what is the equation?

Answer:

1.5 units squared

Step-by-step explanation:

Area of a Triangle formula: A = 1/2bh

Pythagorean Theorem: a² + b² = c²

Since you are missing the h to find the area of the triangle, you must use Pythagorean to find the 3rd missing side (it is a right triangle so you can use Pythagorean).

Step 1: Use Pythagorean

2.5² = 1.5² + b²

4 = b²

b = 2

Step 2: Switch variables

b (from Pythagorean) = h (height for Area)

Step 3: Solve for Area

A = 1/2(1.5)(2)

A = 1.5

And you have your final answer.

ANSWER

1.23

EXPLANATION:

Given information:

Step 1: Convert the decimals into fraction

Hence, the answer is 2.3

Answer:

10

Step-by-step explanation:

TV=TL-VL. TL=5x+3 and VL=5x-7. (5x+3)-(5x-7)=5x+3-5x+7=3+7=10. TV=10.

Answer: 10?

Step-by-step explanation:

Answer:

\(Given~quadratic ~function : 1=x^2-6x\)

\(here,a=1,b=-6\)

\(so, the~numbers~which ~we ~need ~to ~add....\)

➜ \((\frac{b}{2} )^2\)

➜ \(=(\frac{-6}{2})^2\)

➜\(=(-3)^2\)

➜ \(=9\)

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

hope it helps...

have a great day!!

Answer:

\(y = -2x +7\)

Step-by-step explanation:

Given

\((x_1,y_1) = (-3,13)\)

\((x_2,y_2) = (6,-5)\)

Required

Determine the equation in slope intercept form

First, we calculate the slope:

\(m = \frac{y_2 - y_1}{x_2 - x_1}\)

The equation becomes:

\(m = \frac{-5 - 13}{6 - (-3)}\)

\(m = \frac{-5 - 13}{6 +3}\)

\(m = \frac{-18}{9}\)

\(m = -2\)

The equation is then calculated using:

\(y -y_1 = m(x - x_1)\)

Substitute values for y1, m and x1

\(y - 13 = -2(x -(-3))\)

\(y - 13 = -2(x +3)\)

\(y - 13 = -2x -6\)

Make y the subject

\(y = -2x - 6 + 13\)

\(y = -2x +7\)

Step-by-step explanation:

the area of :

1) inside surface = (3.14× 1.25²)+(3.14×2.5×1.5)

= 4.90625 + 11.775 = 16.68125 m²

2) upper side surface= (3.14 × (1.35²-1.25²))

= 3.14× (1.8225-1.5625)= 3.14×0.26=0.8164m²

3) lateral surface= 3.14×2.7×1.6=13.5648m²

the total amount of vinyl required for the spa =

16.68125+0.8164+13.5648 = 31.06245 m²

The expected value if you play this game is 25 cents.

What is probability?

The ratio of good outcomes to all possible outcomes of an event is known as probability.

Formula

Probability(Event) = Favorable Outcomes/Total Outcomes.

The total number of marbles is 2+10+20 = 32 marbles

The total probability of getting gold marble is P(g) = 2/32 = 0.0625

The total probability of getting silver marble isP(s) = 10/32 =0.3125

The total probability of getting black marble isP(b) = 20/32 =0.625

By multiplying the price by the likelihood and adding them together with the price for each scenario, we can determine the game's expected value.

E= 4P(g) + 2P(s) - 1P(b)

E= 4*0.0625 + 2*0.3125 - 1* 0.625

E= $0.25 or

E=25 cents

Hence, the expected value if you play this game is 25 cents.

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Answer:

-3

Step-by-step explanation:

Answer:

Step-by-step explanation:

log=(x+3)

x=1

(1+3)=4

log=4

Answer:

x = 2

Step-by-step explanation:

x + 3 > 0

x > -3

x > 0

log [x(x+3)]= log 10

log (x² + 3x) = log 10

x² + 3x = 10

x² + 3x - 10 = 0

(x+5)(x-2) = 0

x = -5 (not acceptable)

x = 2

True. In Oymyakon, Russia, which is considered the coldest inhabited village on Earth, temperatures can indeed sink to -88°F (-71°C). In such extreme cold, eyelashes can freeze, and food items can become frozen quickly.

