what does scaled version mean in this case its 3:5 scaled version but i just want to know what it means

Answer:

  43.8 feet

Step-by-step explanation:

In a triangle with angle K = 110°, J = 36°, and k = 70 feet, you want the measure of side j using the law of sines.

The law of sines tells you side lengths in a triangle are proportional to the sine of the opposite angle. This means ...

  j/sin(J) = k/sin(K)

  j = k·sin(J)/sin(K) = (70 ft)·sin(36°)/sin(110°)

  j ≈ 43.8 ft

The length of side j is about 43.8 feet.

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Answer: -14

Step-by-step explanation:

Break up the question.

(-11 + 3) + (-6)

   V           V

  (-9)       (-14)

-11 + 3 = -9

-9 + (-6) = -14

Answer:

The answer is -14

Step-by-step explanation:

-11+3+(-6)

= -11+3-6

= -14

Answer:

The profit equation is

Profit = Revenue - Cost

Let's assume the revenue per batch is $50,000 and the cost per batch is $35,000. Then the profit equation becomes:

Profit = ($50,000 x number of batches) - ($35,000 x number of batches)

Profit = $15,000 x number of batches

We want to find the number of batches that will give a profit of -$190,000, so we can set up the equation:

-$190,000 = $15,000 x number of batches

Solving for the number of batches, we get:

number of batches = -$190,000 / $15,000

number of batches = -12.67

This indicates that the firm would have to produce and sell around 13 batches of tyres in order to make a -$190,000 profit. However, because you can't produce and sell a fraction of a batch, the corporation would have to sell at least 14 batches to make the needed profit.

Answer:

380.1327 square units

Step-by-step explanation:

A=pi*r^2

A=pi*121

A=380.1327

if one of the end points of the diameter is at the origin and the radius is 3 then the the equation of the circle in general form is:x² + y² - 3x = 0

An equation is a statement that shows the relationship between two or more variables using mathematical symbols. It expresses the equality or inequality between the values of the variables on either side of the equation.

According to the given information :

Since one of the endpoints of the diameter is at the origin, we know that the center of the circle is also at the origin. Let (x, y) be any point on the circle. Then, using the distance formula, we have:

√(x² + y²) = 3

Squaring both sides, we get:

x² + y² = 9

So, the equation of the circle in standard form is:

x² + y² - 9 = 0

Another way to write the equation of the circle is in general form, which is:

x² + y² + Dx + Ey + F = 0

where D, E, and F are constants. To find the values of D, E, and F, we substitute the coordinates of one of the points on the circle into the general form equation:

(0)² + (0)² + D(0) + E(0) + F = 0

F = 0

So, the equation of the circle in general form is:

x² + y² + Dx + Ey = 0

To find the values of D and E, we substitute the coordinates of another point on the circle into this equation. Let's use the point (3, 0) since we know it lies on the circle. Substituting these values, we get:

(3)²+ (0)² + D(3) + E(0) = 0

9 + 3D = 0

D = -3

Therefore, the equation of the circle in general form is:

x² + y² - 3x = 0

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The scale factor used is Option B: One fourth.

What is scale factor?

The scale factor of a shape refers to the amount by which it is increased or shrunk. It is applied when a 2D shape, such as a circle, triangle, square, or rectangle, needs to be made larger.

To find the scale factor, we can compare any corresponding side lengths between the original triangle and the dilated triangle.

Let's choose the longest side of triangle D, which is 5.2, and compare it to the longest side of triangle D′, which is x.

We know that a dilation multiplies all corresponding side lengths by the same factor, so -

scale factor = length of corresponding side in D′ / length of corresponding side in D

scale factor = x / 5.2

We don't have enough information to find x directly, but we can use the fact that the other two corresponding side lengths are 1.2 and 1.3.

Since the side lengths of triangle D were scaled by the same factor, we can set up the following equation -

1.2 / 3.6 = 1.3 / 4.8 = x / 5.2

Simplifying the equation -

0.3333... = 0.2708... = x / 5.2

x = 5.2 × 0.2708...

x ≈ 1.41

Now we can find the scale factor -

scale factor = x / 5.2 ≈ 1.41 / 5.2 ≈ 0.271

Therefore, the scale factor used was approximately 0.271.

Answer: One fourth.

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Answer:

1/4

Step-by-step explanation:

The before that answered first was correct! I also took the quiz so you guys dont have to!

