Which list correctwhich list correctly identifies the steps to solving a word problem?ly identifies the steps to solving a word problem?

Step-by-step explanation:

<c =90 °

So, Pythagoras theorem can be used,

Hypotenuse ² = base ² + altitude ²

AB²=AC²+BC²

11²=AC²+4²

11²-4²=AC²

121-16=AC²

Root 105=AC

AC=10.2 cm

The length of AC is 10.25 cm

If ΔABC is a right angle triangle, then

AB² = BC²+AC²

where AB = Hypotenuse, BC & AC are adjacent sides of the right angle

Given, hypotenuse = AB = 11 cm

One of adjacent sides = BC = 4 cm

We have to find the length of AC.

Using pythagorean theorem,

AB² = BC²+AC²

⇒ AC² = AB² - BC²

⇒ AC² = 11²-4²

⇒ AC² = 121-16

⇒ AC = √105

⇒ AC = 10.25

So the length of AC = 10.25 cm

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Answer:

123334

Step-by-step explanation:

Answer:

see explanation

Step-by-step explanation:

4a + 8               4

2a² + 8a            2a

12a² - 8a           4a

4 - 6a                2

Match each expression with its greatest common factor as follows;

4a + 8               4

2a² + 8a            2a

12a² - 8a           4a

4 - 6a                2

The largest number that is found in the common factors is called the greatest common factor.

The given expression are;

4a + 8              

2a² + 8a            

12a² - 8a      

4 - 6a              

The greatest common factor of the expression are as follows;

4a + 8  = 4(a+2) = common factor = 4    

2a² + 8a = 2a(a+4a) = common factor = 2a

12a² - 8a = 4a(3a-2) = common factor = 4a

4 - 6a = 2(2-3a) = common factor = 2

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The given data is,A matched pairs experiment compares the taste of instant with fresh-brewed coffee. Each subject tastes two unmarked cups of coffee, one of each type, in random order and states which he or she prefers.

Of the 60 subjects who participate in the study, 21 prefer the instant coffee. We need to find the probability that a randomly chosen subject prefers fresh-brewed coffee to instant coffee, let's say p. The formula to calculate the proportion of the population is:

p = (n1 + n2) / (x1 + x2)n1 and n2 are the sample sizes of two categories and x1 and x2 are the number of favorable outcomes from the respective categories. Here, n1 = n2 = 60 and x1 = 39 (since 21 out of 60 prefer instant coffee, the remaining 39 must prefer fresh-brewed coffee).Now, p = (60 + 60) / (39 + 21) = 1.2. Since p is a probability, it must be between 0 and 1. But here, p is greater than 1, which is not possible. Therefore, there is an error in the given data and we cannot proceed with the calculation.

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Answer: Correct me if I am wrong, but this is how I think you should solve it.

Step-by-step explanation:

1. Simplify 8×5 to 40.

−2×(40+9)−6×7

2. Simplify 40+9 to 49.

−2×49−6×7

3. Simplify −2×49 to −98.

−98−6×7

4. Simplify 6×7 to 42.

−98−42

5. Simplify

−140

Your all done! Hope this helps.

The given circle has its center at (−3,3) and has a radius of 5 units. Then, the shortest distance D between the point and the circle is given by.

Answer:

First option (top left)

Step-by-step explanation:

Since the coefficient of this equation, \(2(3)^{x}\), is 2, when x is 0, then y must be 2. The graph must have a y-intercept of 2. You can find this by plugging this in.

I cannot see the fourth graph, but the second graph does not have a y-intercept of 2, therefore it can immedeately be ruled out.

Then we plug in the coordinates they give.

It just so happens that the first one, \(2(3)^1\) is indeed equal to 6.

We can check that this is right by disproving the third one (top right).

\(2(3)^2=18\), not 8, therefore our third answer choice is false.

The fourth one is definetly wrong because the y-value at x=2 (as we have already calculated) is 18, not 12.

Therefore, our first answer, the one on the top left, is correct.

note: for this problem you did not even need to find the y-intercepts. Plugging in the coordinates would be fine by its own (the second answer choice is already wrong just because of the coordinates since 9≠6(found in answer choice 1)). However, having the y-intercept handy will be very helpful if there is more than one answer choice with correct coordinates.

Answer:

Step-by-step explanation:  i think the answer is A

The set of all images of the elements in the domain of a function is called the "range" or "codomain" of the function.

The set of all images of the elements in the domain of a function is called the range. The domain of a function refers to the set of input values or independent variables that the function can accept. It represents the set of values for which the function is defined. On the other hand, the range of a function refers to the set of output values or dependent variables that the function can produce. It represents the set of values that the function can take on as the input values change. The range is determined by evaluating the function for all possible input values in the domain. Thus, it is essential to determine both the domain and range of a function to fully understand its behavior and properties.

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(i) The probability of the arrow pointing to 7 is 1/12.
(ii) The probability of the arrow pointing to a prime number is 5/12.
(iii) The probability of the arrow pointing to a composite number is 1/2.

The probability of an event is determined by dividing the number of favorable outcomes by the total number of possible outcomes.

(i) To find the probability of the arrow pointing to 7, we need to determine the number of favorable outcomes and the total number of possible outcomes. In this case, there is only one favorable outcome (7) and the total number of possible outcomes is 12 (numbers 1 to 12). Therefore, the probability of the arrow pointing to 7 is 1/12.

(ii) To find the probability of the arrow pointing to a prime number, we need to determine the number of favorable outcomes (prime numbers) and the total number of possible outcomes. The prime numbers between 1 and 12 are 2, 3, 5, 7, 11, making a total of 5 favorable outcomes. The total number of possible outcomes is still 12. Therefore, the probability of the arrow pointing to a prime number is 5/12.

(iii) To find the probability of the arrow pointing to a composite number, we need to determine the number of favorable outcomes (composite numbers) and the total number of possible outcomes. The composite numbers between 1 and 12 are 4, 6, 8, 9, 10, 12, making a total of 6 favorable outcomes. The total number of possible outcomes is still 12. Therefore, the probability of the arrow pointing to a composite number is 6/12, which can be simplified to 1/2.

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The decimal number system uses nine different symbols is False as the decimal number system actually uses ten different symbols: 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9. These ten symbols, also known as digits, are used to represent all possible numerical values in the decimal system.

Each digit's position in a number determines its value, and the combination of digits creates unique numbers. This system is widely used in everyday life and forms the basis for arithmetic operations and mathematical calculations. Thus, the decimal number system consists of ten symbols, not nine.

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(a) The confidence intervals for the sample proportion (P = 0.82) with a 95% confidence level are approximately [0.782, 0.858], and with a 99% confidence level are approximately [0.769, 0.871].

(b) The confidence intervals for the sample proportion (P = 0.19) with a 95% confidence level are approximately [0.161, 0.219], and with a 99% confidence level are approximately [0.153, 0.227].

To construct confidence intervals for the sample proportions, we can use the formula:

Lower Confidence Bound = P - z * sqrt((P * (1 - P)) / n)

Upper Confidence Bound = P + z * sqrt((P * (1 - P)) / n)

Where:

P is the sample proportion

n is the sample size

z is the z-score corresponding to the desired confidence level

Let's calculate the confidence intervals for the given sample proportions.

(a) For n = 275 and P = 0.82:

For a 95% confidence level, the z-score is 1.96.

For a 99% confidence level, the z-score is 2.58.

95% Confidence Interval:

Lower Confidence Bound = 0.82 - 1.96 * sqrt((0.82 * (1 - 0.82)) / 275)

= 0.82 - 1.96 * sqrt((0.82 * 0.18) / 275)

≈ 0.782

Upper Confidence Bound = 0.82 + 1.96 * sqrt((0.82 * (1 - 0.82)) / 275)

= 0.82 + 1.96 * sqrt((0.82 * 0.18) / 275)

≈ 0.858

99% Confidence Interval:

Lower Confidence Bound = 0.82 - 2.58 * sqrt((0.82 * (1 - 0.82)) / 275)

= 0.82 - 2.58 * sqrt((0.82 * 0.18) / 275)

≈ 0.769

Upper Confidence Bound = 0.82 + 2.58 * sqrt((0.82 * (1 - 0.82)) / 275)

= 0.82 + 2.58 * sqrt((0.82 * 0.18) / 275)

≈ 0.871

Therefore, the confidence intervals for the sample proportion (P = 0.82) with a 95% confidence level are approximately [0.782, 0.858], and with a 99% confidence level are approximately [0.769, 0.871].

(b) For n = 700 and P = 0.19:

For a 95% confidence level, the z-score is 1.96.

For a 99% confidence level, the z-score is 2.58.

95% Confidence Interval:

Lower Confidence Bound = 0.19 - 1.96 * sqrt((0.19 * (1 - 0.19)) / 700)

= 0.19 - 1.96 * sqrt((0.19 * 0.81) / 700)

≈ 0.161

Upper Confidence Bound = 0.19 + 1.96 * sqrt((0.19 * (1 - 0.19)) / 700)

= 0.19 + 1.96 * sqrt((0.19 * 0.81) / 700)

≈ 0.219

99% Confidence Interval:

Lower Confidence Bound = 0.19 - 2.58 * sqrt((0.19 * (1 - 0.19)) / 700)

= 0.19 - 2.58 * sqrt((0.19 * 0.81) / 700)

≈ 0.153

Upper Confidence Bound = 0.19 + 2.58 * sqrt((0.19 * 0.81) / 700)

≈ 0.227

Therefore, the confidence intervals for the sample proportion (P = 0.19) with a 95% confidence level are approximately [0.161, 0.219], and with a 99% confidence level are approximately [0.153, 0.227].

