I could really use your help:)

Answer:

Step-by-step explanation:

a. (I) x = 65

(ii) vertically opposite angles are equal.

b. (i) 71 degrees

(ii) alternate interior angles are equal

c. (i) z = 180 - 71 = 109 degrees

(ii) angles on a line add up to 180 degrees

Answer:

x = 65°, y = 71°, z = 44°

Step-by-step explanation:

x and 65 are vertical angles and congruent, thus

x = 65°

y and 71 are alternate angles and congruent, thus

y = 71°

The sum of the 3 angles in a triangle = 180°, thus

z = 180° - (65 + 71)° = 180° - 136° = 44°

Hence

x = 65°, y = 71° and z = 44°

Daniel and Maria must babysit for 6 hours for their total fees to be the same.

To find the number of hours at which Daniel and Maria have the same total fee, we need to compare their fee structures and determine when their fees are equal.

Daniel charges a flat fee of $10 plus $6 per hour. So his total fee can be represented by the equation:

Total fee (Daniel) = $10 + $6 * Number of hours

Maria's total fee is given in the table. We can see that the total fee increases by $4 for every additional hour. So we can represent Maria's total fee by the equation:

Total fee (Maria) = $22 + $4 * Number of hours

To find the number of hours at which their fees are equal, we set the two equations equal to each other and solve for the number of hours:

$10 + $6 * Number of hours = $22 + $4 * Number of hours

Simplifying the equation, we get:

$6 * Number of hours - $4 * Number of hours = $22 - $10

$2 * Number of hours = $12

Dividing both sides by $2, we find:

Number of hours = $12 / $2

Number of hours = 6

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Check the picture below.

\(tan(\theta )=\cfrac{\stackrel{opposite}{282}}{\underset{adjacent}{137}}\implies \theta =tan^{-1}\left( \cfrac{282}{137} \right)\implies \theta \approx 64^o\)

Make sure your calculator is in Degree mode.

B. 4y - 2

Hope this helps! :)

Answer:

B. 4y - 2

Step-by-step explanation:

2( y + 1 ) + 2( y - 2 )

= 2y + 2 + 2y - 4

= 2y + 2y + 2 - 4

= 4y - 2

= 4y - 2

Answer:

1. )0.35

2. )1.15

3.)0.5 (5 repeating's)

4.)2.72

Step-by-step explanation:

7 divide  20=0.35

-23 divide 20=1.15

-60 divide 22 = 2.727272 but it is 2.72

The first constraint is a linear equation that relates the variables x1, x2, and x3, and the second constraint is an inequality constraint involving x1 and x2The given problem is a linear programming problem in its primal form.

The objective is to maximize the expression z = 7x1 - 5x2 - 2x3, subject to two constraints.. The goal is to find the values of x1, x2, and x3 that maximize the objective function while satisfying the given constraints.

In the primal problem, the objective is to maximize the expression z, which is a linear combination of the decision variables x1, x2, and x3. The coefficients 7, -5, and -2 represent the weights assigned to each variable in the objective function. The constraints represent the relationships and limitations imposed on the variables. The first constraint is an equality constraint, which means that the left-hand side of the equation must equal the right-hand side. The second constraint is an inequality constraint, indicating that the value of the expression 2x1 + x2 must be less than or equal to a certain value.

To solve this linear programming problem, various optimization techniques such as the simplex method or interior point methods can be applied. These methods iteratively adjust the values of the decision variables to find the optimal solution that maximizes the objective function while satisfying the given constraints. By solving the primal problem, the values of x1, x2, and x3 can be determined, leading to the maximum value of the objective function z.

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Answer:

750 gallons per hour

Step-by-step explanation:

divide 18000 by 24 and you get 750

Answer:

x = 1/4 y

Step-by-step explanation:

Step 1: Flip the equation.

4x+4=y+4

Step 2: Add -4 to both sides.

4x+4+−4=y+4+−4

4x=y

Step 3: Divide both sides by 4.

4x/4 = y/4

Therefore, x = 1/4 y

If your looking for what y equals, here you go:

Add -4 to both sides.

y + 4 + −4 = 4x + 4 + −4

y = 4x

Answer:

y = 4x

The equation will be y = 4x. Then the graph is a line that goes through the points (1,4) and (2,8).

A linear system is one in which the parameter in the equation has a degree of one. It might have one, two, or even more variables.

The equation is given below.

y + 4 = 4(x + 1)

Then we have

y = 4x

If x = 1. Then y will be

y = 4

If x = 2. Then y will be

y = 8

The graph is a line that goes through the points (1,4) and (2,8).

Then the correct option is B.

The graph is given below.

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Answer:

AB = 2

Step-by-step explanation:

Using the secant- secant theorem, that is

PA × PB = PD × PC , substitute values

10(10 + AB) = 8(8 + 7)

100 + 10AB = 8 × 15 = 120 ( subtract 100 from both sides )

10AB = 20 ( divide both sides by 10 )

AB = 2

Answer:

x = 8

Step-by-step explanation:

A^2 + B^2 = C^2

6^2 + x^2 = 10^2

36 + x^2 = 100

x^2 = 64

x = 8

The perpendicular distance from the line -3-7X(t), g(t), z(t)2+5t-5+8t to the point (-1,7,9) is approximately 6.34 units. The line intersects the yz-plane at the point (0, -1, -16/3) when t = -4/3.

To find the distance from the line to the point, we can use the formula for the distance between a point and a line in 3D space

d = |(P - P₀) x (V)| / |V|

where P is the given point, P₀ is a point on the line, V is the direction vector of the line, x represents the cross product, and | | denotes the magnitude of a vector.

First, we need to find a point P₀ on the line. We can do this by setting t = 0 in the parametric equations of the line

P₀ = (-3, -5, 2)

Next, we need to find the direction vector V of the line. We can do this by subtracting the initial point from a second point on the line. We can use t = 1 for convenience

V = (2 + 5(1) - (-3), 8 - (-5), 7 - 2(1)) = (10, 13, 5)

Now, we can substitute the given values into the formula for the distance and simplify

d = |(-1, 7, 9) - (-3, -5, 2) x (10, 13, 5)| / |(10, 13, 5)|

= |(2, 12, 7) x (10, 13, 5)| / sqrt(10^2 + 13^2 + 5^2)

= |(-31, 60, -146)| / sqrt(354)

= 6.34 (rounded to two decimal places)

Therefore, the perpendicular distance from the line to the point (-1, 7, 9) is approximately 6.34 units.

To find the point at which the line r(t) = (8, – 5, – 4) + t(6, – 3, – 8) intersects the yz-plane, we need to find the value of t that makes the x-coordinate of the point equal to zero (since the yz-plane has equation x = 0).

Setting the x-coordinate of r(t) equal to zero, we get

8 + 6t = 0

Solving for t, we get

t = -4/3

Substituting this value of t back into the equation for r(t), we get

r(-4/3) = (8, -5, -4) + (-4/3)(6, -3, -8)

= (8 - 8, -5 + 4, -4 - (32/3))

= (0, -1, -16/3)

Therefore, the point at which the line r(t) intersects the yz-plane is (0, -1, -16/3).

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Answer:

hope this helps you a lot

God bless you

Answer:

Because the cake pan holds 234 in.³ and the four round cake pans hold a total of around 226.19 in.³

Edit: I multiplied the diameter as the radius. Answer has now been corrected.

Step-by-step explanation:

To solve this, we need to figure out how much each batter can hold.

For this one, the formula is simple. we multiple everything together to get the volume.

13×9×2=234 in.³

For this one, you will have to use pi or π. A round cake pan is most likely a cylinder. Therefore, we will use the cylinder volume formula, which is:

V=πr²h

V=π(3)²(2)

V=π(9)(2)

V=18π

V is around 56.5486678 or 56.55. However, if you are using 3.14 for π, you will get something else, 56.52.

But remember that this is only one cake pan. There are 4 of them. So, we can simply multiple the number by 4. To help this be more accurate, I will go back to 18π first.

V=18π(4)

V=72π

=226.194671058

or around 226.19.

If you are using 3.14, just multiply by 3.14 instead of π. You will get a very similar result, with only a minor difference. It all depends on which one you are using.

Good luck with your homework! If this is correct, please give me brainliest :)

Answer:

Step-by-step explanation:

You want to know the volumes of a 13×9×2 inch rectangular cake pan, and of four 2-inch deep round cake pans 6 inches in diameter.

The volume of the rectangular cake pan is given by ...

  V = LWH

  V = (13 in)(9 in)(2 in) = 234 in³

The volume of four round cake pans with diameter d is given by ...

  V = 4×(π(d/2)²h) = πd²h

  V = π(6 in)²(2 in) = 72π in³ ≈ 226.2 in³

The rectangular pan holds more cake batter.

The cake pan holds 234 in³, and the four round pans hold 226.2 in³.

__

Additional comment

You often see the formula for the volume of a cylinder as ...

  V = πr²h

Since r = d/2, and the diameter is given here, we used the diameter in the formula above. We also made the formula apply to four (4) cake pans, which simplified our math.

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The variability of these data is low, as the range is only 1.

The researcher recorded the following data: 4, 4, 4, 4, and 3. To describe the variability of these data, we can use the term "range."

The range is the difference between the highest and lowest values in a data set. In this case, the range would be 4 - 3 = 1.

Therefore, the variability of these data is low, as the range is only 1.

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Answer:

linear

Step-by-step explanation:

We can write this  in the form

y = mx+b

where m is the .75 per mile and b is the 39 dollars

y = .75x + 39

When two tables have a one-to-many relationship, you typically need to add a foreign key to the table on the "many" side to link the records to the corresponding record in the "one" table.

In a one-to-many relationship, the table on the "one" side is usually the primary key table, and the table on the "many" side is usually the foreign key table. The foreign key is used to link the records in the "many" table to the corresponding record in the "one" table. This is done by adding a column to the "many" table that contains the primary key value from the "one" table.

When designing a database, it is important to establish relationships between tables to ensure data integrity and avoid redundant data. In a one-to-many relationship, one record in the primary key table can be associated with many records in the foreign key table. To establish a one-to-many relationship, you need to create a primary key in the "one" table and a foreign key in the "many" table. The foreign key is a column that contains the primary key value from the "one" table. For example, if you have a "customers" table and an "orders" table, the "customers" table would be the primary key table and the "orders" table would be the foreign key table. Each record in the "orders" table would have a foreign key column that contains the customer ID from the "customers" table.

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We may calculate the corresponding value of z = 1.476 using a conventional normal right-tailed z-table.

Find the value corresponding to one decimal place of the z-score by first looking at the left side column of the z-table (e.g. whole number and the first digit after the decimal point). It is 1.0 in this instance. We then look up the last number, which in our example is 0.09, from across table (on top).

The amount of standard deviations a scoring or value (x) is from the mean is the number of Z scores (Z value). Z-score quantifies data dispersion in other terms. Z-score, informally, indicates however many standard deviations a number (x) is below or above population mean (µ).

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Answer: The slope is 2

Step-by-step explanation:

Given:

We will find the zeros of the function:

Factor the given function:

So, there are four zeros

So, the answer will be:

initial class boundary of 1.5

ending class boundary of 13.5

Number of classes: 6

Class width: Subtract initial class boundary from ending class boundary and divide the result into the number of classes:

Classes:

1.5 - 3.5

3.5 - 5.5

5.5 - 7.5

7.5 - 9.5

9.5 - 11.5

11.5 - 13.5

Order the given data to find easily the frequency of each class:

Then, you get frequencies of:

1.5 - 3.5: 4

3.5 - 5.5: 2

5.5 - 7.5: 2

7.5 - 9.5: 2

9.5 - 11.5: 6

11.5 - 13.5: 3

And you get the next histogram:

Answer:

Step-by-step explanation:

it is the same. it cannot be factored

The probability that the system will function tomorrow is 0.2495 or 24.95%.

To find the probability that the system will function tomorrow, we need to find the probability that at least 4 out of the 6 components will function.

On a rainy day, the probability of 4 components functioning is given by:

P(rainy day and 4 components functioning) = C(6, 4) × (0.5)⁴ × (0.5)² = 15 × 0.0625 × 0.25 = 0.2344

On a non-rainy day, the probability of 4 components functioning is given by:

P(non-rainy day and 4 components functioning) = C(6, 4) × (0.8)⁴ × (0.2)² = 15 × 0.4096 × 0.04 = 0.2534

Now we can find the overall probability of the system functioning tomorrow by using the law of total probability:

P(system functioning tomorrow) = P(rainy day and 4 components functioning) × P(rain) + P(non-rainy day and 4 components functioning) × P(non-rain)

= 0.2344 × 0.20 + 0.2534 × 0.80

= 0.0468 + 0.2027

= 0.2495

Therefore, the probability that the system will function tomorrow is 0.2495 or 24.95%.

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--The given question is incomplete; the complete question is

"A k out of n system is one in which there is a group of n components, and the system will function if at least k of the components function. For a certain 4 out of 6 systems, assume that on a rainy day, each component has a probability of 0.5 of functioning and that on a non-rainy day, each component has a probability of 0.8 of functioning.

Assume that the probability of rain tomorrow is 0.20. What is the probability that the system will function tomorrow?"--

The relation "r" on the set of all integers, where x = y^2, is not reflexive.

A relation is reflexive if every element in the set is related to itself. In this case, for the relation x = y^2 to be reflexive, every integer "x" should be related to itself, meaning that x = x^2. However, this is not true for all integers.

For example, if we consider x = 2, it is not equal to 2^2 = 4. Similarly, if we consider x = -3, it is not equal to (-3)^2 = 9.

Since there are integers that do not satisfy the condition x = x^2, the relation x = y^2 is not reflexive on the set of all integers.

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Answer:

the answer is 62

Step-by-step explanation:

57+(-4)+9

53+9=62

The correlation coefficient of 0.49 indicates a moderate positive relationship between study times and test scores. This suggests that as study times increase, there is a tendency for test scores to also increase. However, the relationship is not extremely strong.

The correlation coefficient, denoted by 'r', ranges from -1 to 1. A positive value indicates a positive relationship, meaning that as one variable increases, the other tends to increase as well. In this case, the correlation coefficient of 0.49 indicates a moderate positive relationship between study times and test scores.

It's important to note that the correlation coefficient of 0.49 falls between 0 and 1, closer to 1. This suggests that there is a tendency for test scores to increase as study times increase, but the relationship is not extremely strong. Other factors may also influence test scores, and the correlation coefficient does not imply causation.

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Using polynomial concepts, it is found that the sorting of the polynomial expressions from least to greatest based on their degree is given by: I, III, II, IV.

The degree of a polynomial is given by it's largest exponent.

In this problem, the polynomials are given by:

Hence, the respective degrees are: 1, 3, 2, 4, and the ordering from least to greatest is: I, III, II, IV.

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The transformation of f(x) to g(x) is g(x) = (x + 6)² + 4

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

The functions f(x) and g(x)

Where, we have

f(x) = x²

The translation 6 units left and 4 units up means that

g(x) = f(x + 6) + 4

So, we have

g(x) = (x + 6)² + 4

This means that the transformation of f(x) to g(x) is g(x) = (x + 6)² + 4

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Answer:

C)1m

Step-by-step explanation:

So the length and width is

x²-13x+42=0

(x-7)(x-6)=0

x-7=0

x-6=0

x=7 (length)

x=6 (width)

So the difference between length and width is

=7-6

=1m

Answer:

\(C.1\ m\)

Step-by-step explanation:

\(We\ are\ given\ that,\\Area\ of\ the\ rectangle=x^2+13x+42\\Hence\ lets\ factorize\ this\ area\ completely:\\x^2+13x+42\\=x^2+6x+7x+42\\=x(x+6)+7(x+6)\\=(x+7)(x+6)\\Hence,\\Area\ of\ the\ rectangle=(x+7)(x+6)\\As\ we\ know\ that,\\Area\ of\ a\ rectangle=Length*Width\\Area\ of\ a\ rectangle=lw\\Here,\\lw=(x+7)(x+6)\\Hence,\\l=(x+7),w=(x+6)\ or\ l=(x+6),w=(x+7)\\But\ generally\ the\ length\ of\ a\ rectangle\ is\ greater\ than\ it's\ width.\\Hence\ the\ first\ solution\ is\ suitable\ here.\\\)

\(Hence,\\l=(x+7),w=(x+6)\\Hence\ in\ order\ to\ find\ the\ difference\ between\ the\ length\ and\ width\\ we\ must\ perform\ the\ operation :l-w\\Hence,\\(x+7)-(x+6)\\=x+7-x-6\\=1\ m\)

All of the following equations have the same solution except x + 6.5 = 6.3   , the correct option is (c) .

In the question ,

four equations are given ,

we have to select the option that has a different solution form the given options .

Part(a) the equation is 7.5x = 1.5

simplifying further ,

we get ,

x = 1.5/7.5 = 0.2

Part(b) the equation is x/5 = 0.04

simplifying further ,

we get ,

x = 5*0.04 = 0.2

Part(c) the equation is x + 6.5 = 6.3

simplifying further ,

we get ,

x = 6.3 - 6.5 = -0.2

Part(d) the equation is -1.8 + x = -1.6

simplifying further ,

we get ,

x = -1.6 + 1.8 = 0.2

Therefore , the equation that is having a different solution (x = -0.2) is (c) x + 6.5 = 6.3   .

The given question is incomplete , the complete question is

All of the following equations have the same solution except _____.

(a) 7.5x = 1.5

(b) x/5 = 0.04

(c) x + 6.5 = 6.3

(d) -1.8 + x = -1.6

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