashion Victim #1 and $59.17 for Fashion Victim #2.

b) To find out how much each pair of plaid cargo pants cost, we follow the same method as above.

Fashion Victim #1 paid $230 for 4 pairs of plaid cargo pants, so:

$230 ÷ 4 pairs = $57.50 per pair

Fashion Victim #2 paid $355 for 5 pairs of plaid cargo pants, so:

$355 ÷ 5 pairs = $71.00 per pair

Therefore, each pair of plaid cargo pants costs $57.50 for Fashion Victim #1 and $71.00 for Fashion Victim #2.

Mean of the sampling distribution of xo: Not enough information provided.

Standard deviation of the sampling distribution of xo: 7 points.

In the given scenario, we have a group of 50 students, and we are comparing their blood pressures before and after watching a violent movie. It is mentioned that, on average, blood pressure increases by 5 points after watching something violent with a standard deviation of 7 points.

The mean difference in blood pressure (x1 - x2) is 5 points, and the standard deviation of the differences (the standard deviation of the sampling distribution of xo) is 7 points.

Since n = 50 and od = nd = 5, it appears that "od" and "nd" refer to the standard deviation of the population (before watching the movie) and the standard deviation of the differences (after watching the movie), respectively.

The mean of the sampling distribution of xo (the mean difference in blood pressure) can be calculated as:

Mean of xo = Mean of (x1 - x2) = Mean of x1 - Mean of x2

Given that blood pressure increases by 5 points after watching the violent movie, we can express the mean of xo as:

Mean of xo = Mean of x1 - (Mean of x2 + 5)

However, we are not provided with the specific value of the mean blood pressure before watching the movie. Without that information, we cannot determine the exact value of the mean of xo.

As for the standard deviation of the sampling distribution of xo, it is the standard deviation of the differences, which is given as 7 points.

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The equation we get for the amount of bacteria with  with time T

T(t)=15×2ⁿ where n is the number of hours.

Exponent is a mathematical operation, written as an. Here the expression an involves two numbers, the base 'a and the exponent or power 'n'. Exponents are used to simplify algebraic expressions.

Given here: A certain type of bacteria doubles every hour

Now number of hours between 9-12 pm

is 15 hours

if at 9 a.m the amount of bacteria is x then we have in 15 hours

at t=1 we have the number of bacteria was

T=2×15

=30

Similarly we have for t=15 we get

T=15×2¹⁵

Hence, The equation we get for the amount of bacteria with  with time T

T(t)=15×2ⁿ where n is the number of hours.

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Answer:

3

Step-by-step explanation:

substitute where x=3 into the equation

so 4*3-1=11

4×3-1=11

12-2=11

11=11

proved..

Answer:

Graphing y=1/2x-2 will look like this on the graph

Answer:

Step-by-step explanation:

the 1/2 is a gradient so you go up 1 for every 2 to the right

the -2 is the Y intercept so you start graphing the gradient from -2 on the Y axis

Symbolic logic is a way of representing propositions, which are statements about the world, using symbols.

The use of symbols allows us to simplify complex statements and to manipulate them algebraically.In this problem, there are three propositions:1. If I take the bus or subway,

then I will be late for my appointment.2.

If I take a cab, then I will not be late but I will be broke.3. I will be on time.To represent these propositions using symbols, we need to assign a variable to each statement.

Let B stand for "I take the bus", S stand for "I take the subway", C stand for "I take a cab", L stand for "I am late", and R stand for "I am broke". Using these variables,

we can represent the three propositions as follows:1. (B ∨ S) → L2. C → (~L ∧ R)3. ~LNow, let us analyze each of the conclusions given in the question:

Conclusion (a): I will take a cab. To determine whether this conclusion is valid, we need to use logical deduction. We know from proposition 2 that if we take a cab, we will not be late but we will be broke.

We also know from proposition 3 that we will be on time. Therefore, we can conclude that we will take a cab. This conclusion is valid because it follows logically from the given propositions.

Conclusion (b): I will be broke.To determine whether this conclusion is valid, we need to use logical deduction. We know from proposition 2 that if we take a cab, we will be broke.

We also know from conclusion (a) that we will take a cab. Therefore, we can conclude that we will be broke. This conclusion is valid because it follows logically from the given propositions.

Conclusion (c): I will not take the subway.To determine whether this conclusion is valid, we need to use logical deduction. We know from proposition 1 that if we take the bus or subway, we will be late. We also know from proposition 3 that we will be on time.

Therefore, we can conclude that we will not take the subway. This conclusion is valid because it follows logically from the given propositions. Conclusion (d): If I become broke, then I took a cab.

To determine whether this conclusion is valid, we need to use logical deduction. We know from proposition 2 that if we take a cab, we will be broke. However, we do not know if we will become broke.

Therefore, we cannot conclude that if we become broke, then we took a cab. This conclusion is invalid because it does not follow logically from the given propositions.

The correct conclusion should be "If I took a cab, then I may become broke.

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There are several different sampling methods that could be employed for this study, including:

Simple random sampling: This method involves randomly selecting a certain number of students from each campus and measuring the distance between their hometowns and their campuses.

Stratified random sampling: This method involves dividing the student population at each campus into different strata (e.g. by major or year in school) and then randomly selecting a certain number of students from each stratum.

Cluster sampling: This method involves randomly selecting a certain number of campuses and then measuring the distance between the hometowns of all students at those campuses and their respective campuses.

Multi-stage sampling: This method involves using a combination of the above methods, such as first using cluster sampling to select a certain number of campuses and then using stratified random sampling to select a certain number of students from each campus.

This study would be an enumerative study because it seeks to measure the characteristics of a population, in this case, the average distance between the hometowns of students and their campuses, by counting and measuring them.

It is not an analytic study because it doesn't involve testing a hypothesis or making causal inferences.

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The lines to use to solve the equation are y = –3x – 2  and y = 2x + 8

The graph of the line is attached

From the question, we have the following parameters that can be used in our computation:

–3x – 2 = 2x + 8

The above equation can be splitted by introducing the variable y

using the above as a guide, we have the following:

y = –3x – 2

y = 2x + 8

This means that the lines to use to solve the equation are y = –3x – 2  and y = 2x + 8

The graph of the line is added as an attachment

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Answer:

B. 71°

Step-by-step explanation:

∠1 and ∠2 are corresponding angles.

Corresponding angles are congruent.

m∠1=m∠2=71°

The value of x is 34.9cm( 1d.p)

A diagonal is the line segment that join two opposite vertices.A diagonal of a rectangle divides it into two congruent right triangles. The diagonals of a rectangle are the same length.

angle C = angle D

therefore 52+C +D = 180

2C = 180-52

C = 64°

To find BD

sin64/OD = sin52/17

OD = sin64 × 17/sin52

= 15.3/0.788

= 19.4

BD = 2 × 19.4 = 38.8

x = √ 38.8²-17²

x = √1505.44 - 289

x = √1216.44

x = 34.9 cm( 1 d.p)

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Assuming a simple interest rate of 2%, the investment will earn $4 in interest.

Simple interest is calculated based on the principal amount and the interest rate. In this case, the principal amount is $200 and the interest rate is 2%, which means that the investment will earn 2% of $200 per year.

Therefore, the annual interest earned would be $4 ($200 x 0.02). Simple interest is not compounded, which means that the interest earned each year is based solely on the principal amount, and does not take into account any previously earned interest.

So if the investment is held for one year, the total value of the investment would be $204 ($200 + $4). If it is held for multiple years, the interest earned each year would remain at $4 per year.

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Answer:

Step-by-step explanation:

8.1

Answer:

15 minutes

Step-by-step explanation:

60/4=15 8/4=2

Answer:

Circumference: 50.27 cm

Area: 201.06 cm²

Step-by-step explanation:

Hi there!

1) Determine the circumference

\(C=\pi d\) where d is the diameter of the circle

Plug in the diameter (16 cm)

\(C=16\pi\\C=50.27\)

Therefore, the circumference is 50.27 cm when rounded to the nearest hundredth.

2) Determine the area

\(A=\pi r^2\) where r is the radius

Plug in the radius (16/2=8)

\(A=\pi (8)^2\\A=64\pi\\A=201.06\)

Therefore, the area of the circle is 201.06 cm² when rounded to the nearest hundredth.

I hope this helps!

Answer: $45

Step-by-step explanation:

Let the original price be x.

Since there was a discount of 20%, it means the person bought the frying pan at (100% - 20%) = 80% of the original price. This can then be formed into an equation as:

80% × x = $36

0.8 × x = $36

0.8x = $36

x = $36/0.8

x = $45

The original price was $45

Answer:

120 degrees

Step-by-step explanation:

Angles 1 and 3 are congruent, because they are vertical angles, so we must set them equal to each other, solve for x and plug in x.

Hope this helps :-)

Answer:

3 = 108 degrees

Step-by-step explanation:

2x + 80 = 3x + 60

get the variable and number on different sides

2x + 80 = 3x + 60

2x + 80 - 80 = 2x

3x + 60 - 3x = 60

2x + 3x = 5x

60 + 80 = 140

5x = 140

now divide each side by 5

5x / 5 = x

140 / 5 = 28

x = 28

28 + 80 = 108

Hello !

Answer:

\(\boxed{\sf C\approx62.8 ft}\)

Step-by-step explanation:

To find the circumference of a circle with its radius, we will apply the following formula:

\(\sf C=2\pi r\)

Where r is the radius of the circle.

Given :

We know that the diameter is equal to two times the radius, so \(r=10\) ft.

Let's substitute our value into the formula :

\(\sf C=2\times \pi\times 10\\\boxed{\sf C\approx62.8 ft}\)

Have a nice day !

Answer:

Step-by-step explanation:

We know that

So,

→ R = 20/2

→ R = 10

Now,

We know that,

Circumference of circle = 2πr

→ 2 × 22/7 × 10

→ 440/7

→ 62.8 ft

Hence ,

Answer:

12(2A+B)=12*3

Step-by-step explanation:

Answer:

\(12\)

Step-by-step explanation:

We know that \(24=12*2\), \(12=12*1\), and \(36=12*3\).

So, we can re-write the equation as \(12*2*A+12*1*B=12*3\).

We can factor out a \(12\) from both sides to get \(12(2A+B)=12(3)\).

The insides can't be simplified anymore, so the final equation is \(12(2A+b)=12(3)\) and the gcf is \(\boxed{12}\)

Step-by-step explanation:

(a): √8 = √4√2 = 2√2. => k = 2

(b): √50 = √25√2 = 5√2. => k = 5

(c): √98 = √49√2 = 7√2. => k = 7

(d): √12 = √4√3 = 2√3. => k = 2

(e): √300 = √100√3 = 10√3. => k = 10

(f): √45 = √9√5 = 3√5. => k = 3

(g): √125 = √25√5 = 5√5. => k = 5

(h): √28 = √4√7 = 2√7. => k = 2

The data should come from a binomial distribution. There should be no non-response or other forms of bias. The sample size should not be more than 10% of the population size, and the sample should be independent of one another.

When making inferences about one population proportion, the following assumptions need to be made:

Option 1: The sample is a simple random sample from the population.

Option 2: The sample size should be large enough so that both np ≥ 10 and n(1 − p) ≥ 10.

Option 3: The data comes from a binomial distribution.

Option 4: There is no non-response or other forms of bias.

Option 5: The sample size is no more than 10% of the population size.

Option 6: The sample is independent of one another.In order to make inferences about one population proportion, the assumptions mentioned above need to be made. It is vital to make sure that the sample is a simple random sample from the population, and that the sample size is large enough so that both np ≥ 10 and n(1 − p) ≥ 10.

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Answer:

65

Step-by-step explanation:

Answer:

21

Step-by-step explanation:

Answer:

BAC and DAE are two acronyms for BAC and DAE, respectively. Since they are angles at a point, an arc measuring 204 degrees is 360 degrees. BAC is measured at 11 degrees. 5(11)° = 55° is the measure of DAE.

Step-by-step explanation:

side length1 = x

side length2 = y

2x + 2y = perimeter

2(4x) + 2(4)y = new perimeter

8x + 8y = new perimeter

new perimeter = 4 times the old perimeter

Answer:

$115.2

Step-by-step explanation:

Step one:

Given data

A store used to sell an MP3 for $72 and we are told that this 50% of the wholesale price.

Therefore the wholesale price is

72*2= $144

Required:

The special sales cost at 20% discount

Step two:

We are told that the special sale is at a 20% discount on the wholesale

= 20/100*144

=0.2*144

=$28.8

Therefore the special sales price is

= 144-28.8

=$115.2

The equations are

a) Julie can type 25 words in 1 minute and Debbie can type 20 words in 1 minute

b) Julie can type 1500 words in 1 hour and Debbie can type 1200 words in 1 hour

What is an Equation?

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the number of words typed by Julie be = J

Let the number of words typed by Debbie be = D

a)

Now ,

Julie can type 50 words in 2 minutes

So , the number of words Julie can type in 1 minute = 50 / 2

Number of words Julie can type in 1 minute = 25 words

And ,

Debbie can type 300 words in 15 minutes

So , the number of words Debbie can type in 1 minute = 300 / 15

Number of words Debbie can type in 1 minute = 20 words

b)

1 hour = 60 minutes

The number words Julie can type in 1 hour = Number of words Julie can type in 1 minute x 60

Substituting the values in the equation , we get

The number words Julie can type in 1 hour = 25 x 60

The number words Julie can type in 1 hour = 1500 words

And ,

The number words Debbie can type in 1 hour = Number of words Debbie can type in 1 minute x 60

Substituting the values in the equation , we get

The number words Debbie can type in 1 hour = 20 x 60

The number words Debbie can type in 1 hour = 1200 words

Hence , the number of words per hour for Julie and Debbie are 1500 and 1200 respectively

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Answer: 2 points

Step-by-step explanation:

It will take 19 weeks for the students in both classes to know how to write the same number of letters. At that point, each class will have taught and learned 16 letters.

1. To calculate the time it takes for the students in both classes to know the same number of letters, we need to find the common multiple of the numbers of letters taught per week in each class. Mr. Wu teaches 1 letter per week, and Ms. Walton teaches 2 letters per week. The common multiple of 1 and 2 is 2, so it will take 2 weeks for the number of letters taught in both classes to become equal.

2. To find the total number of letters the students will know at that point, we add up the letters they have already learned and the letters they will learn during those 2 weeks. Mr. Wu's class has already learned 10 letters, and Ms. Walton's class has learned 3 letters. During the 2 weeks, Mr. Wu's class will learn 2 letters (1 letter per week), and Ms. Walton's class will learn 4 letters (2 letters per week). Therefore, at the end of the 2 weeks, each class will have taught and learned a total of 12 letters.

3. It will take 19 weeks for the students in both classes to know the same number of letters. At that point, each class will have taught and learned 16 letters. This is calculated by finding the common multiple of the letters taught per week and adding the letters already learned to the letters taught during that time.

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Answer:

t = 1

Step-by-step explanation:

Answer:

t=1

Step-by-step explanation:

1.Move the variable to the left hand side and change its sign.

2.move the constant to the right hand side and change its sign.

3.collect like terms.

4.calculate the difference.

5.divide both sides of the equation by -7.

Solution is t=1

your welcome