what’s the equation for y.

4x = -2y

A.) y = 1/2x + 2

B.) y = -1/2x

C.) y = -2x

D.) y = x + 2

Problem 61

The nth triangular number is

T(n) = n(n+1)/2

I'll rewrite this into

T(n) = 0.5n(n+1)

The triangular number right after this is

T(n+1) = 0.5(n+1)(n+2)

I replaced every n with n+1 and simplified

Let's see what we get when we add up the two expressions

T(n) + T(n+1)

0.5n(n+1) + 0.5(n+1)(n+2)

0.5n^2+0.5n + 0.5(n^2+3n+2)

0.5n^2 + 0.5n + 0.5n^2 + 1.5n + 1

n^2+2n+1

(n+1)^2

This shows that the sum of any two consecutive triangular numbers results in a square number

Here's a few examples

Note each sum is a perfect square, which visually would plot out a square figure.

For quick reference, the set of the first few triangular numbers is {0, 1, 3, 6, 10, 15, 21, 28, 36, 45, 55,...}

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Problem 64

Let's say we go with n = 5.

This means,

T(n) = 0.5n(n+1)

T(n-1) = 0.5(n-1)(n-1+1)

T(n-1) = 0.5n(n-1)

T(5-1) = 0.5*5(5-1)

T(4) = 10

This says that when n = 5, the 4th triangular number is 10

Triple that result and add on n = 5

3*T(4) + n = 3*10+5 = 35

This result is beyond obvious which category of figurate number it belongs to. It's not a triangular number since it's not in the form n(n+1)/2. It's not a square number either.

Through a bit of trial and error, you should find it's a pentagonal number

Pentagonal numbers are of the form n(3n-1)/2

If you plugged n = 5 into that, it leads to 35

n(3n-1)/2 = 5*(3*5-1)/2 = 5*14/2 = 70/2 = 35

The diagram shown below represents the first few pentagonal numbers. The number of blue dots corresponds to the pentagonal number itself. Note the equal spacing when dealing with dots on each segment (eg: some interior blue dots are midpoints, others are quarter points, etc.)

Answer:

$1.5

Step-by-step explanation:

9÷6= 1.5

1.5× 1 = 1.5

Answer:

70!km is the right answer

Step-by-step explanation:

The distance between two cities on a map is 3.5 centimeters. the map is uses a scale in which 1 centimeters represents 20 kilometers.

Answer- 9 shelves

In order to find out how many shelves are need we must divided 175 into 20. 175 divided by 20 is 8.75. But, because you cannot have have .75 of a shelf, you have to round this to a whole. This means that 9 shelves will be the least needed number of shelves need to store 175 books. To check this answer 20 books X 8 shelves is 160 books, which means eight shelves can only store 160 books, we will need and additional shelf to store the last 15 books.

HOPE THIS HELPS & GOOD LUCK!

Answer:

X=1

(3(1)+2)

3+2

5

In this problem, we are asked to find the probability that Lindsay was able to work out for 40 minutes straight at the gym.

To do this, we must take into account the probabilities of her getting either a stairmaster or a stationary bike, and the probability of being able to use it for 40 minutes straight given the equipment she gets.

To find the probability that Lindsay worked out for 40 minutes straight, we need to use the law of total probability. The probability of working out for 40 minutes straight can be expressed as:

P(40 minutes straight) = P(Stairmaster) * P(40 minutes straight | Stairmaster) + P(Bike) * P(40 minutes straight | Bike)

Plugging in the values given, we have:

P(40 minutes straight) = 0.20 * 0.10 + 0.80 * 0.50 = 0.22

So, the probability that Lindsay worked out for 40 minutes straight today is 0.22.

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The correct answer on the hours spend a fortnight in front of a screen is C. ) 80

To find out how many hours you spend in front of a screen in a fortnight, you need to add the hours you spend on the computer and the hours you spend watching TV each day and multiply that by the number of days in a fortnight.
Add the hours you spend on the computer and the hours you spend watching TV each day: 4 + 2 = 6
Multiply that by the number of days in a fortnight: 6 × 14 = 84
Subtract the hours you spend on the computer from the total hours you spend in front of a screen: 84 - 4 = 80 hence the answer is 80 hours in a fortnight.

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The true option about the randomized design is (c) Betty should prepare all 60 cookies.

Each cookie will receive a number.

The numbers will be written on slips of paper, put into a hat, and shuffled well.

The first 15 numbers drawn will indicate the cookies to be baked at 300°, the next 15 will indicate the cookies to be baked at 325°, and so on until all 60 cookies are allocated.

The given parameters are:

n=60

batches=4

cookies=15 ---- the number of cookies in each batch

Temperature=300,325,350,375.

