what is the slope of the line given by the equation?

Answer:

what is the amount of money Kim earn per hour of babysitting? Also I need to know how much trip cost to find out how many hours she need to work.

Step-by-step explanation:

Answer:

85 can

Step-by-step explanation:

21 x 4 = 84

Then you add one more because there is still 1/4 of a pint left and each cup can hold that much too.

Answer: The angles at each vertex of the rectangle are right angles

Step-by-step explanation:

The correct statement can be used to justify the first step is,

⇒ The angles at each vertex of the rectangle are right angles.

An angle is a combination of two rays (half-lines) with a common endpoint. The latter is known as the vertex of the angle and the rays as the sides, sometimes as the legs and sometimes the arms of the angle.

Given that;

The diagram below shows rectangle RSTU with two diagonals drawn.

Here, Justin wrote the following steps;

1. m ∠STR + m ∠RTU = 90°

2. m ∠RTU = 27

3. 6x -  15 = 27

4. 6x = 42

5. x = 7

Thus, The correct statement can be used to justify the first step is,

⇒ The angles at each vertex of the rectangle are right angles.

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Given that 16 families went on a trip and the cost of the trip was Rs. 2,16,352.The amount paid by each family is to be determined by unitary method Hence each family paid Rs.13522

Now, let's solve this by using the method of unitary method. To find the cost of 1 family trip, we will divide the total cost of the trip by the number of families.2,16,352 / 16 = 13,522 So, the cost of the trip per family is Rs. 13,522.Hence, each family paid Rs. 13,522 for the trip.

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Answer:

Step-by-step explanation

1. The total cost of the trip for all 16 families is Rs 2,16,352.
2. To find out how much each family paid, we need to divide the total cost by the number of families: Rs 2,16,352 ÷ 16.
3. When we do the division, we get the result: Rs 13,522.

Now let's check if this result is correct:

1. If each family paid Rs 13,522 for the trip, then the total cost for all 16 families would be: 16 × Rs 13,522 = Rs 2,16,352.
2. This is exactly the same as the total cost given in the problem statement.

So we have shown that each family paid **Rs 13,522** for the trip

Explanation:

A = set of odd numbers = {1,3,5}

B = set of factors of 12 = {1,2,3,4,6}

A U B = union of set A and set B

A U B = {1,3,5} union {1,2,3,4,6}

A U B = {1,3,5,       1,2,3,4,6}

A U B = {1,2,3,4,5,6}

The set union operation combines two sets into one bigger set. Duplicates are tossed out.

There are 6 elements in the set A U B = {1,2,3,4,5,6} out of 6 faces of the number cube.

Therefore, the probability event  A U B happens is 6/6 = 1 = 100%; i.e. it is guaranteed to happen. Each face of the number cube is either odd, a factor of 12, or both.

Side notes:

Given the following five-number summary: 2.9, 5.7, 10.0, 13.2, 21.1, so Q₁ = 5.7. This can be solved using the concept of quartile.

A kind of percentile is a quartile. The first quartile (Q₁, or the lowest quartile), which corresponds to the 25th percentile of the data, is below which 25% of the data are found. The second quartile (Q₂, or the median), which represents the 50th percentile, indicates that 50% of the data are below this quartile.

There are 5 data points, and the middle value of the lower half of the data set will represent the first quartile. So the second data value is the first quartile. So, Q₁ = 5.7

There are 5 data points, and the middle value of the upper half of the data set will represent the third quartile. The fourth data value is the third quartile. So,

Q₃ = 13.2

SO IQR will be:

= Q₃ - Q₁

= 13.7 - 5.1

= 7.5

Thus, Q₁ = 5.7

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Answer:

Step-by-step explanation:

Answer:

undefined

Step-by-step explanation:

because

the figure does not appear

Answer:

x = 15

Step-by-step explanation:

3x+1+4x-3 = 103

7x = 105

x = 15

The order of the rotational symmetry of the figure is

Rotational symmetry refers to the property of an object or shape that remains unchanged or appears the same after a rotation of a certain angle around a fixed point called the center of rotation.

The degree  or order of rotational symmetry of an object is determined by the number of distinct positions in which it looks the same during a full rotation of 360 degrees (or 2π radians).

In this case the figure will have only one rotational symmetry

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Answer:

The answer to your problem is, D. The range is the best measure of variability, and it equals 32.

Step-by-step explanation:

We know the scores earned in a flower-growing competition are represented in the stem-and-leaf plot.

The key will equal 2|1 means 21

Which we conclude to 17, 19, 21, 25, 29, 30, 31, 32, 46, 49.

Quartile:

Median, Minimum, Maximum, & Range:

Thus the answer to your problem is, D. The range is the best measure of variability, and it equals 32.

Answer:

7

Step-by-step explanation:

Answer:

m=7

Step-by-step explanation:

Answer:

\(volume = 927,587.2ft^3\)

Step-by-step explanation:

The equation to find the volume of a sphere is as follows:

\(volume = \frac{4}{3}\pi r^3\)

We have a radius of 60.5ft, let's plug this into the equation and solve:

\(volume = \frac{4}{3} \pi (60.5)^3 \\volume = 927,587.17\\volume = 927,587.2\)

Therefore, the volume of a sphere with a radius of 60.5ft is 927,587.2ft^3.

Hope this helps!!

- Kay :)

Volume of the sphere is 927587.2 cubic feet (nearest tenth).

"A sphere is a set of points in space that are a given distance r from the center. The volume of a 3 -dimensional solid is the amount of space it occupies."

Formula to find the volume of a sphere

Volume of the sphere = \(\frac{4}{3} \pi r^{3}\)

V = \(\frac{4}{3} \pi (60.5)^{3}\)

V = 927,587.167

Using calculator, we get

V ≅ 927587.2 cubic feet

Hence, Volume of the sphere is 927587.2 cubic feet (nearest tenth).

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Answer:

Step-by-step explanation:

The formula for the volume of a cone is:

V = (1/3)πr^2h

where V is the volume of the cone, r is the radius of the base, and h is the height of the cone.

Substituting the given values, we have:

V = (1/3)π(10 mm)^2(6 mm)

V = (1/3)π(100 mm^2)(6 mm)

V = (1/3)π(600 mm^3)

V = 200π mm^3

Using a calculator to approximate π to 3.14, we get:

V ≈ 628.32 mm^3

Therefore, the answer is O 628 mm³.

Answer: A

Step-by-step explanation:

There are 2 ways to solve this problem.

Solution 1:

Since we are given two equations, we set them equal to each other to find where they intersect, the solution.

3x+3=-2x+3                              [combine like terms]

5x=0                                         [divide both sides by 5]

x=0

Now that we have x=0, we can plug it into either equation to find the point of intersection.

y=3(0)+3

y=3

We know that the point of intersection is (0,3).

-------------------------------------------------------------------------------------------------------------

Solution 2:

This way of solving the problem doesn't require any calculations. All it requires is an understanding of slope-intercept form equation. From the two equations given, we know that they are linear lines. Linear lines can only intersect once. Knowing this, we know that there can only be exactly one solution.

First, we compute f(x) for each x in the domain:

Therefore, the graph of the function is as follows:

The only matrix that is certainly symmetric is a)\((a^2 - b^2).\)

We know that a matrix A is symmetric if it is equal to its transpose, that is \(A = A^T.\)

a) \((a^2 - b^2)\)

We can write the transpose of this matrix as

\((a^2 - b^2)^T = (a^2)^T - (b^2)^T = a^2 - b^2\), which is equal to the original matrix. Therefore, this matrix is symmetric.

b) (A+B)(A-B)

Expanding this expression, we get \((A+B)(A-B) = A^2 - AB + BA - B^2.\)

Taking the transpose of this, we get \((A^2)^T - (AB)^T + (BA)^T - (B^2)^T = A^2 - BA + AB - B^2.\)

Since AB and BA may not be equal, we cannot say for certain that this matrix is symmetric.

c) ABA

Taking the transpose of this matrix, we get\((ABA)^T = A^T B^T A^T\). Since \(A^T and B^T\) may not commute, we cannot say for certain that this matrix is symmetric.

d) ABAB

Taking the transpose of this matrix, we get \((ABAB)^T = B^T A^T B^T A^T\). Again, since \(A^T and B^T\) may not commute, we cannot say for certain that this matrix is symmetric.

Therefore, the only matrix that is certainly symmetric is a) \((a^2 - b^2).\)

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The alternative hypothesis is Ha : μa ≠ μb Ha : μa - μb ≠ 0

Since they want to find out if the difference in the mean times spent studying by the students of the two schools is statistically significant, it means that it is a two directional test. Also called a two tailed test. The hypothesis would be as follows:

Null Hypothesis: There is no difference in the mean times spent by the schools' students.

Alternative Hypothesis: There is at least some difference in the mean times spent by the schools' students.

By using the appropriate symbols, it becomes

The null hypothesis is

H0 : μa = μb H0 : μa - μb = 0

The alternative hypothesis is

Ha : μa ≠ μb Ha : μa - μb ≠ 0

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Answer:

a = 4, b = - 5, c = 5

Step-by-step explanation:

Expand the product of factors on the left side and compare like terms on both sides.

(3x - 1)(ax + b) ← expand using FOIL

= 3ax² + 3bx - ax - b

= 3ax² + (3b - a)x - b

Equating coefficients of like terms with 12x² - 19x + c , then

3a = 12 ( divide both sides by 3 )

a = 4

3b - a = - 19

3b - 4 = - 19 ( add 4 to both sides )

3b = - 15 ( divide both sides by 3 )

b = - 5

c = - b = - ( - 5) = 5

Answer:

30

Step-by-step explanation:

150/5 = 30

Answer: 30

Step-by-step explanation:

Answer:

It is integer and rational .....

Step-by-step explanation:

Hope it helps

Answer:

Oook, quick setup: pick a cartesian plane, be \((0;y(t))\)the position of the helicopter as time passes, and \((x(t);0)\) your position as you start running. In my horrible sketch, the green line is the distance when you start running, the red line is the distance you need,  in general what you want is to move one end of the segment up, the other right, and stretch it.

That distance is easily found with the formula for the distance between two points in the plane, or \(d=\sqrt{(\Delta x)^2+(\Delta y)^2}= \sqrt{x^2(t)+y^2(t)}\) (playing a bit with the squares). At this point we need to write down expressions for both \(x(t), y(t)\) and find at what value of t we need to evaluate our distance.

For the sake of semplicity, let's start measuring times the moment you start running. Since speed is constant, both expressions will be of the form \(s=vt+s_0\)

The equation for the runner becomes simply \(x(t)=10t\), since you haven't moved until the heli is high enough.

The equation of the helicopter is \(y=25t+30\) since the heli is 30ft above ground when you start running.

Finally, we need to know how many seconds have passed when the heli is at 60 ft above ground. that happens when \(60=25t+30 \rightarrow t=\frac{30}{25} = 1.20s\). in this time, you are at  \(x(1.2)=10(1.2)=12ft\) from the origin.

Plugging it in the distance formula you get: \(\sqrt{12^2+60^2}= \sqrt{144+3600}=4\sqrt {234}\approx 61.2ft\)

Answer:

To find the quotient of 3 divided by 1/6 you must multiply by the reciprocal of the fraction, in this case it is 6.

So you would rewrite it as,

3*6=18

So your answer is multiply 3 by 6.

P.S * represents multiplication.

Step-by-step explanation:

The total area from the graph is 2.737.

Area is the amount of space occupied by a two-dimensional figure. In other words, it is the quantity that measures the number of unit squares that cover the surface of a closed figure. The standard unit of area is square units which is generally represented as square inches, square feet, etc.

First of all, lets calculate the points of intersection (P, Q, R)

x²+3=(x+2) +5

x²-2=√(x+2)

x⁴+4-4x²=x+2

x⁴-4x²-x+2=0

(x-2)(x³+2x²-1)=0

(x-2)(x+1)(x²+x-1)=0

x=2, -1, -1±√(1+4)/2

Clearly, the x-coordinate of Q is -1, P is -1-√5/2, R is -1+√5/2, S is 2

So the limit of integration will be

P( (-1-√5)/2, (-1-√5/2)² +3)=P((-1-√5)/2, (3+√5/2))

Q(-1, (-1)²+3)=Q(-1, 4)

Area A:

\(\int\limits^\frac{3+\sqrt{5} }{2} _4 {-\sqrt{-y-3}-((y-5)^2 -2)} \, dx\)

= \([\frac{-(y-3)^\frac{3}{2} }{\frac{3}{2} }-\frac{(y-5)^3}{3}+3y]^{\frac{3+\sqrt{5} }{2} }_4\)

= 2.07

Area B:

\(\int\limits^\frac{-1+\sqrt{5} }{2} _4 {-\sqrt{x+2}+5-(x^2+3)} \, dx\)

= \([\frac{-(x+2)^\frac{3}{2} }{\frac{3}{2} }+5x-\frac{x^3}{3}-3x]^{\frac{-1+\sqrt{5} }{2} }_{-1}\)

= 0.667

Total area = 2.07+0.667

= 2.737

Therefore, the total area from the graph is 2.737.

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An equation that relates Juan's age j to Maria's age m can be expressed as j = m + x, where x is the age difference between Juan and Maria.

An equation is a pair of algebraic equations with the equal sign (=) in the middle and the same value.

Given:

Amara is 18 years old.

Let's assume that Amara is y years younger than Maria, then we can write an equation relating their ages as:

Amara's age = Maria's age - y

Substituting Amara's age as 18 in the above equation, we get:

18 = m - y

Rearranging the equation, we get:

m = 18 + y

Therefore, an equation that relates Amara's age to Maria's age m is

m = 18 + y.

Therefore, we don't have enough information to determine Maria's age as we don't know the value of y.

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if you divide "1" into two equal parts, each part would be 0.5. If you divide it into four equal parts, each part would be 0.25.

The concept of "1" in mathematics typically represents a whole unit or a single entity. However, your question about how many parts "1" equals to requires clarification. If you are referring to dividing a whole into parts, then "1" can be divided into any number of parts, as long as each part is equal.

For instance, if you divide "1" into two equal parts, each part would be 0.5. If you divide it into four equal parts, each part would be 0.25, and so on. In this context, "1" can be divided into an infinite number of parts, depending on the desired level of precision or subdivision.

On the other hand, if you are referring to expressing "1" as a fraction or a ratio, it can be written as 1/1 or 1:1, indicating that there is one part in total, and that one part is the whole itself.

In this case, "1" is not divided into multiple parts but represents the entirety of a single unit.

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The solution to the variables are x = 7 and y = 4

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

Shape = Triangle

The marks on the triangles imply that

So, we have the following representation

3x - 5 = 5y - 4

3x - 5 = y + 12

Substitute 3x - 5 = y + 12 in 3x - 5 = 5y - 4

y + 12 = 5y - 4

Evaluate the like terms

4y = 16

So, we have

y = 4

Substitute y = 4 in 3x - 5 = y + 12

3x - 5 = 4 + 12

So, we have

3x = 21

This gives

x = 7

Hence, the values are x = 7 and y = 4

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The sequence that represents the arithmetic sequence will be {-6, 1, 8, 15, 22,...}. Then the correct option is A.

Arithmetic succession or arithmetic sequential is a numerical series in which the difference between subsequent terms is uniform.

Let's check all the options, then we have

A.  {-6, 1, 8, 15, 22,...}, then the common difference is given as,

d = 1 - (-6) = 8 - 1 =

d = 7 =  7

B.  {64, 32, 16, 8, 4,...}, then the common difference is given as,

d = 32 - 64 = 16 - 32
d = -32 ≠ - 16

C.  {1, 2, 4, 8, 16,...}, then the common difference is given as,

d = 1 - 2 = 2 - 4

d = - 1 ≠ - 2

D.  {1, 3, 6, 10, 15,...}, then the common difference is given as,

d = 1 - 3 = 3 - 6

d = - 2 ≠ - 3

The sequence that represents the arithmetic sequence will be {-6, 1, 8, 15, 22,...}. Then the correct option is A.

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Answer:

a )i) 0.117

ii)0.4126

b)0.7769