The valid conclusions about the data being surveyed is Option A: Of the students who attended the basketball game, fewer than half of them also attended the school play.

What is a survey?

Questioning a group of people in a survey is one way to collect information from them. Surveys can be carried out using a variety of methods, including paper and pencil, online forms, the telephone, or in-person interviews.

A. Of the students who attended the basketball game, fewer than half of them also attended the school play. (True)

To calculate this, we need to divide the number of students who attended both the basketball game and the school play (55) by the total number of students who attended the basketball game (118).

55/118 = 0.466 = 46.6%, which is less than half.

B. More than half of the students who were surveyed attended the school play and did not attend the basketball game. (False)

To calculate this, we need to add up the number of students who attended the school play and did not attend the basketball game (63) and divide by the total number of students surveyed (221).

63/221 = 0.285 = 28.5%, which is less than half.

C. Students who attended the school play were more likely not to attend the basketball game. (False)

To calculate this, we need to compare the number of students who attended the school play and did not attend the basketball game (63) to the number of students who did not attend the school play and did not attend the basketball game (15).

63/78 = 0.808 = 80.8% and 15/78 = 0.192 = 19.2%. Since 80.8% is greater than 19.2%, we can conclude that students who attended the school play were more likely to attend the basketball game.

Therefore, valid conclusions is A.

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On a fair 8-sided die, the probability of rolling a 3 is 1/8, or 0.125, which is equivalent to 12.5% in percentage terms.

The possibility or likelihood that an event will occur is measured by probability.

A number between 0 and 1, where 0 indicates that the occurrence is hypothetical and 1, meaning it is inevitable, is used to express it.

To put it another way, probability is the ratio of likely outcomes to real outcomes that pertain to a particular occurrence.

Every result (rolling any number from 1 to 8) is equally likely since the die is fair.

There are only two ways to roll a 3, and there are a total of eight outcomes.

As a result, the probability of rolling a 3 is:

P(rolling a 3) = 1/8

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Answer:

The motorist's rate is:

rate = distance / time

where distance is measured in kilometers and time is measured in hours.

We are given that the motorist travels 228 kilometers in 6 hours, so we can use this information to find the rate:

rate = distance / time = 228 km / 6 hours = 38 km/hour

To find how long it will take the motorist to travel an additional 247 kilometers at this rate, we can use the same formula and solve for time:

time = distance / rate = 247 km / 38 km/hour ≈ 6.5 hours

Therefore, it will take the motorist approximately 6.5 hours to travel an additional 247 kilometers at the same rate of 38 km/hour.

Answer:

it can be rewritten as a percent

Step-by-step explanation:

According to the question of drop factor, the answer is 53.3ml that will be infused per hour.

Drop factor is a mathematical concept related to the concept of rate. It is a unitless coefficient used to adjust a given rate. Drop factor is commonly used to represent the rate of change in a linear equation, and can be used to calculate the rate at which a given value decreases over time. The drop factor is calculated by subtracting the previous value from the current value and dividing it by the change in time. This value can then be used to calculate the rate of change over time.

The calculation for the amount of ml that will be infused per hour is as follows:

Volume (L) x Drop Factor (gtt/ml) = Total Drops

0.8 L x 60 gtt/ml = 480 drops

Total Drops / Time (hours) = Drops/Hour

480 drops / 9 hours = 53.3 drops/hour

Since 1 drop is equal to 1 ml, this means 53.3 ml of fluid will be infused per hour.

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It is proved that [tex]x[n-n_1] × h[n-n_2] = y[n-n_1-n_2][/tex]

How to prove [tex]x[n-n_1] × h[n-n_2] = y[n-n_1-n_2][/tex]?

To prove that [tex]x[n-n_1] × h[n-n_2] = y[n-n_1-n_2][/tex] , we need to express the convolution sum of

[tex]x[n-n_1] \: and \: h[n-n_2][/tex], and then simplify it to obtain [tex]y[n-n_1-n_2][/tex]

Let's start by expressing the convolution sum of [tex]x[n-n_1] \: and \: h[n-n_2][/tex]

:[tex]x[n-n_1] ×h[n-n_2] = ∑ x[k-n_1] × h[n-n_2-k][/tex] where the summation is over all possible values of k.