In these extremely cold regions, temperatures can indeed drop to very low levels, often below -50°C (-58°F) during the winter months. In such extreme conditions, it is possible for eyelashes to freeze and for items such as dinner to freeze quickly. While the specific temperature mentioned (-88°F) may not be accurate for a particular location, it is not far-fetched considering the extreme cold experienced in these regions.

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a). The elements of Gn are {e^(2πi/n), je^(2πi/n), j^2e^(2πi/n), ..., j^(n-1)e^(2πi/n)}. b). The abelianization is isomorphic to Gn.  c). The character table has n irreducible characters.

a) The set of elements of Gn is {e^(2πi/n), je^(2πi/n), j^2e^(2πi/n), ..., j^(n-1)e^(2πi/n)}. The conjugacy classes can be determined by considering the conjugates of e^(2πi/n).

Each conjugate is of the form j^ke^(2πi/n) for some k ∈ {0, 1, 2, ..., n-1}. Thus, there are n distinct conjugacy classes, each containing one element.

b) The abelianization of Gn can be found by considering the commutator subgroup [Gn, Gn]. Since Gn is abelian, [Gn, Gn] is the trivial subgroup {e}. Therefore, the abelianization of Gn is isomorphic to Gn itself.

c) Since the abelianization of Gn is isomorphic to Gn, the character table of Gn will have the same number of irreducible characters as elements in Gn.

In this case, there are n irreducible characters.

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The new mean, new variance, and new standard deviation would be 9, 7, 2.6458, respectively that is in option (d)

If you multiply each value in the dataset by 2, you will get the following new dataset: 6, 12, 4, 14, 8, 10.

Mean = Sum total of observation / Number of Observation

The new sample mean is 9,

Mathematically, Variance is represented as,

σ2 = ∑ (Xi – μ)2 / N, where, Xi = ith data point in the data set

μ = Sample mean

N = Number of data points in the Sample

The new sample variance is 7,

Standard deviation is determined as the square root of the variance and is denoted by the Greek letter (sigma).

the new sample standard deviation is 2.6458.

So the correct answer is: d. 9, 7, 2.6458

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If the owner's beliefs are correct,  the probability of being awarded the second job (Event B) is 0.5 . Event A and Event B are not mutually exclusive and are independent and must be true for event A and event B.

Simply put, the probability is the likelihood that something will occur. When we don't know how an event will turn out, we can discuss the likelihood or likelihood of several outcomes.

By simply dividing the favorable number of possibilities by the entire number of possible outcomes, the probability of an occurrence can be determined using the probability formula. Because the favorable number of outcomes can never exceed the entire number of outcomes, the chance of an event occurring might range from 0 to 1. Additionally, the proportion of positive outcomes cannot be negative. In the sections that follow, let's go into greater detail on the fundamentals of probability.

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Nick's taxable income will be $(x - 390).

Given is that Nick is paid every other week. He has 390$ taken out of each paycheck for federal taxes.

Assume that his income without tax is ${x}. Then, his taxable income will be -

taxable income = original income - federal tax

taxable income = $(x - 390)

Therefore, Nick's taxable income will be $(x - 390).

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The Solomon four-group design includes two control groups: one that is not pretested and does not receive treatment, and another that is not pretested but receives treatment.

In the Solomon four-group design, there are two treatment groups and two control groups. The purpose of this design is to examine the interaction effect between pretesting and treatment.

The first control group does not receive any treatment, while the second control group also does not receive treatment but is pretested. These two control groups help to measure the impact of pretesting on the dependent variable.

The two treatment groups receive the treatment being studied, with one group being pretested and the other group not being pretested. By comparing the pretested and non-pretested treatment groups, researchers can determine if there is an interaction effect between pretesting and the treatment.