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Answer:

Adult tickets= 390

Student ticket= 410

Step-by-step explanation:

4A + 2.5S= 2585

A+ S = 800

A= 800-S

Substitute into the first equation

The graph of the function y = 2x² + 6x + 3 is graph A

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

y = 2x² + 6x + 3

When converted to vertex form, we have

y = 2(x  + 3/2)² - 3/2

The above function is a quadratic function that has been transformed as follows

From the list of options, the graph tha has the above transformation features is graph A

Hence, the graph of the function is (a)

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Answer:

Step-by-step explanation:

Slope intercept form is y = mx + b

b is the y intercept

m is the slope

the y intercept is 40

y = mx + 40

the slope is -1

y = -1x + 40

The kind of parallelism where two lines communicate the same truth but use different words is called semantic parallelism.

Semantic parallelism is a rhetorical device used to emphasize and reinforce a particular idea or concept. It involves using different expressions, but with similar meanings, to convey the same message. Semantic parallelism is used to create repetition and enhance the overall impact of the statement.

In summary, semantic parallelism is a powerful literary technique that adds depth and resonance to written or spoken communication.

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Answer:

x = 2

Step-by-step explanation:

x + 1/2 (6x - 4) = 6

Expand the brackets.

x + 3x - 2 = 6

Add like terms.

4x - 2 = 6

Add 2 on both sides.

4x = 6 + 2

4x = 8

Divide 4 into both sides.

x = 8/4

x = 2

Answer:

x=5/4

Step-by-step explanation:

Answer:

69 mph

Explanation:

The equation that represents this situation is:

We are required to determine Brian's average speed on the return drive.

To do this, we first find the value of x.

Using the value of x, we find the average speed on the return drive.

Therefore, the average speed on the return drive will be 69 mph.

Answer:

all 3 options are true : A, B, C

Step-by-step explanation:

warning : it has come to my attention that some testing systems have an incorrect answer stored as right answer for this problem.

they say that A and C are correct.

but I am going to show you that if A and C are correct, then also B must be correct.

therefore, my given answer above is the actual correct answer (no matter what the test systems say).

originally the information about the alignment of the point F in relation to point E was missing.

therefore, I considered both options :

1. F is on the same vertical line as E.

2. F is not on the same vertical line as E.

because of optical reasons (and the - incomplete - expected correct answers of A and C confirm that) I used the 1. assumption for the provided answer :

the vertical line of EF is like a mirror between the left and the right half of the picture.

A is mirrored across the vertical line resulting in B. and vice versa.

the same for C and D.

this leads to the effect that all 3 given congruence relationships are true.

if we consider assumption 2, none of the 3 answer options could be true.

but if the assumptions are true, then all 3 options have to be true.

now, for the "why" :

remember what congruence means :

both shapes, after turning and rotating, can be laid on top of each other, and nothing "sticks out", they are covering each other perfectly.

for that to be possible, both shapes must have the same basic structure (like number of sides and vertices), both shapes must have the same side lengths and also equally sized angles.

so, when EF is a mirror, then each side is an exact copy of the other, just left/right being turned.

therefore, yes absolutely, CAD is congruent with CBD. and ACB is congruent to ADB.

but do you notice something ?

both mentioned triangles on the left side contain the side AC, and both triangles in the right side contain the side BD.

now, if the triangles are congruent, that means that each of the 3 sides must have an equally long corresponding side in the other triangle.

therefore, AC must be equal to BD.

and that means that AC is congruent to BD.

because lines have no other congruent criteria - only the lengths must be identical.

The inequality that can be used to represent the number of doll Johnny can buy is x ≤ 10.61

Johnny is budgeting for his trip to the toy store.  He does not want to spend more than $80 on Christmas presents.

He wants to buy a toy car that costs $32.25 and some dolls that cost $4.50 each. The number of dolls he can buy can be represented with the inequality as follows:

let

x = number of dolls

Therefore,

4.50x + 32.25 ≤ 80

subtract 32.25 from both sides of the inequality

4.50x + 32.25 ≤ 80

4.50x + 32.25 - 32.25 ≤ 80 - 32.25

4.50x ≤ 47.75

divide both sides by 4.50

4.50x/ 4.50 ≤ 47.75 / 4.50

x ≤ 10.6111111111

x ≤ 10.61

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Answer:

b

Step-by-step explanation:

eachone got to go there minus 6

The hollow sphere must have an angular speed of ω1 in order to have the same kinetic energy (k1) as the uniform sphere.

The kinetic energy (K) of a rotating object can be calculated using the formula K = (1/2) I ω², where I is the moment of inertia and ω is the angular speed. For a hollow sphere, the moment of inertia (I) is given by I = (2/3) m R², where m is the mass and R is the radius.

If the kinetic energy of the hollow sphere is k1, we can set up the equation (1/2)(2/3) m R² ω1² = k1. Simplifying this equation, we get (1/3) m R² ω1² = k1.

Now, let's consider a uniform sphere with the same mass and radius as the hollow sphere. The moment of inertia for a uniform sphere is given by I = (2/5) m R². Since the kinetic energy (k1) is the same for both the hollow and uniform spheres, we can set up another equation: (1/2)(2/5) m R² ω2² = k1. Simplifying this equation, we get (1/5) m R² ω2² = k1.

Since k1 is the same in both equations, we can equate the right sides: (1/3) m R² ω1² = (1/5) m R² ω2². Canceling out the mass and radius terms, we have (1/3) ω1² = (1/5) ω2².

Therefore, in order for the hollow sphere to have the same kinetic energy as the uniform sphere, it must have an angular speed of ω1, which is related to the angular speed of the uniform sphere (ω2) by the equation ω1² = (3/5) ω2².

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Blank #1 : The arc length of the sector is approximately 3.8 yards.

Blank #2:  The area of the sector is approximately 14.1 square yards.

To find the arc length of the sector, we can use the formula:

Arc Length = (θ/360°) * 2πr

where θ is the angle of the sector and r is the radius of the circle.

Given that the radius is 6 yards and the angle of the sector is 45°, we can substitute these values into the formula:

Arc Length = (45°/360°) * 2π * 6

Arc Length = (1/8) * 2π * 6

Arc Length ≈ 1.2π yards

Rounding to the nearest tenth, the arc length of the sector is approximately 3.8 yards.

To find the area of the sector, we can use the formula:

Area = (θ/360°) * πr^2

Again, substituting the given values:

Area = (45°/360°) * π * 6^2

Area = (1/8) * π * 36

Area ≈ 4.5π square yards

Rounding to the nearest tenth, the area of the sector is approximately 14.1 square yards.

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Answer:

\(\frac{36}{49}\)

Step-by-step explanation:

the pattern identified in the sequence is to add 1/49 after each step in the sequence.

When you add 1/49 to 34/49 you get 35/49, which can be simplified to 5/7.

To get the next value in the sequence just add 1/49 to 35/49, which equals 36/49.

this answer can not be simplified further.

The area of the right triangle that is given would be = 60.

To calculate the area of the given triangle, the base of the triangle should first be calculated using the Pythagorean theorem.

That is ;

C² = a²+b²

c = 17

a = 8

b = ?

make b the subject of formula;

b² = c²-a²

= 17²-8²

= 289-64

= 225

b = √225 = 15

The area = ½ base ×height

= 1/2× 15 × 8

= 60

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The formula ½ bh finds the area of a triangle.

Please check the picture.

Answer:

Triangle

Step-by-step explanation:

b -  base of the triangle

h - height or altitude

Answer:

15.13 units

Step-by-step explanation:

The solution of the DTDS is xn = (0.63)^n * 41 grams, where n represents time in hours.

a) The updating function f(x) for the discrete time dynamical system (DTDS) can be derived from the given information that the body eliminates 37% of the alcohol present in the body per hour.

Since 37% of the alcohol is eliminated, the amount remaining after one hour can be calculated by subtracting 37% of the current amount from the current amount. This can be expressed as:

f(x) = x - 0.37x

Simplifying the equation:

f(x) = 0.63x

b) The initial condition for the DTDS is given as Peter having 41 grams of alcohol in his body after consuming three alcoholic drinks. Therefore, the initial condition is:

x0 = 41 grams

c) To find the solution of the DTDS with the given initial condition, we can use the updating function f(x) and iterate it over time.

For n hours, the solution is given by:

xn = f^n(x0)

Applying the updating function f(x) repeatedly for n times:

xn = f(f(f(...f(x0))))

In this case, since the function f(x) is f(x) = 0.63x, the solution can be written as:

xn = (0.63)^n * x0

Substituting the initial condition x0 = 41 grams, the solution becomes:

xn = (0.63)^n * 41 grams

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Answer:

the missing value is 7

Step-by-step explanation:

mode means the highest occuring number and from the figures above, the numbers the occured the most are 3,5and7. they appeared two times and since from the question it's said that 7 is the mode, it means that 7 should occure more than 3 and 5. so the missing value is 7.