Now, we can replace k with [tex]n - n_1 - m[/tex], which gives:

[tex]x[n-n_1] × h[n-n_2] = ∑ x[n-n_1-m] × h[n-n_2-n+n_1+m][/tex]

Next, we can rearrange the terms inside the summation to obtain:

[tex]x[n-n_1] × h[n-n_2] = ∑ x[n-m] × h[n-n_1-n_2+m][/tex]

Notice that the expression inside the summation is identical to the definition of y[n], so we can replace it with y[n] and simplify:

[tex]x[n-n_1] × h[n-n_2] = ∑ x[n-m] × h[n-n_1-n_2+m] = ∑ y[n-m] [/tex]

The last expression is the convolution sum of x[n] and h[n], which we know equals y[n]. Therefore:

[tex]x[n-n_1] × h[n-n_2] = y[n-n_1-n_2][/tex]

And we have proven that [tex]x[n-n_1] × h[n-n_2] = y[n-n_1-n_2][/tex]

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The percdentile is 69.15 for z=0.5.Next, take the two percentiles apart.

The normal distribution is an illustration of a continuous distribution of probabilities in which most data points are grouped in the middle of the range and the remaining ones taper off equally to either extreme. The middle of the range is sometimes referred to as the distribution's mean.

The mean, median, and mode are all equal in normal distributions, which are symmetric, unimodal, and asymptotically distributed. A normal distribution is perfectly symmetrical on both sides.

Percentage of data points with z=a and b between two supplied data points

Add the a% sign and subtract the table percentile for z=a from the table percentile for z=b.

The percentile for the data table for z=-0.5 is 30.85.

the percdentile is 69.15 for z=0.5.Next, take the two percentiles apart.

69.15-30.85= 38.3%

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Approximately 38.30% of data points in a normal distribution fall between z = -0.5 and z = 0.5.

A special kind of normal distribution called a "standard normal distribution" has a mean () of 0 and a standard deviation () of 1.

When comparing alternative normal distributions with arbitrary mean and standard deviation, the standard normal distribution is frequently used as a reference distribution in statistics and probability theory.

We employ a procedure called standardisation, which entails dividing by the standard deviation and removing the mean from any normal distribution to get a standard normal distribution.

The percentage of data items in a normal distribution that lie between z = -0.5 and z = 0.5 can be found using a standard normal distribution table or a calculator with normal distribution capabilities.

Using a standard normal distribution table, the value for z = -0.5 is 0.3085, and the value for z = 0.5 is 0.6915. Subtracting these values gives:

0.6915 - 0.3085 = 0.3830

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The value of x in the right triangle is 5.6 units.

A right triangle is a triangle that has one of its angles as 90 degrees. The sum of angles in a triangle is 180 degrees.

Therefore, the side length x of the right triangle can be found using trigonometric ratios as follows:

tan 48 = opposite / adjacent

where

opposite side = x

adjacent side = 5

Hence,

tan 48 = x / 5

cross multiply

x = 5 tan 48

x = 5 × 1.11061251483

x = 5.55306257415

Therefore,

x = 5.6 units

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6 bottles would hold 3 liters of water.

In general, the total capacity of x bottles would be 0.5x liters, where x represents the number of bottles.

If nine bottles have a total capacity of 4.5 liters, we can determine the capacity of each bottle by dividing the total capacity by the number of bottles.

In this case, we have:

Capacity per bottle = Total capacity / Number of bottles

= 4.5 liters / 9 bottles

= 0.5 liters per bottle.

Now, if we want to find out how much x bottles would hold, we can simply multiply the capacity per bottle by the number of bottles (x). Therefore, the formula to calculate the total capacity of x bottles would be:

Total capacity of * bottles = Capacity per bottle *  Number of bottles

= 0.5  liters per bottle *  x  bottles

= 0.5x liters.

So, x bottles would hold 0.5x liters of water.

For example, if we wanted to find out how much 6 bottles would hold, we could substitute x with 6 in the formula:

Total capacity of 6 bottles = 0.5 * 6 liters

= 3 liters.

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In order to create 728 millilitres of the medication, 273 millilitres of component A are required.

A compound in chemistry is a material comprised of two or more separate chemical elements mixed together in a certain proportion. Chemical connections that are challenging to break are created when the elements interact with one another.

Compound A:Compound B ratio in the medication is 3:5. In other words, there are 3 millilitres of compound A and 5 millilitres of compound B for every 3+5=8 millilitres of the medicine.

