The area of the triangle below is 2/15 square feet. What is the length of the base? Express your answer as a fraction in simplest form.

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!

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

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:

I do not have access to Annexure A and Annexure B, so I cannot collect the data, draw the frequency table or pie chart, or answer the last question. However, I can provide a general explanation of how to calculate the mean, mode, median, and range from a set of data.

To find the mean (average) of a set of data, add up all the values in the set and divide by the number of values. For example, if the maximum temperatures of the 30 days are:

25, 28, 29, 27, 26, 30, 31, 32, 29, 27, 26, 24, 23, 25, 28, 30, 32, 33, 34, 31, 29, 28, 27, 26, 25, 24, 23, 21, 20, 22

The sum of the values is:

25 + 28 + 29 + 27 + 26 + 30 + 31 + 32 + 29 + 27 + 26 + 24 + 23 + 25 + 28 + 30 + 32 + 33 + 34 + 31 + 29 + 28 + 27 + 26 + 25 + 24 + 23 + 21 + 20 + 22 = 813

Dividing by the number of values (30), we get:

Mean = 813/30 = 27.1

To find the mode of a set of data, identify the value that occurs most frequently. In this example, there are two values that occur most frequently, 27 and 29, so the data has two modes.

To find the median of a set of data, arrange the values in order from smallest to largest and find the middle value. If there are an even number of values, take the mean of the two middle values. In this example, the values in ascending order are:

20, 21, 22, 23, 23, 24, 24, 25, 25, 26, 26, 27, 27, 27, 28, 28, 29, 29, 29, 30, 30, 31, 31, 32, 32, 33, 34

There are 30 values, so the median is the 15th value, which is 28.

To find the range of a set of data, subtract the smallest value from the largest value. In this example, the smallest value is 20 and the largest value is 34, so the range is:

Range = 34 - 20 = 14

To create a frequency table for the maximum temperature data, we need to group the data into intervals and count the number of values that fall into each interval. For example, we could use the following intervals:

20-24, 25-29, 30-34

The frequency table would look like this:

Interval | Frequency

20-24 | 4

25-29 | 18

30-34 | 8

To calculate the size of the angles for the pie chart, we need to find the total frequency (30) and divide 360° by the total frequency to get the proportion of each interval in degrees. For example, for the interval 25-29:

Proportion = Frequency/Total frequency = 18/30 = 0.6

Angle = Proportion * 360° = 0.6 * 360° = 216°

We can repeat this calculation for each interval to obtain the angles for the pie chart.

In terms of the last question, it is not clear what is meant by "which data collection best describe the maximum and why?". If you could provide more context or clarification, I would be happy to try to help.

Answer:

57° + 124° + 140° = 321°

360° - 321° = 39° (measure of missing interior angle)

39° + c = 180°, so c = 141°.

Answer:

c=141

Step-by-step explanation:

140+57+124=321

360-321=39

180-39=141

The total distance covered by Jeremy is 1320 m

What is a line segment ?

A line segment in geometry is bounded by two separate points on a line. Another way to describe a line segment is as a piece of the line that joins two points. A line segment has two fixed or distinct endpoints while a line has no endpoints and can stretch in both directions indefinitely.

For sapling 1 = No distance is covered.

For sapling 2, distance covered = 10 m

Return distance=10 m

For sapling 3, distance covered =20 m

Return distance=20 m and so on

Thus the distances covered for saplings can be represented as : 0,2(10), 2(20),...i.e. 0,20, 40,...

Therefore total distance covered by Jeremy for planting 12 saplings and coming back to original position = S 12

Total distance covered = 122 [2(0) + (12 − 1) 20 ]

Total distance covered = 6 (11)(20) = 1320 m

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Complete question:

There are 12 saplings to be planted in a straight line at an interval of 10 m between

two consecutive saplings. Jeremy can carry only one sapling at a time and he has to

come back to the original point to take the next sapling. He plants 12 saplings in this

manner, planting the first sapling at the original point. After planting all the saplings,

he comes back at the original point,

In the process, what is the total distance that Jeremy covers?

​

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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Answer:

First, we need to figure out how many socks are in the drawer.

5 black socks + 5 striped socks + 9 polka dot socks + 11 white socks + 5 blue socks + 1 sock with photos of small socks = 36 socks

Pay attention to the polka dot socks now. There are 9 polka dot socks in the drawer; the odds of picking one on the first draw are 9/36 socks.

If we don't replace the first sock and draw again, there will be 8 polka dot socks remaining out of a total of 35 socks in the drawer.

As a result, the likelihood of picking a second polka dot sock after selecting the first is 8/35.

To calculate the likelihood of picking a pair of polka dot socks, multiply the odds of selecting a polka dot sock on the first draw by the probability of selecting another polka dot sock on the second draw.