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Answer:

C

Step-by-step explanation:

Seven more is addition (+7)

Half a number would be represented by 1/2, and since the number is unknown, it would be represented by a variable (in this case, x)

C is the correct response

Hope this helps!

Satoko has 303030 tokens to spend at an arcade, and the three lines indicate the cost of playing her favorite games. She must also consider her personal preference for each game, as enjoyment plays a crucial role.

Satoko's objective is to make the most out of her 303030 tokens while enjoying her three favorite games at the arcade. To achieve this, she needs to allocate her tokens wisely across the three games. By analyzing the cost of playing each game for various numbers of times, she can determine the optimal strategy.

First, Satoko should identify the game with the lowest cost per play. If one game stands out as the most affordable, she can prioritize it to maximize the number of plays within her token budget. However, she must also consider her personal preference for each game, as enjoyment plays a crucial role.

Next, Satoko can distribute the remaining tokens among the other two games. She should aim to strike a balance, ensuring she has a reasonable number of plays for each while still getting the most out of her tokens. It might be beneficial to allocate more tokens to the game she enjoys the most among the remaining two.

By carefully analyzing the cost per play and her personal preferences, Satoko can make informed decisions on how to allocate her 303030 tokens at the arcade. This strategic approach will help her maximize her enjoyment and extend her gaming experience within the given budget.

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Answer:

£21.15 (rounded to nearest penny)

Step-by-step explanation:

100% + 4% --- £22

104% --- £22

100% --- \(\frac{100}{104}\) × £22 = £21.15 (rounded to nearest penny)

Answer:

£21.15 (rounded to nearest penny)

Step-by-step explanation:

Options:

(–3, 5) and (–2, 5)         (–3, 5) and (–9, 3)

(5, 3) and (9, 3)             (5, –9) and (3, –5)

(2, 3) and (7, 3)

Answer:

(–3, 5) and (–2, 5)

(5, 3) and (9, 3)

(2, 3) and (7, 3)

Step-by-step explanation:

To do this, have to compare the both x and both y coordinates of the points.

If the x coordinates are equal or the y coordinates are equal, then that option is true

For (a): (-3,5) and (-2,5)

The y coordinates are the same:

i.e.

\(y_1 = y_2 = 5\)

This option is true

For (b): (-3, 5) and (-9, 3)

None of the coordinates are the same;

i.e.

\(x_1 \ne x_2\)

\(y_1 \ne y_2\)

Hence, this option is false.

For (c): (5, 3) and (9, 3)

The y coordinates are the same:

i.e.

\(y_1 = y_2 = 3\)

This option is true

For (d): (5, -9) and (3, -5)

None of the coordinates are the same;

i.e.

\(x_1 \ne x_2\)

\(y_1 \ne y_2\)

Hence, this option is false.

(2, 3) and (7, 3)

The y coordinates are the same:

i.e.

\(y_1 = y_2 = 3\)

This option is true

Answer:

(-3,5) & (-2,5)

(5,3) & (9,3)

(2,3) & (7,3)

Step-by-step explanation:

Answer:

g(-3) = 16

Step-by-step explanation:

To find g(-3), we need to plus -3 into the given function. So, g(-3) = |2(-3) - 10|. Now we solve using PEMDAS. Two times -3 is -6, then we have g(-3) = |-6-10| which is essentially g(-3) = |-16|. Lastly, we take the absolute value of |-16| which is just 16, therefore g(-3) = 16.

Answer:

2/3x + 2 = y

Step-by-step explanation:

you subtract 3y to both side

subtract 6 to both side

divide both side by 3

Answer: 5

Step-by-step explanation: because 5x5 is 25, and in the ones place is 5, and 5 is a factor of 25 so it works

Answer: The digits present in the one's place of a number that has a factor of 5 are 0 and 5.

Step-by-step explanation:

Given the information provided, we know that the average (mean) length of time people keep their cars before replacing is 9 years, and the standard deviation is 2 years.

We are asked to analyze a randomly selected person in this context.

To determine the probability or characteristics related to this randomly selected person, we need more specific information or a question to address.
Without additional details or a specific inquiry, we cannot provide a meaningful answer or analysis.

However, based on the average and standard deviation provided, we can make general statements about the distribution of car ownership duration within the population.

The average of 9 years suggests that, on average, people tend to keep their cars for around 9 years before replacing them.
The standard deviation of 2 years indicates that there is some variability in car ownership duration, with some individuals keeping their cars for longer or shorter periods.

If you have a specific question or scenario related to the randomly selected person, please provide more details, and I'll be happy to assist you further.
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Answer:

Salamander Trail is longer than The Great Oaks Trail.

Step-by-step explanation:

Scale factor = \(\frac{\text{Dimensions of the park on map}}{\text{Actual dimensions of the park}}=\frac{1}{6}\)

For the actual length of Great Oaks Trail,

\(\frac{4.5}{\text{Actual length of the Great Oaks Trail}}=\frac{1}{6}\)

Actual length of Great Oaks Trail = 27 mi

Scale for the same park to the different map = \(\frac{1}{8}\)

\(\frac{\text{Length of Salamander Trail on map}}{\text{Actual length of Salamander Trail}}=\frac{1}{8}\)

\(\frac{3.5}{\text{Actual length of Salamander Trail}}=\frac{1}{8}\)

Actual length of Salamander Trail = 8 × 3.5 = 28 mi.

Therefore, Salamander Trail is longer than The Great Oaks Trail.

1. The break-even point in unit sales and in dollar sales is 4,500 units and $324,000 respectively.

2. If the variable expenses per stove increase as a percentage of the selling price, will it result in a higher break-even point.

3. Income statements before and after changes are implement net income of $36,000 and $(28,000) respectively.

4. The company has to sell 5,401 units to achieve the target profit of $35,000 per month.

1. The break-even point in unit sales and dollar sales is computed as follows:

Break-Even Point in Unit Sales = Fixed Costs / Contribution Margin per Unit = $108,000 / ($50 - $32) = 4,500 units

Break-Even Point in Dollar Sales = Fixed Costs / Contribution Margin Ratio = $108,000 / ($50 / $18) = $324,000

2. If variable expenses per stove increase as a percentage of selling price, it will result in a higher break-even point. Since variable expenses would have a higher percentage of revenue, contribution margin would be lower, making it more challenging to cover fixed costs.

3. Present Income Statement

Sales (8,000*$50) $400,000

Less variable expenses (8,000*$32) (256,000)

Contribution Margin $144,000

Less fixed expenses 108,000

Net Income $36,000

Income Statement if Changes are Implemented

Sales (8,000*$45) $360,000

Less variable expenses (8,000*$35) (280,000)

Contribution Margin $80,000

Less fixed expenses 108,000

Net Loss $(28,000)

4. The contribution margin ratio is 36% ($18/$50). So, the sales revenue required to achieve the target profit is:

$35,000 / 0.36 = $97,222

The number of units required to be sold is:

$97,222 / $18 = 5,401 units

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Step 1: There are four consecutive integers that add up to - 362

Step 2: Let's write the equation to find the four consecutive integers, as follows:

• Let x to represent the first consecutive integer

• Let x + 1 to represent the second consecutive integer

• Let x + 2 to represent the third consecutive integer

• Let x + 3 to represent the fourth consecutive integer

Therefore,

x + x + 1 + x + 2 + x + 3 = -362

Step 3: Let's solve for x

4x + 6 = -362

Subtracting 6 at both sides:

4x + 6 - 6 = -362 - 6

4x = -368

Dividing by 4 at both sides:

4x/4 = -368/4

x = -92

Step 4: Let's find the four consecutive integers based on x = -92

• x + 1 = -92 + 1 = -91

• x + 2 = -92 + 2 = -90

• x + 3 = -92 + 3 = -89

Step 5: The four consecutive numbers that add up to -362 are:

-89, -90, -91 and -92