16 ft
Find the area.
20 ft
12 ft
10 ft
15 ft A = [?] ft²
Round to the nearest
hundredth.

Answer:

3/8

Step-by-step explanation:

3 1/3 = 10/3

1 1/4 = 5/4

Remember when dividing by a fraction you can also multiply by its reciprocal meaning flip the numerator and denominator.

so

(3 1/3) / (1 1/4) = (10/3) / (5/4) = (10/3) x (4/5) which is the same as (3/10) x (5/4)

= (3 x 5) / (10 x 4) = 15 / 40

the numerator and denominator have a common factor of 5 so divide the  numerator and denominator by 5

15 / 40 = 3/8

In the transformation ABC A'B'C', the preimage of B' is B.

It's a triangle, ABC. ABC is changed so that the resulting image is A'B'C'. It should be noted that there are many other forms of transformations, including dilation, vertical shift, horizontal shift, rotation about a point, reflection on a line, etc.

Corresponding vertices will be matched in all transformations. In other words, A will change to A', B to B', and C to C'.Preimage of B' would just be B itself due to the transformation's ability to maintain image similarity and convert vertices appropriately.

In conclusion, it is B.

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In the transformation ABC A'B'C', the preimage of B' is ____

Answer:

44

yes. the total cost is 68 which is less than 70

Step-by-step explanation:

There is positive proportionality is two variables are positively related to each other.

The equation for direct proportionality =

y = bx

where y = dependent variable

b = constant

x = independent variable

amount of gasoline = b x length of the trip  

16 = b x 145

b = 16/145 = 0.110345

a. 400 x 0.110345 = 44

total litres used for the trip = 44 + 16 = 60

total cost of the trip = 60 x 1.13 = 67.8

total amount spent on gasoline is 67.8. this is less than the budget

The sets of vectors which are linearly dependent are:

(0,8,4),(0,48,24) and

(8,0,4),(−9,8,5),(2,−2,6),(4,−4,0)

and the sets of vectors which are linearly independent are:

(3,0,5),(4,−7,3),(8,1,6) and

(3,8,0),(18,9,0).

The set of vectors (0,8,4),(0,48,24) are linearly dependent because the second vector is exactly six times the first vector.

The set of vectors (3,0,5),(4,−7,3),(8,1,6) are linearly independent. We can see this by trying to solve the equation a(3,0,5) + b(4,-7,3) + c(8,1,6) = (0,0,0). This leads to the system of equations:

3a + 4b + 8c = 0

-7b + c = 0

5a + 3b + 6c = 0

Solving this system gives us a unique solution a=b=c=0 which means that the vectors are linearly independent.

The set of vectors (8,0,4),(−9,8,5),(2,−2,6),(4,−4,0) are linearly dependent because we can see that the fourth vector is the sum of the first three.

The set of vectors (3,8,0),(18,9,0) are linearly dependent because the second vector is exactly six times the first vector.

Therefore, the sets of vectors which are linearly dependent are:

(0,8,4),(0,48,24) and

(8,0,4),(−9,8,5),(2,−2,6),(4,−4,0)

and the sets of vectors which are linearly independent are:

(3,0,5),(4,−7,3),(8,1,6) and

(3,8,0),(18,9,0).

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To write the expression in its simplest form, we need to simplify each term and then combine like terms.

The first term of the expression is 2x²y. This term is already in its simplest form and doesn't require any further simplification.

The second term of the expression is xy. This term is also in its simplest form and doesn't require any further simplification.

The third term of the expression is -3x. This term is also in its simplest form and doesn't require any further simplification.

The fourth term of the expression is 12x.xy. To simplify this term, we need to distribute the 12 over the x and y. So, we get 12x.y.

Now that all terms are simplified, we can combine like terms. Since the terms xy and 12x.y are the same, we can add them together to get (12+1)xy = 13xy.

So, the expression in its simplest form is 2x²y + 13xy - 3x.

We can further simplify the above expression by combining x²y and xy together as (x²+1)xy = x³y

So, the final expression in its simplest form is x³y + 13xy - 3x.

Answer:

9.11

Step-by-step explanation:

√83=9.110433579

round 9.110433579 to get 9.11

Answer:

i think it is the first answer

Step-by-step explanation:

The length of the common chord is 6 cm.

A line that touches ellipses or circles only once is said to be tangential.

Given:

Circles intersect at two points, so we can draw the above figure.