To randomly assign the cookies to the given temperatures, all cookies have to be subjected to the same conditions (except for the difference in the temperature).

Normal human body temperature is the typical temperature range found in humans. The normal human body temperature range is typically stated as 36.5–37 °C. Human body temperature varies.

This means that she can bake all the cookies at once at different temperatures while noting down the cookies with a given number.

Hence, the true option is (c)

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Answer: C : completely randomized experimental design

Step-by-step explanation: edge 2023

Answer:

A, B, D because the sum of them is equal to 18

Step-by-step explanation:

Adding them

Answer:

it is 2.66*

Step-by-step explanation:

24 / 9 = 8/3

8/3 = 2.66*

Answer:

x=1

Step-by-step explanation:

3x−1+2=4

Add −1 and 2 to get 1.

3x+1=4

Subtract 1 from both sides.

3x=4−1

Subtract 1 from 4 to get 3.

3x=3

Divide both sides by 3.

x=

3

3

​

Divide 3 by 3 to get 1.

x=1

Answer:

5

Step-by-step explanation:

The probability that fewer than five of the 11 randomly selected adult smartphone users will use their phones during meetings or classes is 0.6747

When adults with smartphones are randomly selected, 53% use them during meetings or classes. You need to find the probability that fewer than five of the 11 selected adults use their smartphones during meetings or classes. Here's how to calculate the probability that fewer than five of the 11 randomly selected adult smartphone users will use their phones during meetings or classes:

\(P(X < 5) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4)\)

Where X represents the number of smartphone users in the selected group who use their phones in meetings or classes. Using the binomial probability formula, you can calculate each of these probabilities separately.

\(P(X = 0) = (11C0)(0.53)^0(1 - 0.53)^11 = 0.0026\\P(X = 1) = (11C1)( 0.53)^1(1 - 0.53)^10 = 0.0247\\P(X = 2) = (11C2)(0.53)^2(1 - 0.53)^9 = 0.1012\\P(X = 3) = (11C3)(0.53) ^3(1 - 0.53)^8 = 0.2346\\P(X = 4) = (11C4)(0.53)^4(1 - 0.53)^7 = 0.3116\\\)

Therefore, the probability that fewer than five of the 11 randomly selected adult smartphone users will use their phones during meetings or classes is:

\(P(X < 5) = 0.0026 + 0.0247 + 0.1012 + 0.2346 + 0.3116 = 0.6747\)

Therefore, the probability is 0.6747.

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Answer:

-9x+8

Step-by-step explanation:

15x - 3+11 should be the answer

The balance increase for card i is $89.24 greater than the balance increase for card h. Card i has a balance of $1,522.16 and an interest rate of 12.05%, compounded monthly. Now, we can calculate the balance for both cards after three years using the compound interest formula: A = P(1 + r/n)^(nt)

Given, Card h has a balance of $1,186.44 and an interest rate of 14.74%, compounded annually.

Card i has a balance of $1,522.16 and an interest rate of 12.05%, compounded monthly. Now, we can calculate the balance for both cards after three years using the compound interest formula: A = P(1 + r/n)^(nt),

where A = final amount, P = principal (initial balance), r = annual interest rate (as a decimal), n = number of times compounded per year, t = time (in years)

For card h,

A = 1186.44(1 + 0.1474/1)^(1*3)

A = 1883.99

For card i, A = 1522.16(1 + 0.1205/12)^(12*3)

A = 1973.23

Therefore, the balance for card i will have increased more than that of card h, and the difference in the increase is: 1973.23 - 1883.99 = 89.24

The balance increase for card i is $89.24 greater than the balance increase for card h. Hence, the required answer is card i.

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Answer:

27

Step-by-step explanation:

PEMDAS : PARENTHESIES, EXPONENTS, MULTIPLY, DIVISIOIN, ADD, SUBTRACT

14/2 + 20

7 +20=27

Answer:

2

Step-by-step explanation:

If the common difference is d we can write:

-5 + 9d = 13

9d = 18

d = 2

Answer:

d = 2.

Step-by-step explanation:

First term = -5

10th term = -5 + 9d    where d is the common difference, so

-5 + 9d = 13

9d = 18

d = 2.

Answer:

x + y = 55

(1/3)x + (1/5)y = 13

25

Step-by-step explanation:

edge 2020

Answer:

x + y = 55

(1/3)x + (1/5)y = 13

25

Step-by-step explanation:

Answer:

A. (3, 5)

Step-by-step explanation:

J is currently at (3, -5). As it's reflected, the x coordinate will stay the same, and the y coordinate will switch signs since we're going from negative to positive. Our answer is (3, 5).

Simplifying the top:

(2* a^3 * b^5)^2 * (6ab)

4* a^6 *b^10 * (6ab)

24 *a^7 * b^11

so we have

(24 *a^7 * b^11) / (-3* a^5 *b)

immediately we can simplify 24 and -3

(-8 *a^7 * b^11) / ( a^5 *b)

a^7 and a^5 can cancel into just a^2

(-8 *a^2 * b^11) / (b)

b^11 and b cancels to b^10

-8 *a^2 * b^10

so that is your answer:

-8\(a^{2}\)\(b^{10}\)

A Type I error in this context would be the hypothesis that the true mean completion time, μ, is less than 44 minutes when, in fact, μ is equal to or greater than 44 minutes.

In other words, the managers would incorrectly conclude that there has been a significant decrease in the mean completion time, even though the true mean has remained the same or increased. Type I errors occur when we reject a null hypothesis (in this case, the null hypothesis would be that the mean completion time is 44 minutes) when it is actually true. In statistical hypothesis testing, we set a significance level (often denoted as α) that represents the probability of making a Type I error. If the computed test statistic falls in the critical region, determined by the significance level, we reject the null hypothesis. In this scenario, if the managers reject the null hypothesis and conclude that the mean completion time has decreased based on the sample mean of 41 minutes, it would be a Type I error if the true mean completion time is indeed 44 minutes. This means that the managers would falsely believe that there has been a significant change in the mean completion time when there hasn't been any change or even an increase in the mean completion time.

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The statement is false. The most common order of model-building is to test the interaction terms after testing the quadratic terms.

In the field of statistical modeling and regression analysis, the order of model-building typically involves testing the main effects (including linear and quadratic terms) before considering interaction terms.

The common approach is to start with a baseline model that includes the main effects (linear terms) of the variables of interest. Once the main effects are established and their significance is assessed, quadratic terms (squared terms) can be added to capture potential nonlinear relationships between the variables.

After incorporating the quadratic terms, the next step in model-building may involve considering interaction terms. Interaction terms allow for investigating the combined effect of two or more variables on the outcome variable, beyond their individual effects.

Therefore, the correct order of model-building is typically to test the quadratic terms after the linear terms and then consider the interaction terms. Thus, the statement "The most common order of model-building is to test the quadratic terms before you test the interaction terms" is false.

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Step-by-step explanation:

\( \underline{ \underline{ \text{Given}} }: \)

\( \underline{ \underline{ \text{To \: find}}} : \)

Let E ( -3 , 2 ) be ( x₁ , y₁ ) & H ( 1 , -1 ) be ( x₂ , y₂ )

\( \underline{ \underline{ \text{Solution}}} : \)

\( \sf{Midpoint = ( \frac{x_{1} + x_{2}}{2} \: , \frac{ y_{1} + y_{2}}{2} )}\)

⟶ \( \sf{( \frac{-3 + 1}{2} \: , \frac{2 + ( - 1)}{2} )}\)

⟶ \( \sf{( \frac{-2}{2} \:, \frac{2 - 1}{2} )}\)

⟶ \( \sf{( -1 \: ,\frac{1}{2} )}\)

\( \pink{ \boxed{ \boxed{ \tt{Our \: final \: answer : \boxed{ \underline{ \tt{(-1 \: , \: \frac{1}{2} )}}}}}}}\)

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Have a wonderful day / night ! ツ

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The intensity of a rock concert measuring 120 dB is approximately 5623.41 times more intense than a whisper measuring 45 dB.

To compare the intensity of a whisper measuring 45 dB and a rock concert measuring 120 dB using the equation I = 10^(d/20), where I is the intensity in comparison to a reference intensity and d is the sound level in decibels, we can calculate the ratio of their intensities.

For the whisper measuring 45 dB:

\(I_{whisper} = 10^{45/20}\)

For the rock concert measuring 120 dB:

\(I_{rock concert} = 10^{120/20}\)

To find the ratio of their intensities, we divide \(I_{rockconcert}\) by \(I_{whisper}\):

Ratio = \(I_{rockconcert} / I_{whisper} = (10^{120/20}) / (10^{45/20})\)

Simplifying the equation, we can subtract the exponents:

Ratio = \(10^{(120-45)/20}\)

Calculating the exponent:

Ratio = \(10^{75/20}\)

Evaluating 75/20:

Ratio ≈ 5623.41

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A) the three inequalities that must be satisfied are:

B) Graph shaded and satisfying all conditions is attached.

An inequality in mathematics is a relationship that makes a non-equal comparison between two integers or other mathematical expressions.

It is most commonly used to compare the sizes of two numbers on a number line.

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Answer:

1 4/5 hours

Step-by-step explanation:

3/5 x 3 = 9/5 or 1 4/5

Answer:

28 is one, but I can't find the other.

Step-by-step explanation:

28 divided by 4 is 7.