If you are traveling 14 miles per hour, how many inches would you travel in 3 seconds? (1 mile = 5280 feet; 1 foot = 12 inches) (Convert 3 seconds to inches)

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Answer:

x = 1

Step-by-step explanation:

5(2x - 8) + 15 = -15

First, let's move the 15 to the opposite side of the equation. We'll do this by subtracting 15 from BOTH sides of the equation.

5(2x - 8) + 15-15 = -15-15

5(2x-8) + 0 = -30

5(2x-8) = -30

Now let's expand that first term.

5(2x)-5(8) = -30

10x - 40 = -30

Now let's move the -40 to the opposite side of the equation. We'll do this by ADDING 40 to both sides of the equation.

10x - 40 + 40 = -30 + 40

10x -0 = 10

10x = 10

Now to solve for x, we divide BOTH sides by 10 to "isolate the variable" aka get x alone.

10x/10 = 10/10

x = 1

The answer is x = 1.

Let's check if our answer is correct!

Original equation: 5(2x - 8) + 15 = -15

Substitute 1 for x.

5(2*1-8) + 15 =

5(2-8) + 15 =

5(-6) + 15 =

-30 + 15 = -15 >>> which is exactly what we started with! So x is 1.

The angle measure that belongs in the green box is given as follows:

70.67º.

We consider a triangle with side lengths and angles related as follows, as is the case for this problem:

Then the lengths and the sines of the angles are related as follows:

sin(A)/a = sin(B)/b = sin(C)/c.

The relation for this problem is given as follows:

sin(x)/12  = sin(76º)/12.34

Applying cross multiplication, the missing angle measure is given as follows:

sin(x) = 12 x sine of 76 degrees/12.34

sin(x) = 0.9436.

x = arcsin(0.9436)

x = 70.67º.

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Answer:

2 Gallons of Soda

Step-by-step explanation:

that is the answer above

Answer:

The proportions differ from those reported in the survey.

Step-by-step explanation:

The Chi-square goodness of fit test would be used to determine whether the proportions differ from those reported in the survey.

The hypothesis for the test can be defined as follows:

H₀: The proportions does not differ from those reported in the survey.

Hₐ: The proportions differ from those reported in the survey.

Assume that the significance level of the test is, α = 0.01.

The Chi-square test statistic is given by:

\(\chi^{2}=\sum\limits^{n}_{i=1}{\frac{(O_{i}-E_{i})^{2}}{E_{i}}}\)

Consider the Excel sheet provided.

The Chi-square test statistic value is 191.32.

The p-value of the test is:

\(p-value=P(\chi^{2}_{(n-1)}>191.32)\\\\=\text{CHISQ.DIST.RT}(191.32,2)\\\\=0.0000\)

The p-value of the test is very small. The null hypothesis will be rejected at 1% level of significance.

Thus, concluding that the proportions differ from those reported in the survey.

tip: you can use a calculator

Hope you could understand.

If you have any query, feel free to ask.

Answer:

\(\large \boxed{\ \ \dfrac{63}{5} \ \ }\)

Step-by-step explanation:

Hello,

"Find the sum of the following infinite geometric series"

infinite

   We will have to find the limit of something when n tends to \(+\infty\)

geometric series

   This is a good clue, meaning that each term of the series follows a geometric sequence. Let's check that.

The sum is something like

           \(\displaystyle \sum_{k=0}^{+\infty} a_k\)

First of all, we need to find an expression for \(a_k\)

First term is

   \(a_0=7\)

Second term is

    \(a_1=\dfrac{4}{9}\cdot a_0=7*\boxed{\dfrac{4}{9}}=\dfrac{7*4}{9}=\dfrac{28}{9}\)

Then

   \(a_2=\dfrac{4}{9}\cdot a_1=\dfrac{28}{9}*\boxed{\dfrac{4}{9}}=\dfrac{28*4}{9*9}=\dfrac{112}{81}\)

and...

   \(a_3=\dfrac{4}{9}\cdot a_2=\dfrac{112}{81}*\boxed{\dfrac{4}{9}}=\dfrac{112*4}{9*81}=\dfrac{448}{729}\)

Ok we are good, we can express any term for k integer

   \(a_k=a_0\cdot (\dfrac{4}{9})^k\)

So, for n positive integer

\(\displaystyle \sum_{k=0}^{n} a_k=\displaystyle \sum_{k=0}^{n} 7\cdot (\dfrac{4}{9})^k=7\cdot \dfrac{1-(\dfrac{4}{9})^{n+1}}{1-\dfrac{4}{9}}=\dfrac{7*9*[1-(\dfrac{4}{9})^{n+1}]}{9-4}=\dfrac{63}{5}\cdot [1-(\dfrac{4}{9})^{n+1}}]\)

And the limit of that expression when n tends to \(+\infty\) is

   \(\large \boxed{\ \ \dfrac{63}{5} \ \ }\)

as

   \(\dfrac{4}{9}<1\)

Hope this helps.

Do not hesitate if you need further explanation.

Thank you

Part 1

Angles of a quadrilateral add to 360 degrees.

\(7x+65+85+105=360\\\\7x+255=360\\\\7x=105\\\\x=15\)

Part 2

If \(x=15\), then \(7x=105^{\circ}\). Thus, the angles measuring \(7x\) and \(105^{\circ}\) are opposite angles since opposite angles of a kite are congruent.

This means the remaining angles, which are the angles measuring \(65^{\circ}\) and \(85^{\circ}\), are also opposite using the process of elimination.

A function's codomain is a subset of its range. Although it is not a true subset, it is conceivable for the range to be equal to the codomain, in which case it is also a subset of the codomain.

A set that includes all or a portion of another set's elements is known as a subset. For instance, because every even integer is also an integer, the set of even integers is a subset of the set of integers. A subset that contains some, but not all, of the members of another set is said to be a proper subset. Because it contains some, but not all, of the positive integers, the set of positive integers less than 10 is a valid subset of the set of positive integers.

A function's codomain is a subset of its range. Although it is not a true subset, it is conceivable for the range to be equal to the codomain, in which case it is also a subset of the codomain.

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Answer:

7.011%

Step-by-step explanation:

61/(300+100+7+61+402) = 0.07011

Multiply the result of that by 100 to get 7.011%.

Answer:

Isolate the angle 2x, by following the reverse "order of operations".

Step-by-step explanation:

Explanation:

Step 1: Add 1 to both sides:

2

cos

2

(

2

x

)

=

1

Step 2: Divide both sides by 2:

cos

2

(

2

x

)

=

1

2

Step 3: Take the square root of both sides:

cos

(

2

x

)

=

√

2

2

or

cos

(

2

x

)

=

−

√

2

2

(don't forget the positive and negative solutions!)

Step 4: Use inverse of cosine to find the angles:

2

x

=

cos

−

1

(

√

2

2

)

or

2

x

=

cos

−

1

(

−

√

2

2

)

Step 5: Find angles that work:

2

x

=

π

4

or

2

x

=

7

π

4

or

2

x

=

3

π

4

or

2

x

=

5

π

4

Step 6: Solve for x:

x

=

π

8

,

7

π

8

,

3

π

8

,

5

π

8

or .785, 5.5, 2.36, 3.93

(decimal approximations are seen on the graph below)

Answer:

1. He kept 8x negative

2. The solution is 8

Step-by-step explanation:

So first of all, we'll simplify -4(7 - 2x):

-4(7) - 4(-2x)

-28 - (-8x)

-28 + 8x <---- The 8x is positive

Next, we'll solve for x:

-4(7 - 2x) = 3(x + 4)

-28 - (-8x) = 3x + 12

  -28 + 8x = 3x + 12

          -3x   -3x

  -28 + 5x = 12

  +28        +28

            5x = 40

         5x/5 = 40/5

                x = 8

Answer:

9

Step-by-step explanation:

You don't need to pass through each edge once.

If we name the top vertex 1 and the bottom vertex 2 then here are the possible combinations:

A-1-B

A-B

A-2-B

A-1-B-A-2-B

A-2-B-A-1-B

A-B-1-A-2-B

A-B-2-A-1-B

A-1-B-2-A-B

A-2-B-1-A-B

Some people say 6 because they think you need to pass through all the edges. But the only restriction with travelling on the edges is you can't pass one twice. The point is read the wording and it becomes easy.

Hope this helps!

Answer:

123.8

Step-by-step explanation:

nearest tenth is 7 and the sixes aftr it are over half of a full decimal, so they round to 123.8

Answer:

Step-by-step explanation:

Figure 1 = (-1,1)

Figure 2 = (-2,5)

So the answer should be x + (-1) and y + (4)

Answer:

Step-by-step explanation:

A) Commission = 2450 shillings * 25 % = 2450 shillings * (25/100) = 2450 shillings * (0.25) = 612.50 shillings

Commission = 612.50 shillings

B) If the total sale is 2,450.00 shillings, after the seller gives buyers a 2% discount. We must re-enter the discount:

2,450.00 shillings = X - X * 2% = X - 0.02 X --->

------> 0.98 X = 2,450.00 shillings

------>X= 2,450.00 / 0.98

------> X = 2,500.00  shillings

NEW COMMISSION = 2,500.00 shillings * 25 % = 2,500.00 shillings *(25/100) =2,500.00 shillings * (0.25) = 625 shillings

NEW COMMISSION = 625 shillings

Answer:

a=4

Step-by-step explanation:

that's the answer . ask me if u don't get it

The expenditure on rent as a percentage of the employee's take-home pay is approximately 17.9%.

What is an expenditure?

we need to calculate the actual expenditure in Ghana cedis (GHS) for each item using the percentages given in the table:

Social security: 5% of GHS 1800 = GHS 90

Income tax: 25% of GHS 1800 = GHS 450

Food: 40% of GHS 1800 = GHS 720

Transport: 10% of GHS 1800 = GHS 180

Rent: 12.5% of GHS 1800 = GHS 225

Others: 7.5% of GHS 1800 = GHS 135

The total actual expenditure is GHS 1800, which matches the gross monthly salary.

To calculate the expenditure on rent as a percentage of the employee's take-home pay, we need to subtract the social security and income tax from the gross salary to get the net salary:

Gross salary: GHS 1800

Social security: GHS 90

Income tax: GHS 450

Net salary: GHS 1800 - GHS 90 - GHS 450 = GHS 1260

Then, we can calculate the percentage of the net salary spent on rent:

Rent: GHS 225

Percentage of net salary: (GHS 225 / GHS 1260) x 100% ≈ 17.9%

Therefore, the expenditure on rent as a percentage of the employee's take-home pay is approximately 17.9%.

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Complete question is: The expenditure on rent as a percentage of the employee's take-home pay is approximately 17.9%.

The length AC in the kite is 8.7 cm.

A kite is a quadrilateral that has two pairs of consecutive equal sides and

perpendicular diagonals. Therefore, let's find the length AC in the kite.

Hence, using Pythagoras's theorem, let's find CE.

Therefore,

7² - 4² = CE²

CE = √49 - 16

CE = √33

CE = √33

Let's find AE as follows:

5²- 4² = AE²

AE = √25 - 16

AE = √9

AE = 3 units

Therefore,

AC = √33 + 3

AC = 5.74456264654 + 3

AC = 8.74456264654

AC = 8.7 units

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No, this shape does not belong in a group of shapes that have more than one pair of perpendicular sides.

In order to determine if the shape belongs to a group of shapes with more than one pair of perpendicular sides, we need to examine the number of right angles in the shape.

A right angle is a 90-degree angle, and shapes with perpendicular sides have right angles at their intersections. By counting the number of right angles in the shape, we can determine if it has more than one pair of perpendicular sides.

If the shape has only one right angle, then it does not have more than one pair of perpendicular sides. But if it has two or more right angles, then it would belong to the group of shapes that have more than one pair of perpendicular sides.

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The surface area and volume of the larger figure are 350 yd² and 3000 yd³ respectively.

The scale factor is a measure for similar figures, who look the same but have different scales or measures. Suppose, two circle looks similar but they could have varying radii. The scale factor states the scale by which a figure is bigger or smaller than the original figure.

In the problem, the scale factor is 1:2 and we have the value of surface area and volume of the smaller figure. To find the surface area and volume of the larger figure, we simply need to multiply the values by two.

Surface area = 175yd²

New surface area = 175 * 2 = 350 yd²

Volume  = 1500 yd³

New volume = 1500 * 2 = 3000yd³

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The required by the principle of mathematical induction, the statement is true for all integers n ≥ 0.

Mathematical induction is a method of proof commonly used in mathematics to prove that a statement is true for all positive integers.

The process involves two steps:

Here,
First, we need to prove the statement is true for the base case n=0,

When n=0, we have,

\(\sum_{i=1}^{1} i * 2^i = 1*2^1 = 2\)

and

\(n * 2^{n+2} + 2 = 0*2^{0+2} + 2 = 2\)

Therefore, the statement is true for n=0.

Next, we assume the statement is true for some arbitrary integer k, meaning:

\(\sum_{i=1}^{k+1} i * 2^i = k * 2^{k+2} + 2\)

We want to show that the statement is also true for n=k+1,

\(\sum_{i=1}^{k+2} i * 2^i = (k+1) * 2^{k+3} + 2\)

We can rewrite the left-hand side of the equation as,

\(=\sum_{i=1}^{k+2} i * 2^i \\= \sum_{i=1}^{k+1} i * 2^i + (k+2) * 2^{k+2} \\= k * 2^{k+2} + 2 + (k+2) * 2^{k+2} \\= (k+1) * 2^{k+3} + 2\)

This last step used the assumption that the statement is true for n=k.

Therefore, by the principle of mathematical induction, the statement is true for all integers n ≥ 0.

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The solution set includes all real numbers less than -5, and all real numbers greater than 1, but does not include -5 or 1 themselves.

Option D is the correct answer.

We have,

We need to isolate the absolute value |x + 2| on one side of the inequality.

We subtract 7 from both sides.

|x + 2| > 3

Next, we can split this inequality into two separate inequalities, one for when the expression inside the absolute value is positive, and one for when it is negative:

x + 2 > 3

or

- (x + 2) > 3

Solving for x in the first inequality.

x > 1

Solving for x in the second inequality.

-x - 2 > 3

Adding 2 to both sides and multiplying by -1.

x < -5

So the solution set for the inequality |x + 2| + 7 > 10 is the set of all x-values that satisfy either x > 1 or x < -5.

Using interval notation.

(-∞, -5) U (1, ∞)

Thus,

The solution set includes all real numbers less than -5, and all real numbers greater than 1, but does not include -5 or 1 themselves.

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The function that would have the greatest value at x = 16 include the following: B. y = x² - 17x + 182.

In Mathematics and Geometry, a function is a mathematical equation which defines and represents the relationship that exists between two or more variables such as an ordered pair in tables or relations.

In this exercise, we would determine the corresponding output value for this function of y based on the x-value (x = 16) in simplified form as follows;

\(y = 10^{16}\)

y = 10,000,000,000,000,000.

y = x² - 17x + 182

y = 16² - 17(16) + 182

y = 256 - 272 + 182

y = 166.

\(y = 1.17^x\\\\y = 1.17^{16}\)

y = 12.330304108137675851908392069373.

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\(101 - 99 = 2\)

101 → 200

99 → 100

\(200 - 100 = 100\)

⇒ the numbers could be: 99 and 101

other pairs of numbers: (199,201), (299,301) ...

According to the data, the average rate of change in the number of crimes per 100 people that occurred from 1920 to 1940 is 0.06

To calculate the average rate of change in the number of crimes per 1000 people that occurred from 1920 to 1940 we have to perform the following procedure:

According to the above, the average rate of change in the number of crimes per 1000 people that occurred from 1920 to 1940 would be 0.06.

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The population is the number of children in gymnastic class = 5.

A parameter is the mean number of steps taken by the 5 children.

What is a parameter?

Four parameters, referred to as hybrid or h Parameters, can be used to assess any linear circuit with input and output terminals. These parameters are one measured in ohm, one in mho, and two dimensionless. Hybrid is short for "mixed." These parameters are referred to as hybrid parameters since they have dual dimensions

Here, we have

Given that,

Suppose that there are 5 children in a gymnastics class.

One day, they count the number of steps each person takes while walking on their hands until they lose balance and come down.

The mean number of steps these children took while walking on their hands is 20 steps.

We have to find the population and parameters.

The area of interest is a particular gymnastic class, therefore all individuals or children belonging to this particular gymnastic class make up the population.

Population = number of children in gymnastic class = 5.

Parameter = mean number of steps taken by the 5 children.

Hence, Population is the number of children in gymnastic class = 5.

A parameter is the mean number of steps taken by the 5 children.

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Using Cramer's rule for first-order condition:

Using Hessian for the second-order condition, critical point (x₁, x₂, x₃) = (-149/444, -69/222, 139/444) is the unique minimum of y.

(a) Using Cramer's rule for the first-order condition:

To optimize the function y, find the critical points where the gradient is equal to zero. The gradient of y is given by:

∇y = [6x₁ - x₂ - 3x₃ - 5, -x₁ + 12x₂ + 2x₃ - 4, 2x₂ + 8x₃ + 2 - 3x₁]

Setting the gradient equal to zero:

6x₁ - x₂ - 3x₃ - 5 = 0 (1)

-x₁ + 12x₂ + 2x₃ - 4 = 0 (2)

2x₂ + 8x₃ + 2 - 3x₁ = 0 (3)

Using Cramer's rule to solve this system of linear equations, the determinant of the coefficient matrix is:

|A| =

| 6 -1 -3 |

|-1 12 2 |

|-3 2 -3|

|A| = 444

The determinant of the matrix obtained by replacing the first column of A with the constants on the right-hand side of the equations is:

|A₁| =

| 5 -1 -3 |

| 0 12 2 |

| 0 2 -3|

|A₁| = -149

The determinant of the matrix obtained by replacing the second column of A with the constants is:

|A₂| =

| 6 5 -3 |

|-1 0 2 |

|-3 0 -3|

|A₂| = -138

The determinant of the matrix obtained by replacing the third column of A with the constants is:

|A₃| =

| 6 -1 5 |

|-1 12 0 |

|-3 2 2|

|A₃| = -278

Therefore, using Cramer's rule:

x₁ = |A₁|/|A| = -149/444

x₂ = |A₂|/|A| = -69/222

x₃ = |A₃|/|A| = 139/444

(b) Using the Hessian for the second-order condition:

To check whether the critical point found in part (a) is a maximum, minimum or saddle point, we need to use the Hessian matrix evaluated at the critical point. The Hessian of y is given by:

(y) =

| 6 0 -3 |

| 0 12 2 |

|-3 2 8 |

Evaluating H(y) at the critical point (x₁, x₂, x₃) = (-149/444, -69/222, 139/444):

H(y) =

| 6 0 -3 |

| 0 12 2 |

|-3 2 8 |

The eigenvalues of H(y) are 2, 6, and 18, which are all positive. Therefore, H(y) is positive definite, and the critical point is a minimum.

Therefore, the critical point (x₁, x₂, x₃) = (-149/444, -69/222, 139/444) is the unique minimum of y.

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