Monica arrives at the dentist office at 12:56 and saw the dentist at 1:33 how long did she wait

Answer:

c

Step-by-step explanation:

the number line says less than 4 so if you solce for all the equations c will be x<4

To answer this question, we need to find the area of the rectangle with sides 14 cm and 9 cm, and, then, we need to subtract from this area, the area of the semicircle with radius = 7 cm (that is, 14 cm /2 = 7 cm).

Therefore, we have:

1. Find the area of the rectangle:

2. Find the area of the semicircle:

The area of a circle is given by:

Therefore, for a semicircle, we have:

Then, we need to subtract this value from the obtained in calculating the area of the rectangle:

From the question, the answer is option D, 49.07 cm squared.

Answer:

5

Step-by-step explanation:

I think you meant 4(x - 3) + 5x - x^2.

Substituting 2 for x, we get 4(-1) + 5(2) - (2)^2 = -1 + 10 - 4  =  5

Answer:

1. The actual height is the measured height.  Therefore the doctor's measurement should be considered the actual height as the doctor measured the height of Clare's brother.

2. The error is the difference between the estimated height and the measured height:

⇒ 4 ft 2 in - 4 ft = 2 inches

3. First convert 4 ft 2 in into inches.

Given 1 ft = 12 inches

Therefore, 4 ft 2 in = 4 x 12 + 2 = 50 inches

\(\mathsf{percentage\ error=\dfrac{difference\ between\ actual\ and\ estimated\ value}{actual\ value}\times100\%}\)

\(\implies \mathsf{percentage\ error=\dfrac{2}{50}\times100\%=4\%}\)

So the error expressed as a percentage was 4% of the actual height.

Answer:

D

Step-by-step explanation:

Answer:

\(\displaystyle \int {\frac{x^3 - 1}{x^2}} \, dx = \frac{x^2}{2} + \frac{1}{x} + C\)

General Formulas and Concepts:

Algebra I

Calculus

Integration

Integration Rule [Reverse Power Rule]:                                                               \(\displaystyle \int {x^n} \, dx = \frac{x^{n + 1}}{n + 1} + C\)

Integration Property [Multiplied Constant]:                                                         \(\displaystyle \int {cf(x)} \, dx = c \int {f(x)} \, dx\)

Integration Property [Addition/Subtraction]:                                                       \(\displaystyle \int {[f(x) \pm g(x)]} \, dx = \int {f(x)} \, dx \pm \int {g(x)} \, dx\)

Step-by-step explanation:

Step 1: Define

Identify

\(\displaystyle \int {\frac{x^3 - 1}{x^2}} \, dx\)

Step 2: Integrate

Topic: AP Calculus AB/BC (Calculus I/I + II)

Unit: Integration

Using proportions, it is found that he bikes:

A proportion is a fraction of a total amount, and the measures are related using a rule of three. Due to this, relations between variables, either direct or inverse proportional, can be built to find the desired measures in the problem.

In this problem, the proportion is that he bikes 9.5 miles each half hour, hence:

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Answer:

x = 139

Step-by-step explanation:

Isosceles triangle.

Let the equal angles = y

y + y + 98 = 180   {Sum of all the angles of triangles}

  2y + 98 = 180

          2y = 180 - 98

          2y = 82

           y = 82/2

          y = 41

x = 41 + 98     { exterior angles equals the sum of interior opposite angles}

x = 139

Answer:

x = 18 and x = 36

Step-by-step explanation:

let unknown value is x

6:x = 1:3

product of means = product of extremes

6*3 = 1 *x

18 = x

x:30=8:5

product of means = product of extremes

5x=180

x=180/5

x=36

Answer:

2g+3

Step-by-step explanation:

Answer:

2g+3

Step-by-step explanation:

Subtract 2g from 4g

Step-by-step explanation:

8 men can do 60 man days of work by dividing 60 man days by the 8 men, which gives us 60/8 = 7 1/2 da

Answer:

The answer is 47200000000

Answer:

C and E

Step-by-step explanation:

Answer:

I believe that the answer is

C and E

Answer:

0.0625

Step-by-step explanation:

You can convert this into a fraction by entering this into a calc

answer

Equilateral Triangle

Answer:

equilateral triangle

Step-by-step explanation:

Answer:

The answer is 119

Step-by-step explanation:

Answer:

119

Step-by-step explanation:

There is a reason why the answer is 119

First, lets take a look at your perfect squares chart ( by tens )

10 x 10 = 100

20 x 20 = 400

30 x 30 = 900

40 x 40 = 1600

50 x 50 = 2500

60 x 60 = 3600

70 x 70 = 4900

80 x 80 = 6400

90 x 90 = 8100

100 x 100 = 10000

110 x 110 = 12100

120 x 120 = 14400

we know that 12100 < 14161 < 14400, so it has to be in between the square root of 110 and the square root of 120

111 x 111 = 12321

112 x 112 = 12544

113 x 113 = 12769

114 x 114 = 12996

115 x 115 = 13225

116 x 116 = 13456

117 x 117 = 13689

118 x 118 = 13924

119 x 119 = 14161

We found out that the square root of 119 = 14161

Therefore, the square root of 119 = 14161

If you want to find out a quicker way to do this, comment me below

Answer:

\(\begin{aligned}SA &= 7.125\pi \text{ in}^2\\& \approx 22.4 \text{ in}^2 \end{aligned}\)

Step-by-step explanation:

We can find the Surface Area of the can by adding the areas of each of its parts:

\(SA = 2( A_{\text{base}}) + A_\text{side}\)

First, we can calculate the area of the circular base:

\(A_{\text{circle}} = \pi r^2\)

\(A_{\text{base}} = \pi (0.75 \text{ in})^2\)

\(A_{\text{base}} = 0.5625\pi \text{ in}^2\)

Next, we can calculate the area of the rectangular side:

\(A_\text{rect} = l \cdot w\)

\(A_\text{side} = (4\text{ in}) \cdot C_\text{base}\)

Since the width of the side is the circumference of the base, we need to calculate that first.

\(C_\text{circle} = 2 \pi r\)

\(C_\text{base} = 2 \pi (0.75 \text{ in})\)

\(C_\text{base} = 1.5 \pi \text{ in}\)

Now, we can plug that back into the equation for the area of the side:

\(A_\text{side} = (4\text{ in}) (1.5\pi \text{ in})\)

\(A_\text{side} = 6\pi \text{ in}^2\)

Finally, we can solve for the surface area of the can by adding the area of each of its parts.

\(SA = 2( A_{\text{base}}) + A_\text{side}\)

\(SA = 2(0.5625\pi \text{ in}^2) + 6\pi \text{ in}^2\)

\(\boxed{SA = 7.125\pi \text{ in}^2}\)

\(\boxed{SA \approx 22.4 \text{ in}^2}\)

If D be a region bounded by a simple closed path C in the xy-plane, then the centroid of the quarter circle is  (4a/3π , 4a/3π)   .

In the question ,

it is given that D is the region bounded by a simple closed path C in the xy-plane .

the radius of the circle is = "a" ,

let the equation of the circle be x² + y² = a² ,

So , the area of the quarter circle is (A)  = (1/4)*πa²

The coordinate of the centroid x will be :

x = \(\frac{1}{2A} \int\limits x^{2} dy\)

x = \(\frac{1}{2(\frac{\pi a^{2} }{4})} \int\limits^a_0 {a^{2} -y^{2} } \, dy\)

Simplifying further ,

we get ,

x = 2/πa² [{a²(a) - a³/3} - 0 ]

x = 2/πa² [a³ - a³/3 ]

x = 4a/3π

The coordinate of the centroid y will be :

y = \(\frac{1}{2A} \int\limits y^{2} dx\)

y = \(\frac{1}{2(\frac{\pi a^{2} }{4})} \int\limits^a_0 {a^{2} -x^{2} } \, dx\)

Simplifying further ,

we get ,

y = 2/πa² [{a²(a) - a³/3} - 0 ]

y = 2/πa² [a³ - a³/3 ]

y = 4a/3π

Therefore , the coordinates of the centroid is (4a/3π , 4a/3π) .

The given question is incomplete , the complete question is

Let D be a region bounded by a simple closed path C in the xy-plane. The coordinates of the centroid x, y of D are x = \(\frac{1}{2A} \int\limits x^{2} dy\)  ,  y = \(\frac{1}{2A} \int\limits y^{2} dx\) ?  

Find the centroid of a quarter-circular region of radius a.

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1) y = -3x and y = -3x + 2: inconsistent system of equations.

2) y = x - 5 and -2x + 2y = - 10: consistent and independent.