We may set up a percentage using the ratio of compound A to the total volume of the medicine to determine how much compound A is required to make 728 millilitres of the drug:

3 ml x 3 ml x 3 ml

-------- = ----------

728 ml total, 8 ml overall

If we cross-multiply, we obtain:

8(x) = 3(728)

To find x, we use the formula x = 3(728)/8 = 273

In order to create 728 millilitres of the medication, 273 millilitres of component A are required.

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273 milliliters of compound A are needed to make 728 milliliters of the drug.

What are proportions?

In mathematics, a proportion is a statement that two ratios are equal. It expresses the relationship between two or more quantities that are directly proportional to each other. A proportion can be represented as an equation of the form:

a/b = c/d

To determine the amount of compound A needed to make 728 milliliters of the drug, we need to use the given ratio of 3 milliliters of compound A to 5 milliliters of compound B.

Let's start by finding the ratio of compound A to the total amount of ingredients (A+B) in the drug:

3 : (3+5) or 3:8

This means that for every 8 milliliters of the drug, 3 milliliters of compound A are used.

To find out how many milliliters of compound A are needed for 728 milliliters of the drug, we can set up a proportion:

3/8 = x/728

where x represents the amount of compound A needed.

To solve for x, we can cross-multiply:

8x = 3*728

8x = 2184

x = 273

Therefore, 273 milliliters of compound A are needed to make 728 milliliters of the drug.

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Answer:

The answer is 13hours

Step-by-step explanation:

360miles------>5hours

936miles------->x hours

crossmultiply

x×360=936×5

360x=4680

divide both sides by 360

360x/360=4680/360

x=13hours

Accordingly, utilising name-brand microwave popcorn rather than store-brand microwave popcorn is anticipated to yield a higher percentage of popped kernels based on the results of this study.

A test statistic is a numerical summary of a sample used in statistics to evaluate the strength of the evidence presented by the data in support of a certain conjecture about the population from which the sample was taken. A test statistic determines how many standard errors the observed data deviates from the predicted value by comparing it to what would be expected under the null hypothesis. To ascertain if an observed effect or difference between groups is the result of chance or if it is statistically significant, test statistics are employed in hypothesis testing.

Here,

We can compare the mean percentage of popped kernels between the two groups using a hypothesis test to see if using name-brand microwave popcorn yields a higher proportion of popped kernels than store-brand microwave popcorn.

Let μ1 be the mean percentage of popped kernels for name-brand microwave popcorn and μ2 be the mean percentage of popped kernels for store-brand microwave popcorn.

The null hypothesis states that there is no distinction between store-brand and name-brand microwave popcorn in terms of the mean percentage of popped kernels:

H0: μ1 - μ2 = 0

The alternate theory is that name-brand microwave popcorn has a mean percentage of popped kernels that is higher than that of store-brand microwave popcorn:

Ha: μ1 - μ2 > 0

This hypothesis can be examined using a two-sample t-test with unequal variances. For a one-tailed test with 18 degrees of freedom and a significance threshold of 0.05, the crucial t-value is 1.734.

Based on the information provided, we can determine that the sample mean percentage of popped kernels for name-brand microwave popcorn is 90.9% with a sample standard deviation of 5.09% and the sample mean percentage of popped kernels for store-brand microwave popcorn is 85.9% with a sample standard deviation of 4.67%.

We can calculate the test statistic as follows:

t = (x1 - x2 - 0) / √(s1²/n1 + s2²/n2)

t = (90.9 - 85.9) / √((5.09²/10) + (4.67²/10))

t = 2.26

We can reject the null hypothesis and come to the conclusion that there is enough evidence to support the claim that using name-brand microwave popcorn results in a greater percentage of popped kernels than store-brand microwave popcorn at the 0.05 level of significance because the calculated t-value (2.26) is greater than the critical t-value (1.734).

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The correct inequality that represents the graphed region in factored form is: option a.) [tex]y \leq -0.25 (x + 12)(x - 8)[/tex]

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There are 7,776 different outcomes when rolling five 6-sided dice.

In the game of Yahtzee, the dice used has 6 sides. This means that each dice has 6 possible outcomes.  

Dice 1 = 6outcomes  Dice 2 = 6 outcomes  dice 3 = 6outcomes

Dice 4 = 6outcomes dice 5 = 6outcomes

We multiply all the outcomes by the total number of the 6-sided dice will be used for the game, which is 5.