Let AB be the common chord.

Let O and O’ be the centers of the circles, respectively.

So, O’A = 5 cm, OA = 3 cm

OO’ = 4 cm

We can claim that the smaller circle's centre is inside the larger circle itself since the radius of the larger circle is greater than the separation between the two centres.

OO’ is the perpendicular bisector of AB.

So, OA = OB = 3 cm

AB = 3 cm + 3 cm = 6 cm [Since, O is the mid point of AB]

Hence, the length is 6 units.

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Answer:

Hope it will help U......

Answer:

51.048053

Step-by-step explanation:

Answer:

k = -0.25

Step-by-step explanation:

If z varies jointly, that means z = k * x * y

putting in the numbers it gives us,

6 = k * (3) * (-8)

6 = k * (-24)

k = -(1/4) = -0.25

Answer:

Q4. a) 2000 cm³

b) 0.982 cm³ (3 s.f.)

c) 183 cm³ (3s.f.)

d) 2196 cm³

e) 2380 cm³

Q5. 8376 handles

Step-by-step explanation:

Please see the attached pictures for the full solution.

Step-by-step explanation:

Range= 11

Median=25

Mean=27

Answer:

Mean: 27

Median: 25

Range: 8

Midrange: 28

Step-by-step explanation:

Mean: The average.

To find the mean you have to add up all the numbers in the data value and then divide it by how many numbers there are.

I first added, 24+32+25+24+30+30+24=189.

There are 7 numbers in that data value, 189/7=27

Median: Middle number in ascending order.

So first let's rearrange the numbers from lowest to highest, 24, 24, 24, 25, 30, 30, 32.

25 is the number in the middle

Range: Difference between the greatest and lowest number.

The greatest number is 32.

The lowest number is 24.

32-24=8

Midrange: Greatest and lowest number added together and then divided by 2.

The greatest number is 32.

The lowest number is 24.

32+24=56

56/2=28

I hope I could help and this isn't confusing for you!

Answer:

except third all are correct answer

Step-by-step explanation:

please give me brainlest

The null hypothesis is that there is no significant difference in the number of words remembered between the group that texted during the audio clip and the group that did not. The symbol "H0" represents the null hypothesis.

Based on the texting and concentration scenario, let's identify the null hypothesis and what "p" represents in it.
Null hypothesis (H0): There is no significant difference in the number of words remembered by students when they are texting versus when they are not texting during the audio clips. In other words, texting has no effect on concentration.

The null hypothesis is a statistical assumption that says there is no statistical significance in a group of observations. Hypothesis testing is used to test the reliability of a hypothesis using sample data. It is sometimes called "blank" and stands for H0. The null hypothesis, also known as the Conjecture is used in quantitative analysis to test a theory about business, investment, or the economy to determine whether the idea is true or false.

In this hypothesis, "p" represents the difference in the proportions of words remembered while texting and not texting. If p = 0, it means there is no difference in the students' concentration between the treatment (texting) and control (not texting) groups.

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A team that had the best overall record for the season and the best measure of center to compare include the following: C. Eagles; they have a larger mean value of about 22 points.

From the data set for Jaguars, we have:

3, 14, 7, 7, 21, 10, 17, 6, 14, 24, 21, 7, 10, 17, 3

Mean of Jaguars = [3 +14 +7 +7 +21+ 10 +17 +6+ 14+ 24+ 21+ 7+ 10+ 17 +3]/15

Mean of Jaguars = 181/15

Mean of Jaguars = 12.07

Median of Jaguars = 10.

From the data set for Eagles, we have:

3, 24, 14, 27, 10, 13, 10, 21, 24, 17, 27, 7, 40, 37, 55

Mean of Eagles = [3 +24+ 14 +27 +10+ 13+ 10 +21 +24+ 17+ 27+ 7+ 40+ 37 +55]/15

Mean of Eagles = 329/15

Mean of Eagles = 21.93 ≈ 22.

The median of Eagles = 21.

Since Eagles have both a larger mean and median value, the best measure of center to compare would is the mean.

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Answer:

it will take 6 minutes, just keep adding 1.4 to -8.4 until you reach 0

Step-by-step explanation:

Answer: It will take 6 minutes because all you need is to divide 8.4 and 1.4 (don't put the negative sign or ignore it)!