3) 2x - 5y = 10 and 3x + y = 15 : consistent and independent.

The given equation are:

The graph for each system of equations is plotted.

1) y = -3x and y = -3x + 2

From the graph 1 it is shown that the lines for the each equation form the parallel lines.

Thus, system of equations are inconsistent.

2) y = x - 5 and -2x + 2y = - 10

From the graph 2 it is shown that the lines for the each equation form the coincident lines.

Thus, system of equations are consistent and independent.

3) 2x - 5y = 10 and 3x + y = 15

From the graph 2 it is shown that the lines for the each equation form the coincident lines.

Thus, system of equations are consistent and independent.

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Answer:

Step-by-step explanation:

Math 311

Set Proofs Handout and Activity

Recall that a set A is a subset of a set B, written A ⊆ B if every element of the set A is also an element of the set B. To show

that one set is a subset of another set using a paragraph proof, we usually use what is called a “general element argument”.

Here is an example:

Example 1: We will prove that A ∩ B ⊂ A

Proof: Let x be an arbitrary element of A ∩ B. By definition of set intersection, since x ∈ A ∩ B, then x ∈ A and x ∈ B.

In particular, x ∈ A. Since every element of A ∩ B is also an element of A, A ∩ B ⊆ A ✷

Since that was a fairly straightforward example, let’s try another.

Example 2: We will prove that If A ⊆ B, then B ⊆ A.

Proof: Let x ∈ B. By definition of set complement, x /∈ B. Recall that since A ⊆ B, whenever y ∈ A, we also have y ∈ B.

Therefore, using contraposition, whenever y /∈ B, we must have y /∈ A. From this, since x /∈ B, then x /∈ A. Therefore x ∈ A.

Hence B ⊆ A. ✷

Lastly, in order to formally prove that two sets are equal, say S = T, we must show that S ⊆ T and that T ⊆ S. This will

require two general element arguments.

Example 3: We will prove that A ∪ (B ∩ C) = (A ∪ B) ∩ (A ∪ C).

Proof:

“⊆” Let x ∈ A ∪ (B ∩ C). Then x ∈ A or x ∈ B ∩ C. We will consider these two cases separately.

Case 1: Suppose x ∈ A. Then, by definition of set union, x ∈ A ∪ B. Similarly, x ∈ A ∪ C. Thus. by definition of set

intersection, we must have x ∈ (A ∪ B) ∩ (A ∪ C).

Case 2: Suppose x ∈ B ∩ C. Then, by definition of set intersection, x ∈ B and x ∈ C. Since x ∈ B, then again by the

definition of set union, x ∈ A ∪ B. Similarly, since x ∈ C, then x ∈ A ∪ C. Hence, again by definition of set intersection,

x ∈ (A ∪ B) ∩ (A ∪ C).

Since these are the only possible cases, then A ∪ (B ∩ C) ⊆ (A ∪ B) ∩ (A ∪ C)

“⊇” Let x ∈ (A ∪ B) ∩ (A ∪ C). Then, by definition of set intersection, x ∈ A ∪ B and x ∈ A ∪ C. We will once again split

into cases.

Case 1: Suppose x ∈ A. Then, by definition of set union, x ∈ A ∪ (B ∩ C).

Case 2: Suppose x /∈ A. Since x ∈ A ∪ B, then, by definition of set union, we must have x ∈ B. Similarly, since x ∈ A ∪ C,

we must have x ∈ C. Therefore, by definition of set intersection, we have x ∈ B ∩ C. Hence, again by definition of set union,

A ∪ (B ∩ C).

Since these are the only possible cases, then A ∪ (B ∩ C) ⊇ (A ∪ B) ∩ (A ∪ C)

Thus A ∪ (B ∩ C) = (A ∪ B) ∩ (A ∪ C). ✷

Instructions: Use general element arguments to show that following (Note that only 3, 4, and 5 may be used as portfolio

proofs):

1. Proposition 1: B − A ⊆ B

2. Proposition 2: A − (A − B) ⊆ B

3. Proposition 3: A − (A − B) = A ∩ B

4. Proposition 4: (A − B) ∪ (B − A) = (A ∪ B) − (A ∩ B)

5. Proposition 5: A × (B ∩ C) = (A × B) ∩ (A × C)

A hypothesis is an assumption, an idea that is proposed for the sake of argument so that it can be tested to see if it might be true.

a. two-tailed test

b. reject H0 if Z>1.96 or Z<-1.96

c. Z = 1.73

d. we have failed to reject the null hypothesis

e. P-value = 0.0418

We need to find our critical value:

Zα/2 = Z(0.05/2) = 0.025

The Z test will be done using the next equation:

Z = (x⁻1 - x⁻2) - (μ1 - μ2) / √( σ²1/n1 + σ²2/n2

Z = (100.5 - 98.8) - (0) / √( (3.4)²/38 + (5.8)²/51 = 1.7/0.9817 = 1.73

Z<1.96, therefore we have failed to reject the null hypothesis

The P-value for this test would be represented by the probability of Z being greater than 1.73, so we can look for it in any Z table, finding that its value is 0.0418, and because P-value>0.025 we again confirm that we don't have evidence statistically significant to reject the null hypothesis

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Step-by-step explanation:

lenght = x + 8

width = x

\(perimeter = 2(x + 8) + 2(x) \\ 96= 2x + 16 + 2x \\ 4x = 96 - 16 \\ x = \frac{80}{4} \\ x = 20\)

then

Lenght = x + 8 = 20 + 8 = 28

Width = x = 20

Step-by-step explanation:

L=8+2W

P=2L+2W

P=2(8+2W)+2W

P=16+4W+2W

P=16+6W

P=96

96=16-6W

80=6W

W=13.3333

Answer:

Question 1: The appropriate measures of center for this data set would be (1) Mean and (2) Median. There is no mode in this data set as there are no repeating values.

Question 2: To find the standard deviation, we first need to find the mean:

Mean = (513 + 490 + 496 + 380 + 490 + 513 + 503 + 513 + 500 + 492) / 10 = 494.0

Next, we find the difference between each data point and the mean:

(513 - 494.0), (490 - 494.0), (496 - 494.0), (380 - 494.0), (490 - 494.0), (513 - 494.0), (503 - 494.0), (513 - 494.0), (500 - 494.0), (492 - 494.0)

19, -4, 2, -114, -4, 19, 9, 19, 6, -2

Then we square each difference:

361, 16, 4, 12996, 16, 361, 81, 361, 36, 4

The sum of these squared differences is:

361 + 16 + 4 + 12996 + 16 + 361 + 81 + 361 + 36 + 4 = 14136

To find the variance, we divide the sum of squared differences by the number of data points minus one:

Variance = 14136 / 9 = 1570.7

Finally, we find the standard deviation by taking the square root of the variance:

Standard deviation = √1570.7 ≈ 39.6 (rounded to the tenths place)

Step-by-step explanation:

Answer: 6/7 The required option is (3) 6/7

Step-by-step explanation: Explanation : A term is combination of variables and numerals by means of multiplication and division.

Answer:

\(y = 4\)

Step-by-step explanation:

First, find the derivative of f:

\(\displaystyle \begin{aligned} f'(x) & = \frac{d}{dx}\left[ 2x^3 - 3x^2 + 5\right] \\ \\ & = 6x^2 - 6x \\ \\ & = 6x(x-1)\end{aligned}\)

Find the instantaneous slope at x = 1:

\(\displaystyle \begin{aligned} f'(1) & = 6(1)((1)-1) \\ \\ &= 0 \end{aligned}\)

From the point-slope form, find the equation of the line:
\(\displaystyle \begin{aligned}y - y_1 & = m(x-x_1) \\ \\ y - (4) & =(0)(x-(1)) \\ \\ y & = 4 \end{aligned}\)

In conclusion, the equation of the tangent line is y = 4.

Answer:

B) y = 7x

Step-by-step explanation:

Start with:

\(m=\frac{y_2-y_1}{x_2-x_1}\)

Substitute in two points from the graph.

(Let's use (8,56) & (16,112)

\(m=\frac{112-56}{16-8}\)

Combine like terms.

\(m=\frac{56}{8}\)

Simplify.

\(m=7x\)

Answer:

y = 7x

Step-by-step explanation:

We need to find the slope

We have two points (0,0) and (8,56)

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

   = (56-0)/( 8-0)

  = 56/8

  = 7

The proportional relationship is

y= kx where k is the slope

y = 7x

Answer:

Step-by-step explanation:

Answer:13

Step-by-step explanation:

Answer:

Amadi: 20 years old

Chima : 4 years old