The probability of choosing a pair of polka dot socks is (9/36) x (8/35) = 0.0571, or approximately 5.71%.

After solving the equation we know that the mass of Sean and Ian is 62kf and 59.5 ks respectively.

Equation: A statement stating the equality of two expressions containing variables or numerical values.

Equation: A formula that uses the equals sign to combine two expressions and declare their equality.

In essence, equations are questions, and the methodical pursuit of solutions to these questions has served as the driving force behind the creation of mathematics.

Sean mass = x

Lan mass = x - 2.5

Then, form the equation and solve it as follows:

x + (x - 2.5) = 121.5

x + x - 2.5 = 121.5

2x - 2.5 = 121.5

2x = 121.5 + 2.5

2x = 124

x = 124/2

x = 62

Then, x - 2.5 = 59.5.

Therefore, after solving the equation we know that the mass of Sean and Ian is 62kf and 59.5 ks respectively.

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Applying the intersecting secants theorem, the length of segment KL is approximately, 45.8.

According to the intersecting secants theorem, if two lines from a point outside a circle intersect the circle, then the product of the length of one line segment and its portion outside the circle is equal to the product of the length of the other line segment and its portion outside the circle.

Using the theorem, we have:

MN * MO = ML * MK

Substitute:

21 * 48 = 22 * KL

1,008 = 22KL

1,008/22 = KL

KL = 45.8 (nearest tenth)

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Answer:

To perform these operations, we need to ensure that the dimensions of the matrices match. Since k is a row matrix with 1 row and 4 columns, and L is a column matrix with 4 rows and 1 column, we need to transpose one of them to match the dimensions. Let's transpose k to get a column matrix with 4 rows and 1 column:

k^T = 2

3

4

3

Now we can perform the matrix operations:

1. k + L:

2 + 7 = 9 3 + 10 = 13 4 + 5 = 9 3 + 11 = 14

9 + 1 = 10 13 + 6 = 19 5 + 9 = 14 11 + 4 = 15

10 + 11 = 21 4 + 7 = 11 7 + 10 = 17 3 + 7 = 10

= 9 13 9 14

10 19 14 15

21 11 17 10

2. K - L:

2 - 7 = -5 3 - 10 = -7 4 - 5 = -1 3 - 11 = -8

9 - 1 = 8 13 - 6 = 7 5 - 9 = -4 11 - 4 = 7

10 - 11 = -1 4 - 7 = -3 7 - 10 = -3 3 - 7 = -4

= -5 -7 -1 -8

8 7 -4 7

-1 -3 -3 -4

3. 2k + 3L:

2(2) + 3(7) = 20 2(3) + 3(10) = 36 2(4) + 3(5) = 22 2(3) + 3(11) = 37

2(9) + 3(1) = 21 2(13) + 3(6) = 44 2(5) + 3(9) = 23 2(11) + 3(4) = 29

2(10) + 3(11) = 42 2(4) + 3(7) = 29 2(7) + 3(10) = 34 2(3) + 3(7) = 23

= 20 36 22 37

21 44 23 29

42 29 34 23

4. 3L - 2K:

3(7) - 2(2) = 17 3(10) - 2(3) = 27 3(5) - 2(4) = 7 3(11) - 2(3) = 29

3(1) - 2(9) = -15 3(6) - 2(13) = -11 3(9) - 2(5) = 17 3(4) - 2(11) = -14

3(11) - 2(10) = 13 3(7) - 2(4) = 14 3(10) - 2(7) = 16 3(7) - 2(3) = 15

= 17 27 7 29

-15 -11 17 -14

13 14 16 15

Answer:

68°

Step-by-step explanation:

Total angle in a quadrant = 90°

x + 22° = 90°

x = 90 - 22

x = 68°

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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We have expressed the expression 3 sec(-x) + 2 as a single fraction (3 + 2cos(x))/cos(x).

In mathematics, an expression is a combination of symbols and/or numbers that represents a mathematical quantity or relationship. Expressions can be formed by combining variables, constants, and mathematical operations such as addition, subtraction, multiplication, division, exponents, and roots.

To write the expression 3 sec(-x) + 2 as a single fraction, we need to use some trigonometric identities and algebraic manipulation. Here are the steps:

Step 1: Recall that secant is the reciprocal of cosine, so we can rewrite the expression as:

3 (1/cos(-x)) + 2

Step 2: Cosine is an even function, which means that cos(-x) = cos(x). Therefore, we can simplify the expression to:

3 (1/cos(x)) + 2

Step 3: Recall that multiplying by the reciprocal is the same as dividing, so we can rewrite the expression as:

3/cos(x) + 2

Step 4: To add these fractions, we need a common denominator. The denominator of the first fraction is cos(x), and the denominator of the second fraction is 1. To get a common denominator, we can multiply the second fraction by cos(x)/cos(x):

3/cos(x) + 2(cos(x)/cos(x))

Simplifying the second term:

3/cos(x) + 2cos(x)/cos(x)

Step 5: Combining the fractions, we have:

(3 + 2cos(x))/cos(x)

Therefore, we have expressed the expression 3 sec(-x) + 2 as a single fraction (3 + 2cos(x))/cos(x).

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a) The 90% confidence interval for the proportion of adults that have blue eyes is given as follows: (0.087, 0.133).

b) As the interval does not contain 0.08, the belief that 8% of people have blue eyes is misguided.

A confidence interval of proportions has the bounds given by the rule presented as follows:

[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

In which the variables used to calculated these bounds are listed as follows:

The confidence level is of 9%, hence the critical value z is the value of Z that has a p-value of [tex]\frac{1+0.9}{2} = 0.95[/tex], so the critical value is z = 1.645.

The parameters for this problem are given as follows:

[tex]n = 500, \pi = \frac{55}{500} = 0.11[/tex]

The lower bound of the interval is given as follows:

0.11 - 1.645 x sqrt(0.11 x 0.89/500) = 0.087.

The upper bound of the interval is given as follows:

0.11 + 1.645 x sqrt(0.11 x 0.89/500) = 0.133.

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Answer:

it can be rewritten as a percent

Step-by-step explanation:

A scaled version of any object is the object that has undergone a form of increment/enlargement or reduction has been made to the object. in the case of 3:5 scaled version, it tells you the ratio of increment or reduction that has happened to the object in comparison to the original object.

In the height of an object has a 30cm height and perhaps a 12 cm width. Using a scaled version ratio provided which is 3:5. The scaled version f the object would be

3/5 x 30 = 18cm

3/5 x 12 = 7.2cm

A second example is if a rectangular room with dimensions 10 feet by 15 feet and you want to scaled version of  3:5, it becomes  = 10 x (3/5) = 6 feet and 15 x (3/5) = 9 feet

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a). The formula for g, which determines x's half, is g(x) = 1/2 x

b). f(x) = x + 2

c). (fog)(x) = 1/2 x + 2

d). (fog) (52) = 28

The relationship between two sets of data, known as the input and output, is described mathematically by a concept known as a function.

An operation is applied to an input value by a function, which then produces an output value that matches the input value.

a). The formula for g, which determines x's half, is g(x) = 1/2 x

b). The formula for adding 2 to x is: f(x) = x + 2

c). Plugging g(x) into f(x) yields the function (fog)(x), which is as follows:

(fog)(x) = f(g(x))

f(1/2 x) = 1/2 x + 2

d). We must evaluate (fog)(52) to obtain the sale price of a shirt with an original cost of $52 as follows:

= (fog) (52) = 1/2(52) + 2

= 26 + 2

= 28

Thus, the shirt's ultimate retail price is $28.

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The trigonometric function on the graph is:

f(x)= -cos(x)

So the correct option is B.

Here we can see the graph of a trigonometric function. We can see that the x-intercept is -1.

Notice that:

sin(0)= 0

cos(0) = 1

So the function can be an inversion over the x-axis of the cosine function, we coulod write this as:

f(x) = -cos(x)

That is the graphed function.

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Answer:

[tex]y =\frac{x}{4}[/tex]

Step-by-step explanation:

We are given several functions, and we want to figure out which one is linear.

A linear function has both of its variables (x and y) with a power of 1. Variables with other powers do not mean that the function is linear.

Let's go through the list.

Starting with [tex]y=\frac{3}{x} -7[/tex], we can see that x is in the denominator. If this is the case, it means that the power of x is -1.

Even though y has a power of 1, this is NOT linear, because x has a power of -1.

Now, with y=√x-2, this is also not linear. This is because √x = [tex]x^\frac{1}{2}[/tex], even though y has a power of 1.

For x² - 1 = y, we can clearly see that x has a power of 2, while y has a power of 1. This means that the function is not linear.

This leaves us with [tex]y = \frac{x}{4}[/tex]. x is in a fraction, however it is not in the denominator. This means that the power of x in this function is 1. We can also see that the power of y in this function is 1.

This means that [tex]y=\frac{x}{4}[/tex] is linear.

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

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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The percentage increase in the number of archers is 77%.

A value's percentage growth is a way to represent how much it has grown in comparison to its starting point. It is calculated by subtracting the original value from the new value, multiplying the result by 100, and then subtracting the difference between the two values.

The following formula is used to determine the percentage increase:

(New Value - Original Value) / Original Value * 100 is the formula for percentage increase.

The percentage increase is given by the formula:

Percentage Increase = (New Value - Original Value) / Original Value * 100

Now, given that there were 1158 more archers in 2012 and 2013 and from the table we have the archers in 2012-13 = 2645 the archers in 2011-12 is:

2645- 1158 = 1487

Thus,

percentage increase = 1158/ 1487 (100) = 77%

Hence, the percentage increase in the number of archers is 77%.

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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.

On average, it will take us two to three inquiries to discover a kid who enjoys a salad for lunch.

The idea of probability is used to determine the likelihood or probability that a given occurrence will take place.

It is a number between 0 and 1, where 0 indicates that the event is impossible and 1 indicates that it is guaranteed to happen.

Probabilities can be expressed using percentages, decimals, or fractions.

The likelihood that any particular student will choose a salad is 20%, or 0.2, assuming that each student's taste for lunch is independent of the preferences of the others.

There is a 0.2 chance that the first student you question will say they prefer a salad. You go on to the next kid if they don't want a salad.

Given that the first student didn't like a salad, there is a 0.2 chance that the second student will as well. None of the first two pupils had a (1-0.2) (1-0.2) = 0.64 chance of preferring a salad.

Given that none of the n-1 students before them did, the likelihood that the nth student would prefer a salad is similarly 0.2. (1-0.2)n-1 is the likelihood that none of the first n-1 students will choose a salad.

In order to identify a student who prefers a salad, you must thus question an anticipated number of students: E(x) = 1(0.2) + 2(1-0.2)(0.2) + 3(1-0.2)2(0.2) +...

Although this is an infinite series, by truncating it after a predetermined number of words, we may approximate it. Say we decide to quit after ten terms:

E(x) ≈ 1×(0.2) + 2×(1-0.2)(0.2) + 3(1-0.2)²×(0.2) + ... + 10×(1-0.2)⁹ × (0.2) E(x) ≈ 2.48

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The total number of beds in Shelter B is 10.2. This is because the ratio of the occupancy of Shelter A to Shelter B is 14:25, meaning that if Shelter A is 70% occupied, then Shelter B must be 50% occupied.

Occupancy is used to measure the efficiency of a business or facility by determining how often a space is used, how long people stay in the space, and whether or not the space is being used to its full potential.

To calculate the number of beds in Shelter B, we need to first calculate the total number of beds in Shelter A. Since Shelter A is 70% occupied, we can use the following equation to calculate the total number of beds in Shelter A:

Total beds in Shelter A = (Occupied beds in Shelter A ÷ 70%) x 100%

Total beds in Shelter A = (400 ÷ 70%) x 100%

Total beds in Shelter A = 571.43

Since the ratio of the occupancy of Shelter A to Shelter B is 14:25, we can use the following equation to calculate the total number of beds in Shelter B:

Total beds in Shelter B = (Total beds in Shelter A x 25%) ÷ 14

Total beds in Shelter B = (571.43 x 25%) ÷ 14

Total beds in Shelter B = 10.2

Therefore, the total number of beds in Shelter B is 10.2. This is because the ratio of the occupancy of Shelter A to Shelter B is 14:25, meaning that if Shelter A is 70% occupied, then Shelter B must be 50% occupied. As a result, the total number of beds in Shelter B is 10.2.

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If a person does 1.5 hours of bicycling per day for 5 days a week, they would burn approximately 3,750 calories in a week.

A person's age, gender, height, weight, and level of activity determine the average number of calories they need to consume each day to meet their energy needs and maintain their weight.

Individual factors such as age, gender, weight, height, and level of activity influence the average calorie intake.

If an average person burns 250 calories per half-hour while bicycling, then they would burn 500 calories per hour of bicycling.

So, if a person does 1.5 hours of bicycling per day, they would burn 1.5 x 500 = 750 calories per day.

If they work out 5 days a week, then the total number of calories burn in a week would be:

750 calories/day x 5 days/week = 3,750 calories/week

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Answer:

[tex]\huge\boxed{\sf 38}[/tex]

Step-by-step explanation:

= a³ + b (6 + c)

Put a = 2, b = 3 and c = 4

= (2)³ + 3 (6 + 4)

= 8 + 3(10)

= 8 + 30

[tex]\rule[225]{225}{2}[/tex]

Answer:

Step-by-step explanation:

the requied answer is 38.

according to the question the value of a=2,b=3,c=4.

here,

to find the value of   a³ + b (6 + c)we have to do it in steps:

step 1: solve the bracket (6+4) =10.

step 2:  solve the value of a³ =8.

now put these values ,

=8+3(10)

=38.

Answer:

if we substitute x = 3 in the given function f(x) = r + 7, we get:

f(3) = r + 7 (where x = 3)

Therefore, the value of f(3) is r + 7.