Answer:

a₁ = 15

Step-by-step explanation:

the sum to n terms of an arithmetic sequence is

\(S_{n}\) = \(\frac{n}{2}\) [ 2a₁ + (n - 1)d ]

where a₁ is the first term and d the common difference

given S₁₄ = - 63 , then

\(\frac{14}{2}\) [ 2a₁ + 13d ] = - 63

7(2a₁ + 13d) = - 63 ( divide both sides by 7 )

2a₁ + 13d = - 9 → (1)

the nth term of an arithmetic sequence is

\(a_{n}\) = a₁ + (n - 1)d

given a₁₄ = - 24 , then

a₁ + 13d = - 24 → (2)

subtract (2) from (1) term by term to eliminate d

a₁ + 0 = - 9 - (- 24)

a₁ = - 9 + 24 = 15

The equation of the line perpendicular to the given line and passing through (-3, 7) is; y = (-2/3)x + 5

We are given the equation of a line as; y = (3/2)x - 1

Now, the general form of equation of a line in slope intercept form is;

y = mx + c

where;

m is slope

c is y-intercept

Thus, for our given equation we have;

Slope; m = 3/2

y-intercept; c = -1

Now, for a line perpendicular to this, will have a slope of -1/(3/2) = -2/3

Thus, equation of the line perpendicular to the given line and passing through (-3, 7) is;

y - 7 = (-2/3)(x - (-3))

y - 7 = (-2/3)(x + 3)

y = 7 - 2 - (2/3)x

y = (-2/3)x + 5

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Answer:

See Explanation

Step-by-step explanation:

\(5y - x = 10 \\ \\ 5y = x + 10 \\ \\ y = \frac{x + 10}{5} \\ \\ y = \frac{x}{5} + \frac{10}{5} \\ \\ \huge \red{ \boxed{ y = \frac{1}{2} x + 2}}\)

To determine the number of pattern block rhombuses needed to create 2 hexagons, we need to understand the relationship between the two shapes.

A pattern block rhombus is a rhombus-shaped tile commonly used in geometry and math education. It is composed of two equilateral triangles joined together.

A hexagon, on the other hand, is a polygon with six sides. Each side of a regular hexagon is congruent to the others, and all its angles are equal.

In order to create a hexagon using pattern block rhombuses, we need to consider the arrangement of the rhombuses. Let's assume that the hexagons we want to create are regular hexagons.

A regular hexagon can be divided into six equilateral triangles. Each equilateral triangle can be formed using two pattern block rhombuses. Therefore, to create one regular hexagon, we need a total of 6 equilateral triangles x 2 rhombuses per triangle = 12 pattern block rhombuses.

Since we want to create 2 hexagons, we multiply the number of rhombuses required for one hexagon by 2:

12 pattern block rhombuses per hexagon x 2 hexagons = 24 pattern block rhombuses.

Therefore, we would need 24 pattern block rhombuses to create 2 regular hexagons.

The sinusoidal function that satisfies the given attributes is f(x) = 10 * sin(2π/5 * x - π/5) + 31.

To find a sinusoidal function with the given attributes, we can use the general form of a sinusoidal function:

f(x) = A * sin(Bx + C) + D

where A represents the amplitude, B represents the frequency (related to the period), C represents the phase shift, and D represents the vertical shift.

Amplitude: The given amplitude is 10. So, A = 10.

Period: The given period is 5. The formula for period is P = 2π/B, where P is the period and B is the coefficient of x in the argument of sin. By rearranging the equation, we have B = 2π/P = 2π/5.

Midline: The given midline is y = 31, which represents the vertical shift. So, D = 31.

f(3) = 41: We are given that the function evaluated at x = 3 is 41. Substituting these values into the general form, we have:

41 = 10 * sin(2π/5 * 3 + C) + 31

10 * sin(2π/5 * 3 + C) = 41 - 31

10 * sin(2π/5 * 3 + C) = 10

sin(2π/5 * 3 + C) = 1

To solve for C, we need to find the angle whose sine value is 1. This angle is π/2. So, 2π/5 * 3 + C = π/2.

2π/5 * 3 = π/2 - C

6π/5 = π/2 - C

C = π/2 - 6π/5

Now we have all the values to construct the sinusoidal function:

f(x) = 10 * sin(2π/5 * x + (π/2 - 6π/5)) + 31

Simplifying further:

f(x) = 10 * sin(2π/5 * x - 2π/10) + 31

f(x) = 10 * sin(2π/5 * x - π/5) + 31

Therefore, the sinusoidal function that satisfies the given attributes is f(x) = 10 * sin(2π/5 * x - π/5) + 31.

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Answer:

D

Step-by-step explanation:

The rate of change is equal to m, the slope =

rise / run = (32-17) / (6-3)

The given WFF is equivalent to "true" using logical equivalences. Therefore, it is a tautology.

To show that a well-formed formula (WFF) is a tautology, we need to demonstrate that it is logically equivalent to the statement "true" regardless of the truth values assigned to its variables. Let's analyze the given WFF step by step and apply logical equivalences to show that it is equivalent to "true."

The given WFF is:

A → (¬A v ¬B) v B

We'll use logical equivalences to transform this expression:

Implication Elimination (→):

A → (¬A v ¬B) v B

≡ ¬A v (¬A v ¬B) v B

Associativity (v):

¬A v (¬A v ¬B) v B

≡ (¬A v ¬A) v (¬B v B)

Negation Law (¬P v P ≡ true):

(¬A v ¬A) v (¬B v B)

≡ true v (¬B v B)

Identity Law (true v P ≡ true):

true v (¬B v B)

≡ true

Hence, we have shown that the given WFF is equivalent to "true" using logical equivalences. Therefore, it is a tautology.

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Answer:

C

Step-by-step explanation:

by using \(a^{2} + b^{2} = c^2\) 6=a 8=b you would get 100

then \(\sqrt{100}\) = 10.

Answer:

correct answer is : To determine to measure of the unknown angle, be sure to use the total sum of 180°. If two angles are given, add them together and then subtract from 180°. If two angles are the same and unknown, subtract the known angle from 180° and then divide by 2.

For a uniform distribution random variable X, the probability that the random variable has a value between 0.6 and 2.1 is equals to 0.1875. So, option(a) is right one.

The uniform distribution is defined as a continuous probability distribution and the events are equally likely to occur. In other words in this distribution every possible outcome has an equal probability. There is a uniform distribution of variable. Let the random variable be denoted by X be uniformly distributed. The above figure shows uniform density curve for X. That is \( X \: \tilde \: \: U( 0, 8) \).

Probability density function is f(x) = \(\frac{ 1}{8} = 0.125\)

We have to determine probability that the random variable has a value between 0.6 and 2.1, P(0.6 ≤ X ≤ 2.1). So, required probability is P(0.6 ≤ X ≤ 2.1) = \(\int_{0.6}^{2.1} f(x) dx \).

\(= [ 0.125x ]_{0.6}^{2.1}\)

= 0.125 ( 2.1 - 0.6)

= 0.125 ( 1.5)

= 0.1875

Hence, required value is 0.1875.

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Complete question:

the above figure complete the question.

Using the uniform distribution density curve answer the question :

what is the probability that the random variable has a value between 0.6 and 2.1?

a) 0.1875

b) 0.4625

c) 0.3375

d) 0.2125

The average value of the function f(x) = 6x over the interval [0, 9] is 27.

To find the average value of a function over a given interval, you need to take the definite integral of the function over that interval, and divide by the length of the interval. In this case, the function is f(x) = 6x, and the interval is [0, 9].

So first, we need to find the definite integral of 6x over [0, 9]:

∫[0,9] 6x dx = 3x^2 |[0,9] = 243

Next, we need to find the length of the interval, which is simply 9 - 0 = 9.

Finally, we divide the definite integral by the length of the interval:

Average value of f(x) = (1/9) * 243 = 27

So the average value of the function f(x) = 6x over the interval [0, 9] is 27.

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A) We can look at the coordinates of x in the horizontal axis and the coordinates of y in the vertical axis.

Then, we can see that A has coordinates (0,1), B has coordinates (1,2), C has coordinates (2,3) and D has coordinates (3,4).

We can then complete the table as:

Point | x | y

A | 0 | 1

B | 1 | 2

C | 2 | 3

D | 3 | 4

B) If we look at the pattern we can see that the points form a line.

A line will have a constant rate of change. We can see that for each unit increase of x, there is a increase of one in y, and this happens for all the points, so the rate of change is constant.

C) If we continue the pattern, we can create another point from D by adding one unit in x and one unit in y. This way we mantain the same rate of change (one unit of y per unit of x) and find new points.

With this method, we can create the following points: E(4, 5), F(5, 6) and G(6, 7).

We can plot them as: