Which pair of angles must be supplementary?
O 1 and 6
O 2 and 5
O 5 and 4
O Z6 and2

The size of the large tank is 6 liters and the size of the small tank is 3 liters.

The first step is to form a system of equations using the information provided in the question:

3l + 2s = 24 equation 1

2l + 3s = 21 equation 2

Where:

The elimination method would be used to solve the equations:

Multiply equation 1 by 2 and equation 2 by 3:

6l + 4s = 48 equation 3

6l + 9s = 63 equation 4

Subtract equation 3 from equation 4:

5s = 15

Divide both sides of the equation by 5

s = 15 / 5

s = 3 liters

Substitute for s in equation 1 :

3l + 2(3) = 24

3l + 6 = 24

3l = 24 -  6

3l = 18

l = 18 / 3

l = 6

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The probability that 5 hearts are chosen when 7 cards are drawn from a well-shuffled deck of 52 playing cards is option (d) 0.00000962.

Step 1: Determine the total number of ways to choose 7 cards from a deck of 52 playing cards, which can be calculated using the combination formula: C(52, 7) = 52! / (7! * (52 - 7)!), where "!" denotes the factorial.

Step 2: Determine the number of ways to choose 5 hearts from the deck. There are 13 hearts in a standard deck, so we can calculate the number of ways to choose 5 hearts from 13: C(13, 5) = 13! / (5! * (13 - 5)!).

Step 3: Calculate the probability by dividing the number of favorable outcomes (choosing 5 hearts) by the total number of possible outcomes (choosing 7 cards from the deck): P(5 hearts) = C(13, 5) / C(52, 7).

Step 4: Evaluate the probability numerically using a calculator or math software, and the result is approximately 0.00000962.

Therefore, the correct answer is option (d) 0.00000962.

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The step 3 follow the subtraction property of equality.

Given,

The Equation is : 1/4 (12x + 8) + 4 = 3

There is some steps:

Step                          Solution

   1                          3x + 2 + 4 = 3

   2                           3x + 6 = 3

   3                              3x = -3

   4                                 x = -1

To find the which step shows the result of applying the subtraction property of equality?

Now, According to the given steps:

From the table, we can know

From Step 2: 3x + 6 = 3

 Subtract 6 on both sides

3x + 6 - 6 = 3 - 6

3x = -3

Hence, The step 3 follow the subtraction property of equality.

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Answer:

15. x = 4

16. x = 7

Step-by-step explanation:

15.

CD/ ED = DG / DF

48 / (5x - 2) = 40 / (2x + 7)

48 (2x + 7) = 40 (5x - 2)

96x + 336 = 200x - 80

200x - 96x = 336 + 80

104x = 416

x = 4

16.

ST / PL = TU / LM

(x + 1) / 72 = (2x - 3) / 99

99 (x + 1) = 72 (2x - 3)

99x + 99 = 144x - 216

144x - 99x = 99 + 216

45x = 315

x = 7

Answer:

15.  x = 4

16.  x = 7

Step-by-step explanation:

Similar Triangles

In similar triangles, corresponding sides are always in the same ratio.

If ΔCDG ~ ΔEDF then:

From inspection of the given diagram:

Therefore:

\(\implies \sf CD : ED = DG : DF\)

\(\implies 48 : (5x-2) = 40 : (2x+7)\)

\(\implies \dfrac{48}{(5x-2)} = \dfrac{40}{(2x+7)}\)

\(\implies 48(2x+7)=40(5x-2)\)

\(\implies 96x+336=200x-80\)

\(\implies 416=104x\)

\(\implies x=\dfrac{416}{104}\)

\(\implies x=4\)

If ΔSTU ~ ΔPLM then:

From inspection of the given diagram:

Therefore:

\(\implies \sf ST : PL = TU : LM\)

\(\implies (x+1) : 72 = (2x-3) : 99\)

\(\implies \dfrac{(x+1)}{72}= \dfrac{(2x-3)}{99}\)

\(\implies 99(x+1)=72(2x-3)\)

\(\implies 99x+99=144x-216\)

\(\implies 315=45x\)

\(\implies x=\dfrac{315}{45}\)

\(\implies x=7\)

Lantus is a modified form of insulin that has been optimized for stability, solubility, and prolonged action in the body. These modifications make Lantus a more effective and reliable option for managing diabetes.

Lantus differs from "normal" insulin in several ways:

1. The usual insulin molecule has been combined with zinc isophane. This combination helps to prolong the duration of action of Lantus compared to regular insulin. The addition of zinc isophane allows for a slower and more consistent release of insulin into the bloodstream.

2. Glycine has been substituted in at A21, and two new arginines have been added as B31 and B32. These modifications in the structure of Lantus improve its stability and solubility, which are important factors for its effectiveness as an insulin medication.

3. An aspartic acid has been substituted for proline at B28. This modification also contributes to the stability and solubility of Lantus. It helps to prevent the formation of insoluble clumps or aggregates of insulin molecules, ensuring a consistent and reliable supply of insulin.

In summary, Lantus is a modified form of insulin that has been optimized for stability, solubility, and prolonged action in the body. These modifications make Lantus a more effective and reliable option for managing diabetes.

Please let me know if there's anything else I can help you with.

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Lantus differs from "normal" insulin such as proline at B28 and the lysine at B29 have been reversed. The correct option is e. The proline at B28 and the lysine at B29 have been reversed.

Lantus is a modified form of insulin that has been optimized for stability, solubility, and prolonged action in the body. These modifications make Lantus a more effective and reliable option for managing diabetes.

Lantus differs from "normal" insulin in several ways:

1. The usual insulin molecule has been combined with zinc isophane. This combination helps to prolong the duration of action of Lantus compared to regular insulin. The addition of zinc isophane allows for a slower and more consistent release of insulin into the bloodstream.

2. Glycine has been substituted in at A21, and two new arginines have been added as B31 and B32. These modifications in the structure of Lantus improve its stability and solubility, which are important factors for its effectiveness as an insulin medication.

3. An aspartic acid has been substituted for proline at B28. This modification also contributes to the stability and solubility of Lantus. It helps to prevent the formation of insoluble clumps or aggregates of insulin molecules, ensuring a consistent and reliable supply of insulin.

In summary, Lantus is a modified form of insulin that has been optimized for stability, solubility, and prolonged action in the body. These modifications make Lantus a more effective and reliable option for managing diabetes.

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Answer:

c e f

Step-by-step explanation:

C. All rotations take one half of the triangle to the other half of the triangle

E. None of the sides of the triangle have the same length

F. None of the angles of the triangle have the same measure

If a shape has a rotation symmetry, then the shape will look exactly the same after rotation. The conclusions to reach for a triangle that has a rotation symmetry are:

A. All sides of the triangle have the same length

B. All angles of the triangle has the same measure

Of all kinds of triangle, only an equilateral triangle has a rotational symmetry.

This means that:

The above points imply that: options (a) and (b) are true

See attachment for an illustration of rotation symmetry of a triangle.

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Answer:

a) 10.47

b) 10.23

Answer: a) a= 10.47

Step-by-step explanation:

a) a²=9.3²- 4.8²

   a²=86.49+23.04

   a²= 54.45

   a= \(\sqrt 109.53\)

   a= 10.47

Answer:

BC = 4.92

Step-by-step explanation:

cos 35° = \(\frac{?}{6}\)

BC = 6 x cos 35°

BC = 6(.82) = 4.92

Approximately 34% of American adults have a mobile phone but not a landline, based on the given proportions from the study conducted by the Centers for Disease Control.

The proportion of American adults who have a mobile phone but not a landline, we need to subtract the proportion of those who have both a mobile phone and a landline from the proportion of those who have a mobile phone.

Let's denote the proportion of American adults who have a mobile phone as P(M), the proportion who have a landline as P(L), and the proportion who have neither as P(N).

Given information:

P(M) = 89% (proportion with a mobile phone)

P(L) = 57% (proportion with a landline)

P(N) = 2% (proportion with neither)

We can now calculate the proportion of adults who have a mobile phone but not a landline using the following equation:

P(M and not L) = P(M) - P(M and L)

To find P(M and L), we can subtract P(N) from P(L) since those who have neither are not included in the group with a landline:

P(M and L) = P(L) - P(N)

P(M and L) = 57% - 2%

P(M and L) = 55%

Now we can substitute the values back into the equation to find P(M and not L):

P(M and not L) = P(M) - P(M and L)

P(M and not L) = 89% - 55%

P(M and not L) = 34%

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Therefore , the solution of the given problem of circle comes out to be the intersection points can be used to make chords and secants, among other forms and angles.

A circle is formed by each region of a plane that is a certain distance from this extra point (center). It thus consists of spots that are isolated from one another by the surface and is curved. It also revolves about the centre equally from all angles. In the constrained, the double sphere of a circular, every group of endpoints is uniformly separated from the "centre." By tracing a thread through a circle, one can create a line to circular symmetry.

Here,

The sum of the radii determines the distance between the circular centres.

a single intersection

Two circles are said to be "tangent" or "touching" at a particular location when their paths cross. This indicates that there is only one spot in common between the two circles. The difference in radii is equivalent to the distance between the circle centres.

There are two intersections.

Two circles are said to be "intersecting" when they touch at two places. This indicates that there are two similarities between the two spheres. Less than the total of the radii, but larger than the difference of the radii, is the distance between the centres of the circles.

The intersection points can be used to make chords and secants, among other forms and angles.

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Answer:

2.50 is the answer of the question

Answer:

d

Step-by-step explanation:

The derivative of y = x^2 * log2(x^(2/3)) is dy/dx = 2x * log2(x^(2/3)) + (2/3) * x^(5/3) / ln(2), which can be derived using the product rule and chain rule. derivative of y = ln(cos(ln(x))) is dy/dx = -sin(ln(x)) / (x * cos(ln(x))).

(a) To find the derivative of y = x^2 * log2(x^(2/3)), we can use the product rule and chain rule.

Applying the product rule, we have:

dy/dx = 2x * log2(x^(2/3)) + x^2 * d/dx[log2(x^(2/3))]

Using the chain rule, the derivative of log2(x^(2/3)) can be calculated as:

d/dx[log2(x^(2/3))] = (1 / ln(2)) * (2/3) * (1/x^(1/3))

Substituting this back into the equation, we have:

dy/dx = 2x * log2(x^(2/3)) + (2/3) * (x^2 / x^(1/3)) * (1 / ln(2))

Simplifying further, the derivative is:

dy/dx = 2x * log2(x^(2/3)) + (2/3) * x^(5/3) / ln(2)

(b) To find the derivative of y = ln(cos(ln(x))), we can use the chain rule.

Applying the chain rule, we have: dy/dx = (1 / cos(ln(x))) * d/dx[cos(ln(x))]

The derivative of cos(ln(x)) can be calculated as:

d/dx[cos(ln(x))] = -sin(ln(x)) * (1/x)

Substituting this back into the equation, we have:

dy/dx = (1 / cos(ln(x))) * (-sin(ln(x)) * (1/x))

Simplifying further, the derivative is: dy/dx = -sin(ln(x)) / (x * cos(ln(x)))

(c) To find d(dx/dy) at x=0, we need to differentiate the equation y^2 * x - ln(x+y) = 0 implicitly with respect to x.

Differentiating both sides with respect to x, we have:

2y * dy/dx * x + y^2 - (1/(x+y)) * (1+y * dy/dx) = 0

To find d(dx/dy), we need to solve for dy/dx: dy/dx = (-(y^2))/(2xy + 1 + y)

To find d(dx/dy) at x=0, we substitute x=0 into the expression:

dy/dx = (-(y^2))/(2y + 1 + y)

dy/dx = (-(y^2))/(3y + 1)

At x=0, the expression simplifies to: dy/dx∣∣x=0 = (-(y^2))/(3y + 1)

(d) To find the derivative of y = x^(x/ln(x)), for x > 0, we can use the exponential rule and the chain rule.

Taking the natural logarithm of both sides, we have: ln(y) = (x/ln(x)) * ln(x)

Differentiating implicitly with respect to x, we have:

(1/y) * dy/dx = (1/ln(x)) * ln(x) + (x/ln(x)) * (1/x) * ln(x)

Simplifying, we have:

dy/dx = y * [(1/ln(x)) + 1]

dy/dx = x^(x/ln(x)) * [(1/ln(x)) + 1]

(e), (f), (g), and (h) will be answered in separate responses.

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Answer:

The answer is below

Step-by-step explanation:

A football team scored 3 touchdowns, 3 extra points, and 4 field goals.  

a. Write an expression to represent the total points the football team scored.  

b. Write another expression that is equivalent to the one written above.  

c. If each touchdown is worth 6 points, each extra point is 1 point, and each field goal is 3 points, how many total points did the team score?  

Solution:

a) Let t represent the number of points for a touchdown, e represent the number of points for the extra point and f represent the number of points for a field goal.

Total points = 3(t) + 3(e) + 4(f) = 3t + 3e + 4f

b) Total points = 3t + 3e + 4f   OR

Total points = t + t + t + e + e + e + f + f + f + f  OR

Total points = 3(t + e) + 4f

c) Total points = 3(t + e) + 4f = 3(6 + 1) + 4(3) = 3(7) + 4(3)

Total points = 21 + 12 = 33 points

The sum of the points the team has from different point gaining options

give the total number of points the team scores.

Reasons:

The number of touchdowns by the football team, t = 3

Number of extra points by the football team, e = 3

Number of field goals by the team, f = 4

Therefor, the total number of points, P = 3·t + 3·e +4.f

The specified editor is an equation editor, which can be used to write mathematical equations.

Using an equation editor, we have;

\(\mathrm{The \ total \ points \ the \ football \ team \ scored } = 3 \cdot t + 3 \cdot e + 4 \cdot f\)

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The measurement of altitude BE is 4 unit.

As the average level of the sea's surface, sea level is used to measure altitude. A high altitude is defined as being significantly higher than sea level, such as Mount Everest. It is referred to as having a low altitude when something is closer to the ground, like a plane coming in to land.

As ABCD is rectangle

AD = BC = 12

ΔABC = ΔBCD

BE = FD

5² = 3²+BE²

AE = 3

BE = √(5²-3²)

BE = 4

Thus, The measurement of altitude BE is 4 unit.

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The value of x is 1.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

√(x - 1)² = 1 - x

√(x - 1)² can be written as (x - 1).

Now,

x - 1 = 1 - x

x + x = 1 + 1

2x = 2

x = 1

Thus,

x is 1.

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The Taylor polynomials P1, P2, P3, and P4 centered at a0 for f(x) are given as:P1(x) = 1P2(x) = 1 - x²/2!P3(x) = 1 - x²/2! + x⁴/4!P4(x) = 1 - x²/2! + x⁴/4! - x⁶/6!

We will apply the Taylor's theorem formula, which is supplied as follows, to determine the Taylor polynomials P1, P2, P3, and P4 centred at a0 for f(x) in the given question:f'(a)(x-a)/1 = f(x) = f(a) + f'(a)! + f''(a)(x-a)²/2! + ... + fⁿ(a)(x-a)ⁿ/n!We have f(0) = 1f'(0) = 0f''(0) = -1f'''(0) = 0f4(0) = 1 for f(x) = cos(x) at x = 0.We can get the following polynomial expressions by using these values in the Taylor's theorem formula:P1(x) = 1P2(x) = 1 - x²/2!P3(x) = 1 - x²/2! + x⁴/4!P4(x) = 1 - x²/2! + x⁴/4! - x⁶/6!Consequently, the Taylor polynomials P1, P2, P3, and P4 for f(x) are provided as follows:P1(x) = 1P2(x) = 1 - x²/2!P3(x) = 1 - x²/2! + x⁴/4!P4(x) = 1 - x²/2! + x⁴/4! - x⁶/6!

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Standard deviation is the square root of variance .

So,

It is used in measuring any deviation or shift from the calculated mean.  

From a data set, the mean of the data can be determined with which the standard deviation can be measure.

Therefore, Standard deviation is use to measure variation that exist in an individual data set. There are different type of data set from which variation is measured.

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Answer:

smack her or washout her mouth with soap than

Step-by-step explanation:

The margin of error will be larger for a 99% confidence interval than for a 95% confidence interval, assuming the same sample size and level of variability in the data.

The margin of error is the range of values above and below the point estimate within which the true population parameter is likely to fall.

A higher level of confidence requires a larger margin of error. This is because as the level of confidence increases, the range of values that contains the true population parameter becomes wider.

For example, a 95% confidence interval has a margin of error of plus or minus two standard errors of the point estimate.

Increasing the confidence level to 99% would require a wider range of values, and therefore a larger margin of error, such as plus or minus three standard errors of the point estimate.

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Answer:

The height of the left bridge is 26.25 feet

Step-by-step explanation:

Let the left base of the bridge is at the origin and the x-axis represents the roadways as shown in the figure.

The given relationship between the variables x and y is

\(y = a(x - h)^2 + k\)

where x is the horizontal distance from the left bridge support and y is the height of the cable above the roadway, (h,k) is the vertex of the parabola, and a is constant.

The vertex (h,k) of the parabola is the lowest point of the cable bridge.

As the lowest point of the cable is 6ft above the roadway and is a horizontal distance of 90 ft from the left bridge support, so, h=90 and k=6.

The given equation become,

\(y = a(x - 90)^2 + 6\cdots(i)\)

At a horizontal distance of 30 ft, the cable is 15 ft above the roadway, so put x=30 and y=15 in the equation (i) to the value of  constant a.

\(15 = a(30 - 90)^2 + 6\)

\(\Rightarrow 15-6=3600a\)

\(\Rightarrow a= 0.0025.\)

Putting the value of constant \(a\) in the equation (I) to get the required equation, we have

\(y = 0.0025(x - 90)^2 + 6\)

As the left bridge is at the origin, so the the height of the left bridge is the value of y at origin.

Hence, put x=0 in the obtained equation to get the height of the bridge at the left side, we have

\(y= 0.0025(0 - 90)^2 + 6\)

\(y=26.25\)

Hence, the height of the left bridge is 26.25 feet.

Answer:

y=0.0025(x-90)^2+6

26.25ft

180ft

Step-by-step explanation

it is correct.

Answer:

Probably the 1st picture.

Step-by-step explanation:

keep in mind, the center is 0.

Answer:

m∠K = 97°

Step-by-step explanation:

The sum of the measures of the angles of a quadrilateral is 360

127 + 5x + 3 + 10x + 7 + 88 = 360

15x + 225 = 360

15x = 135

x = 9

m∠K = 10x + 7 = 10(9) + 7 = 90 + 7 = 97°

Answer:

135 times

Step-by-step explanation:

The bug changes direction at t = 4. This can be answered by the concept of velocity.

To determine when the bug changes direction, we need to find when its velocity changes sign from positive to negative. From the graph, we see that the bug's velocity is positive for t < 4 and negative for t > 4. Therefore, the bug changes direction at t = 4.

To verify this, we can look at the behavior of the bug's velocity as it approaches t = 4. From the graph, we see that the bug's velocity is increasing as it approaches t = 4 from the left, and decreasing as it approaches t = 4 from the right. This indicates that the bug is reaching a maximum velocity at t = 4, which is when it changes direction.

Therefore, the bug changes direction at t = 4.

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For Maritza to keep her average of 12 points, she needs 14 points in her subsequent game.

An individual data set's mean is its average. The concept of mean informs us of the quantity of data in its entirety.

In other words, this same deviation of data from across all data sets is built on the mean.

Mean = sum of data / Number of data

points given for the 6 games:

11,12,10,8,14 and 15

Let's say this same point in the seventh game is x, keeping the average at 12.

The average for the 7th game is.

(11 + 12 + 10 + 8 + 14 + 15 + x )/7 = 12

(70 + x )/7 = 12

70 + x = 84

x = 24

For Maritza to keep her average of 12 points, she needs 14 points in her subsequent game.

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Answer:

15

Step-by-step explanation:

6.65:5=1.33

1.33х15=19.95$

we need to around the 19.95 and we get a 20$

have a nice day

A. The probability that one selected subcomponent is longer than 122 cm can be found by calculating the area under the normal distribution curve to the right of 122 cm. We can use the z-score formula to standardize the value and then look up the corresponding probability in the standard normal distribution table.

z = (122 - μ) / σ = (122 - 100) / 5.6 = 3.93 (approx.)

Looking up the corresponding probability for a z-score of 3.93 in the standard normal distribution table, we find that it is approximately 0.9999. Therefore, the probability that one selected subcomponent is longer than 122 cm is approximately 0.9999 or 99.99%.

B. To find the probability that the mean length of three randomly selected subcomponents exceeds 122 cm, we need to consider the distribution of the sample mean. Since the sample size is 3 and the subcomponent lengths are normally distributed, the distribution of the sample mean will also be normal.

The mean of the sample mean will still be the same as the population mean, which is 100 cm. However, the standard deviation of the sample mean (also known as the standard error) will be the population standard deviation divided by the square root of the sample size.

Standard error = σ / √n = 5.6 / √3 ≈ 3.24 cm

Now we can calculate the z-score for a mean length of 122 cm:

z = (122 - μ) / standard error = (122 - 100) / 3.24 ≈ 6.79 (approx.)

Again, looking up the corresponding probability for a z-score of 6.79 in the standard normal distribution table, we find that it is extremely close to 1. Therefore, the probability that the mean length of three randomly selected subcomponents exceeds 122 cm is very close to 1 or 100%.

C. If we want to find the probability that all three randomly selected subcomponents have lengths exceeding 122 cm, we can use the probability from Part A and raise it to the power of the sample size since we need all three subcomponents to satisfy the condition.

Probability = (0.9999)^3 ≈ 0.9997

Therefore, the probability that if three subcomponents are randomly selected, all three of them have lengths that exceed 122 cm is approximately 0.9997 or 99.97%.

Based on the given information about the normal distribution of subcomponent lengths, we calculated the probabilities for different scenarios. We found that the probability of selecting a subcomponent longer than 122 cm is very high at 99.99%. Similarly, the probability of the mean length of three subcomponents exceeding 122 cm is also very high at 100%. Finally, the probability that all three randomly selected subcomponents have lengths exceeding 122 cm is approximately 99.97%. These probabilities provide insights into the performance of the automatic machine in terms of producing longer subcomponents.

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The area of the water's surface is approximately 981.25 square units.

Since the water depth is 10, the water fills up half of the hemispheric bowl. Therefore, we need to find the surface area of a circle with radius 25 (the base of the hemisphere) and divide it by 2.

The surface area of a circle with radius r is given by A = πr^2. So, the surface area of the circle with radius 25 is:

A = π(25)^2 = 625π

Dividing by 2, we get

625π/2

So the surface area of the water's surface is 625π/2 square units.

Approximating the value of π as 3.14, we get:

625π/2 ≈ 625(3.14)/2 ≈ 981.25

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