We can express it as follows

6 × 6 × 6 × 6 × 6

It can also be expressed as 6⁵, the power 5 being the number of times that 6 will be multiplied

= 7776

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Answer:

Step-by-step explanation:

if this is decimals, I can totally do this. 10.4 x 15.7 = 163.28

look at the file attached

Answer:

80000

Step-by-step explanation:

4% increase of 50000 is 2000 at the end of each year

so 2000*16=32000

50000+32000=82000

nearest whole dollar is 80000

According to given fraction values, Harry used 4 gallons of paint in total.

What is fraction?

A fraction is a way of representing a part of a whole or a ratio of two numbers. It consists of a numerator (top number) and a denominator (bottom number) separated by a horizontal line.

To find the total amount of paint Harry used, we need to add the amount of paint he used for the living room and the amount of paint he used for his bedroom. We have:

2 1/4 gallons + 1 3/4 gallons

To add these two mixed numbers, we need to find a common denominator. The smallest common denominator of 4 and 4 is 4. So we can rewrite the mixed numbers as improper fractions:

2 1/4 = 9/4

1 3/4 = 7/4

Now we can add the two fractions:

9/4 + 7/4 = 16/4

Simplifying the fraction, we get:

16/4 = 4

Therefore, Harry used 4 gallons of paint in total.

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The value when x approaches to 0 the function approaches to 2.718.

In many different mathematical situations, particularly in calculus and analysis, the special number e is used. Although its precise number is an infinite decimal with no pattern, it is roughly equal to 2.71828. The limit of the formula as n approaches infinity is the definition of the constant e. The letter e stands for this limit, which is real and equivalent to a particular number. In many branches of mathematics and science, including the study of exponential and logarithmic functions, the constant e is crucial. It can be used in physics, probability theory, and mathematics, among other things.

The given function is: [tex]\ lim (x \to 0) \frac{2^x - 1}{x}[/tex].

Substituting the value of x = 0.01 we have:

[tex]\ lim (x \to 0) \frac{2^{0.01} - 1}{0.01}\\[/tex]

f(x) = 2.704

Similarly substituting the values of x from the table we have:

x                   f(x)

0.01            2.704

0.001          2.718

0.0001       2.7182

-0.0001      2.7181

-0.001         2.716

-0.01            2.669

Hence, as the x approaches to 0 the function approaches to 2.718.

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The area of the wooden platform built by Mr. Burns for the drama club at the school is 288 square feet.

What are the dimensions of a rectangle?

A rectangle has two dimensions: a length and a width that are both perpendicular to it. An oval's or a triangle's interior likewise has two dimensions.

The area of a rectangle is determined by dividing its length by its width. Accordingly, the platform's area can be determined as follows:

Area = Length x Width

Area = 24 feet x 12 feet

Area = 288 square feet

Therefore, the area of the wooden platform built by Mr. Burns for the drama club at the school is 288 square feet.

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The value of x that satisfies this equation 4(2.5)2^x= 4 is x = -1.32

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

4(2.5)2^x= 4

This gives

(10)2^x= 4

Divide the equation by 10

So, we have the following

2^x = 0.4

Take the logarithm of both sides and evaluate

x = -1.32

Hence, the solution is x = -1.32

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The equivalent fractions when paired up would be:

We must first simplify each fraction before categorizing them according to their simplified form in order to couple equivalent fractions. Since 2/4 and 4/8 may both be reduced to 1/2, they are equal.

The same is true of 2/3 which may be reduced to 4/6, they are both equivalent. 3/4 is the same as 6/8, they are equivalent.

Since 1/3 may be simplified to 2/6, they are equivalent.

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According to the information, the classification of the fractions would be: 3/4 = 6/8, 1/3 = 2/6, 4/6 = 2/3

To classify the fractions in the correct option box we can carry out two procedures. The first one is to simplify the fractions to identify which ones are equivalent to those in the boxes. On the other hand, we can do the divisions of the fractions and those that have the same results go in the same box. According to the above, the fractions are classified as follows:

Note: This question is incomplete. Here is the complete information:

Attached image

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Answer: y = 2x - 2

Step-by-step explanation:

you can see two points on the graph:

(0, -2) and (3, 3)

Using these to calculate the slope gives us:

(3+2)/(3-0) = 6/3 = 2

the y intercept is -2 as we can see

so the equation in slope intercept form is: