send help my way please​

Answer:

9 is the constan trate of change.

Step-by-step explanation:

Assuming two points of the graph with the form as P=(x,y) you can find the constant rate m using the slope formula.  

m=(y2-y1)/(x2-x1)

Lets say that P1=(0,0) and P2=(1,9), then:  

m= (9 – 0)/(1-0)

m=9

Therefore, the point (0,0) means that when you are not buying any t-shirt then you dont have any waste of money. The point (1,9) means that when you are buying one t-shirt then you have to pay 9 then its result that cost of each t-shirt is 9 so when you are buying two t-shirt then you  have to pay 18, when you are buying three you have to pay 27 likewise.

Answer:

110.5mm

Step-by-step explanation:

Formula : a = hb/2

a = 13(17)/2

221/2 = 110.5

According to the image we can infer that both figures are similar. Their ratio is 11:4; their scale factor is 1:2 and their areas are: 40cm² and 14.54cm²

We know that the two figures are similar because they have the same angles. Therefore they are similar. In this case it can be inferred that they have a scale factor close to half because the small triangle represents more or less half of the large triangle.

The value of the ratio can be found taking as reference the measurements of the base of the triangles. Then it would be a ratio of 11:4, that is to say that for every 11cm of large triangle, the small one has a 4cm base.

Finally, if the area of the large triangle is 40cm², the area of the small triangle would be the following:

11cm base = 40cm²

4 cm base = cm²

4 * 40 / 11 = 14.54cm²

Yes they are similar because they have the same angle values.

According to the graph we can infer that the scale factor of the similarity transformation that takes ABC to CDE is 1:2.

According to the information, we can infer that the ratio of the area of both triangles is 11:4 because those values correspond to their base length.

if the area of the large triangle is 40cm², the area of the small triangle would be the following:

11cm base = 40cm²

4 cm base = cm²

4 * 40 / 11 = 14.54cm²

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Answer:

The answer is C : 2

Hope this helps!

To find a basis for the solution space of the homogeneous system of linear equations, we need to find the vectors that satisfy the equations when all the variables (x, y, z) are set to zero.

The given system of equations is:

−x + y + z = 0    ...(1)

2x - y = 0         ...(2)

4x - 5y - 6z = 0  ...(3)

To solve this system, we can use the method of Gaussian elimination.

Performing row operations on the augmented matrix [A|0]:

Row1: −x + y + z = 0

Row2: 2x - y = 0

Row3: 4x - 5y - 6z = 0

We can eliminate x from Row2 and Row3 by multiplying Row1 by 2 and adding it to Row2, and multiplying Row1 by 4 and adding it to Row3:

Row1: −x + y + z = 0

Row2: 0x + 3y + 2z = 0

Row3: 0x + y - 2z = 0

Simplifying Row2 and Row3:

Row2: 3y + 2z = 0

Row3: y - 2z = 0

Now we can express y and z in terms of a parameter:

y = -2z

z = t   (where t is the parameter)

Substituting these values back into Row1:

−x + (-2z) + z = 0

−x - z = 0

x = -t

Therefore, the solutions to the system of equations can be expressed as:

x = -t

y = -2z

z = t

In vector form, the solutions can be written as:

[ x , y , z ] = [ -t , -2z , t ] = t [ -1 , 0 , 1 ] + z [ 0 , -2 , 0 ]

Now we have two vectors that span the solution space:

v1 = [ -1 , 0 , 1 ]

v2 = [ 0 , -2 , 0 ]

The basis for the solution space is { v1, v2 }. Since we have two linearly independent vectors, the dimension of the solution space is 2.

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The given homogeneous system of linear equations can be represented as a matrix equation AX = 0, where A is the coefficient matrix and X is the column vector of variables.

To find a basis for the solution space, we can perform row reduction on the augmented matrix [A|0] and identify the pivot columns. The variables corresponding to the non-pivot columns form a basis for the solution space. In this case, the solution space is one-dimensional.

The given homogeneous system of linear equations can be represented in matrix form as:

| -1  1  1 |   | x |   | 0 |

|  2 -1  0 | * | y | = | 0 |

|  4 -5 -6 |   | z |   | 0 |

We construct the augmented matrix [A|0]:

| -1  1  1 | 0 |

|  2 -1  0 | 0 |

|  4 -5 -6 | 0 |

Next, we perform row reduction on the augmented matrix to find the row echelon form:

| 1  -1  -1 | 0 |

| 0  -3  -2 | 0 |

| 0   0   0 | 0 |

From the row echelon form, we observe that the first and second columns are pivot columns (leading 1's), while the third column is a non-pivot column.

Let's denote the variables x, y, and z as x = t, y = s, and z = r, where t, s, and r are arbitrary scalars.

From the row echelon form, we have the equations:

x - y - z = 0      (equation 1)

-3y - 2z = 0       (equation 2)

Substituting the values of y and z in terms of s and r from equation 2 into equation 1:

x = y + z = s + r

Hence, the solution to the system is given by x = s + r, y = s, and z = r.

We can express this solution in vector form as X = s * [1, 1, 0] + r * [1, 0, 1], where s and r are scalars.

Therefore, the solution space of the homogeneous system is spanned by the vectors [1, 1, 0] and [1, 0, 1]. Since these two vectors are linearly independent, they form a basis for the solution space. Thus, the dimension of the solution space is 2.

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Answer

The Answer is C) 2, -6

Step-by-step explanation:

Look at the graph as you can see there is only one solution to that graph and on the line intersected there is one point which that would be 2, -6.

Note: Understand that when asking about the point or something else look for the lines intersected each other then you could find your answer. If there is only one line then it is infinite solutions but if the lines don't intersect then it is a no solution.

Have a good day :)

Reject the claim by accepting H0.

What is null hypothesis and alternate hypothesis?

The null hypothesis and the alternative hypothesis are types of conjectures used in statistical tests, which are formal methods of reaching conclusions or making decisions on the basis of data.

Explanation for the answer:

Mean of observations, x bar \(=\frac{(23+19+23+23)}{4}=22\)

Then for each number: subtract the Mean and square the result:

\(1+9+1+1=12\)

Sample Variance:

       \(\frac{12}{3} = 4\)

Sample Standard Deviation:

\(\sqrt{4} = 2\)\((\sqrt{4})^{0.5} = 1.1412\)

Standard error,

  \(se = (\frac{s}{n} )^{0.5}\)

\(se = (\frac{1.1412}{4} )^{0.5}\)

\(se = 0.5341\)

Hypothesis,

\(H_0: Xbar \geq 21, against\)

\(H_1: Xbar < 21\\\)  (Lower tailed test)        

t-statistic:  

\(t-statistic=\frac{xbar-Xbar}{se}=\frac{22-21}{0.5341}=1.8723\)

p value for 3 (=n-1) degrees of freedom = 0.039805 or 3.9805%

As p-value < 1% (level of significance), so, we reject the null hypothesis. Hence, the mean running time of runners is not significantly atleast 21 miles.    

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The graph that matches the given linear inequality is (B) .

In the question ,

it is given that

the linear inequality is y \(>\) -x + 4

on rewriting the inequality

we get

x + y \(>\) 4

to plot the inequality , we need points to plot .

So ,when x = 0 , we have y = 4

and when y = 0 , we have x = 4

so the two points are (0,4) and (4,0) .

For shading the inequality , we put x = 0 and y = 0 ,

and get 0+0 > 4

0>4 , the result is False , So , the shaded region will be away from the origin which is shown in option (b) .

Therefore , The graph that matches the given linear inequality is (B) .

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Answer:

12/13

Step-by-step explanation:

The probability of not drawing an ace is =

1 minus the probability of drawing an ace.

there are 4 aces in a deck

hence the probability of not drawing an ace =

1 - \(\frac{4}{52}\)

= 48/52 = 12/13

The required probability of not drawing an ace would be 12/13.

Probability is defined as the possibility of an event being equal to the ratio of the number of favorable outcomes and the total number of outcomes.

You draw a card from a standard deck of 52 playing cards.

The probability of not drawing an ace is P(E)

There are 4 aces in a deck

So the number of favorable outcomes n(E)= 4

And the total number of outcomes n(S) = 52

Thus, the probability of drawing an ace = n(E)/n(S) = 4 / 52

The probability of not drawing an ace will be:

⇒ P(E) = 1 - n(E)/n(S)

⇒ P(E) = 1 - 4 / 52

⇒ P(E) = 48/52

⇒ P(E) = 12/13

Therefore, the required probability of not drawing an ace would be 12/13.

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Answer:

She can drive for 379 miles.

Step-by-step explanation:

158/ 2.5=63.2=63

63.2*6=379.2=379

Step-by-step explanation:

since sqrt(25)×sqrt(25) = 25, then x can be any number, because x = x in all cases. and then both sides of the equation are always equal, no matter what value we give x, as long as x is a factor in both sides.

sqrt(25)×x×sqrt(25) = 25x

is always true for every x.

if the question would be

sqrt(25)×x×sqrt(25) = 25

then the answer can only be x = 1. because for every other value of x the equality is destroyed.

The 0.085x in the expression represents the sales amount

The expression is given as

(0.085x) + (x−80)

On the expression, we have the following representation:

Sales tax = 8.5%

This means that

Sales amount = Sales tax * x

So, we have

Sales amount = 8.5% * x

Express 8.5% as 0.085

So, we have

Sales amount = 0.085 * x

Evaluate

Sales amount = 0.085x

Hence, 0.085x represents the sales amount

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Answer:

1

Step-by-step explanation:

p ÷ 5 - 2, If p = 15

15/5 - 2

(15/5=3)

3 - 2 = 1

1 is the answer

To find the inverse of a function, we switch out every x for a y and vice-versa.

Original: y = 4x + 8

Flipped: x = 4y + 8

Now, we solve for y again to put this equation into slope-intercept form.

x = 4y + 8

4y = x - 8

y = 1/4x - 2

h(x) = 1/4x - 2

Hope this helps!

Answer:

De value of k is 9

Step-by-step explanation:

6,-1

b(1,3)

(k,8)

am using bodmas

a6-1×1=6a

b1×3=3b

abc=8

6a+3b+8=17-8

=9

Respuesta:

x = 5.656854249

Explicación paso a paso:

[NOTA: Solo quería disculparme de antemano por cualquier mala gramática, ya que estoy usando un traductor para esto.]

x/Sen30°= 8/Sen45° [Multiplica ambos lados por Sen30°]

x = (8/Sen45°) * Sen30° [Resuelve usando una calculadora]

x = 5.656854249

Answer:

-5FStep-by-step explanation:

10-5x3=-5 F

The correct answer is  ITIL (Information Technology Infrastructure Library). The acronym that best fits this description is "ITIL" or Information Technology Infrastructure Library.

ITIL is a framework that provides guidelines for IT service management and includes a set of best practices for managing IT services. ITIL helps organizations to achieve their objectives by establishing appropriate controls to ensure minimum errors and maximizing the benefits of an information system. ITIL (Information Technology Infrastructure Library) is a set of best practices that helps an organization to maximize the benefits of an information system, while at the same time establishing appropriate controls to ensure minimum errors.

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The height of the hot air ballon can be modeled with the linear equation:

y = 300 + 900*x

Remember that a linear equation is written as:

y = a*x + b

Where a is the slope and b is the y-intercept.

Let's define the variables that we need to use for this problem:

y = height of the hot air balloon.

x = time in minutes.

We know that initially, the height of the balloon is at a height of 300 feet, and then it ascends at a constant rate of 900 feet per minute,

So after x minutes, the height will be modeled by the linear equation:

y = 300 + 900*x

Where the y-intercept is 300, the initial height, and the slope is 900, the rate of change.

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This means that for every unit increase in the x-coordinate, the y-coordinate decreases by 11/12 units.To find the slope of the line that contains the points (-3, -5/2) and (3, -8), we can use the formula for slope:

slope = (y₂ - y₁) / (x₂ - x₁)

Let's plug in the given coordinates into the formula:

slope = (-8 - (-5/2)) / (3 - (-3))

Simplifying the numerator and denominator:

slope = (-8 + 5/2) / (3 + 3)

To combine the fractions in the numerator, we need a common denominator:

slope = (-16/2 + 5/2) / 6

slope = (-11/2) / 6

To divide fractions, we multiply the numerator by the reciprocal of the denominator:

slope = (-11/2) * (1/6)

Simplifying the multiplication:

slope = -11/12

Therefore, the slope of the line that contains the points (-3, -5/2) and (3, -8) is -11/12.

The negative sign indicates that the line is sloping downwards from left to right. The magnitude of the slope (11/12) represents the steepness of the line.

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Answer:  None of the above

The central bank of the US is the Federal Reserve.

The product of algebraic expression is \(\rm 2d^3 - 7d^2- 103d + 36\).

We have to determine

What is the product of d - 9 and 2d^2+11d-4?

The product of the algebraic expressions is also an algebraic expression. Lastly, simplify the algebraic expression by the fundamental operations of terms for combining the like terms.

Therefore,

The product of algebraic expression is;

\(\rm = (d - 9) \times (2d^2 + 11d - 4)\\\\= d (2d^2 + 11d - 4)-9 (2d^2 + 11d - 4)\\\\= 2d^3+11d^2-4d-18d^2-99d+36\\\\=2d^3 - 7d^2- 103d + 36\)

Hence, the product of algebraic expression is \(\rm 2d^3 - 7d^2- 103d + 36\).

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Answer:

A. 2d3 – 7d2 – 103d + 36

Step-by-step explanation:

The angles are classified as follows

angle 1 angle of elevation

angle 2 angle of depression

angle 3 angle of elevation

angle 4 angle of depression

The angle of elevation is the angle between the horizontal plane and the line of sight or upward direction to an object or point that is above the observer. It is usually measured from the observer's eye to the object or point of interest, and is expressed in degrees or radians.

The angle of elevation is commonly used in trigonometry to solve problems involving right triangles and heights of objects.

The angle of depression is the angle between the horizontal plane and the line of sight or downward direction to an object or point that is below the observer. It is measured from the observer's eye to the object or point of interest, and is also expressed in degrees or radians.

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To find the worst-case number of boxes you will have to open to get 5 boxes of the same color from 20 boxes of hats of four different colors, we can use the pigeonhole principle.The pigeonhole principle states that if there are n pigeonholes and more than n pigeons, then there must be at least one pigeonhole with at least two pigeons.

In other words, if there are more items than containers to put them in, then at least one container must have more than one item.In this case, we have 20 boxes and 4 different colors. Without loss of generality, we can assume that we have 5 boxes of each color. So, we can think of this as having 5 pigeonholes (one for each color) and 20 pigeons (one for each box).

We want to find the worst-case scenario for getting 5 boxes of the same color, so we want to minimize the number of boxes we have to open. To do this, we want to maximize the number of boxes we can eliminate with each opening. The best strategy is to open a box of each color at each step. That way, we can eliminate 4 boxes with each step and we can be sure that we won't miss any colors if we get to step 5 without finding 5 boxes of the same color.

The worst-case scenario is when we have opened 16 boxes and still haven't found 5 boxes of the same color. At that point, we must have at least 4 boxes of each color left, and we can eliminate at most 3 of them with each step. So, we need at least 2 more steps to find 5 boxes of the same color. Therefore, the worst-case number of boxes we'll have to open is 16 + 2 × 3 = 22.

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The number of cups of dog food fed to the dog per day is 1.5 cups.

Since the same quantity of dog food is fed to the dog per day, the decrease in the cups of dog food can be modelled with a linear equation. A linear equation is an equation that has one variable that is raised to the power of one.

Number of cups of dog food fed to the dog per day = (cups left after the 8th day - cups left after the 3rd day) / change in the number of days

(108 - 115.5) / (8 - 5)

4.5 / 3 = 1.5 cups

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Answer:

(24) 3 - 4b = 10c + 10

(25) 4(3c+5) = 8

(26) - 6

(27) 4

Step-by-step explanation:

These questions require that words are translated into equations and then may be solved.

(24)  Three minus four times a number is equal to ten times a number plus ten.

let the first number be b.

(a)Three minus four times a number ... can be represented as:

3 - (4 x b) = 3 - 4b

(b) ...ten times a number plus 10

let the other number be c. Therefore we have;

(10 x c) + 10 = 10c + 10

Now, three minus four times a number is equal to ten times a number plus ten means that expressions in (a) and (b) above are equal. i.e

3 - 4b = 10c + 10

(25) Four times the quantity of three times c plus 5 is equal to 8.

(a) four times the quantity of three times c plus 5 can be represented as

4 x (3 x c + 5) = 4(3c + 5)

(b) ... is equal to 8. This means that the expression in (a) is equal to 8.

4(3c + 5) = 8

(26) Six less than two thirds of a number is negative ten. Find the number.

(a) six less than can be represented as:

- 6

(b) two thirds of a number can be represented as

(\(\frac{2}{3}\))x           [where x is the number]

(c) six less than two thirds of a number can thus be written as;

(\(\frac{2}{3}\))x - 6

(d) ... is negative 10 means that the expression is (c) above is equal to -10. i.e

(\(\frac{2}{3}\))x - 6 = -10

(e) Find the number.

The number can be found by solving for x in the expression in (d) above.

(\(\frac{2}{3}\))x - 6 = -10         [multiply through by 3]

2x - 18 = -30        [collect like terms]

2x = -30 + 18

2x = -12               [divide both sides by 2]

x = - 6

Therefore, the number is -6

(27) Twenty-nine is thirteen added to four times a number. What is the number.

(a) ... thirteen added to four times a number can be written as:

13 + 4b         [where the number is b]

(b) Twenty-nine is thirteen added to four times a number means that the 29 is equal to the expression in (a) above. i.e

29 = 13 + 4b

(c) Find the number.

The number can be found by solving for b in the expression in (b) above. i.e

29 = 13 + 4b        [collect like terms]

4b = 29 - 13

4b = 16                [divide both sides by 4]

b = 4

Therefore, the number is 4.

Answer:

5 5/8

Step-by-step explanation:

This is in the simplest form

Answer:

Yes

Step-by-step explanation: