10 cm
7 cm
10 cm
4 cm
How many surfaces does the figure contain? Help asap

69.1° is the value of C by Law of Cosines .

What is the cosine law?

The formula for the Law of Cosines is c2=a2+b22ab cosC. With the exception of the third component, which equals 0 if C is a right angle because the cosine of 90° is 0 and we have the Pythagorean Theorem, this is similar to the Pythagorean Theorem.

The Law of Cosines is given as

c² = a² + b² - 2ab-cosC

substitute the values in a, b, c

Plugging in given values, we get

  16² = 8² + 17² - 2 . 8 . 17 . cosC

   256 = 64 + 289 - 272. CosC

    256 = 353 - 272 . cosC

     256 - 353 = 272 . CosC

         -97 =   272 . CosC

            cosC = -97/-272

          C = across(97/272)

            C  = 69.1°

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Answer:

C= 83.04

Step-by-step explanation:

Answer:

To convert inches to centimeters, we multiply the inches by 2.54 (since 1 inch is equal to 2.54 centimeters).

So, to convert Bill's height of 70 inches to centimeters, we can use the following formula:

70 inches * 2.54 centimeters per inch = 177.8 centimeters

Rounding this to the nearest tenth, we get:

177.8 centimeters ≈ 177.8 centimeters

Therefore, Bill's height in centimeters is approximately 177.8 centimeters.

Answer:

Step-by-step explanation:

Convert 70 inches to centimeters

Start with what you are given, which is 70 cm, and use a conversion factor that converts inches to centimeters.

1 inch = 2.54 centimeters

70 in x (2.54 cm/1 in) = 177.8 cm

Note that the inches cancel and you are left with centimeters.

The given system can be written in matrix form as X' = [1 0; 5 -4; 0 1] X + [0; 2; 2]. Therefore, the general solution is X = [t + C1; -2t + C2; t + C3], where C1, C2, and C3 are arbitrary constants.

To find the general solution, we can solve the system by integrating the matrix equation. Integrating the equation X' = [1 0; 5 -4; 0 1] X + [0; 2; 2] with respect to time gives us X = [t + C1; -2t + C2; t + C3], where C1, C2, and C3 are constants.

In the second paragraph, I explained that we can solve the given system by integrating the matrix equation. The matrix equation X' = [1 0; 5 -4; 0 1] X + [0; 2; 2] represents a system of three first-order linear differential equations.

Integrating each equation with respect to time, we obtain the expressions t + C1, -2t + C2, and t + C3, where C1, C2, and C3 are constants of integration.

These expressions represent the general solution to the system, as they satisfy the differential equations for any choice of the constants. Therefore, the general solution is X = [t + C1; -2t + C2; t + C3], where C1, C2, and C3 are arbitrary constants.

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the answer is :

(450/2) = $225 simple interest  

225 / 3000 = 0.075  =  7.5%

Thus, the vertices of the larger square have the following coordinates: (-6, 7),  (1, 7),(1, 0), and  (-6 ,0).

The ratio of the scale of an original thing to a new object that is a representation of it but of a variable size is known as a scale factor (bigger or smaller).

The procedures below can be used to increase form A by a scale factor of 3.5 with the centre of enlargement at (8,-7).

Transform the square so that its origin is where the centre of enlargement is (0,0).

To do this, we deduct each vertex's coordinates from the centre of enlargement (8,-7):

A = (4 - 8, -3+ 7) = (-4, 4)

B = (6 -8, -3 + 7) = (-2, 4)

C = (6 - 8, -5 + 7) = (-2, 2)

D = (4 - 8, -5 + 7) = (-4, 2)

Multiply the coordinates of the each vertex by the scaling factor (3.5) to enlarge the translated square:

A = (-14, 14)

B = (-7, 14)

C = (-7, 7)

D = (-14, 7)

By adding those coordinates of the centre of the enlargement (8,-7) to each vertex, move the square from its larger state back to its original one:

A = (-14 + 8, 14-7) = (-6, 7)

B = (-7 + 8, 14-7) = (1, 7)

C = (-7 + 8, 7-7) = (1, 0)

D = (-14 + 8, 7-7) = (-6 ,0)

As a result, the vertices of the larger square have the following coordinates: (-6, 7),  (1, 7),(1, 0), and  (-6 ,0).

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Given: Pair of parallel lines and a transversal with angles x and y.

Required: To determine which type of angles are formed by x and y.

Explanation: Consider the following figure below showing a pair of parallel lines and a transversal

In the figure, line l is parallel to line m, and line n is the transversal.

Further alternate angles are the pair:

The angles lying inside the parallel lines are alternate interior, while the angles lying outside the parallel lines are the alternate exterior.

While the corresponding angles are the pair:

Finally, the consecutive interior angles are the pair of non-adjacent angles that lie on the same side of the transversal. In the figure above, the consecutive interior angles are:

Hence the given pair of angles x and y are consecutive interior angles.

Final Answer: Option D is correct.

The gcd(26, 20) is 2, so the least common multiple of the periods is 2π / (2) = π. Therefore, it takes π seconds for the object to complete one revolution around the circle.

The position of an object in circular motion is modeled by the parametric equations x = 5 sin(26t) and y = 5 cos(20t), where t is measured in seconds. The path of the object can be described by stating the radius of the circle, the position at time t = 0, the orientation of motion, and the time t it takes to complete one revolution around the circle.

The radius of the circle can be determined from the coefficients of the sine and cosine functions, which are both 5. Therefore, the radius of the circle is 5 units.

At time t = 0, the position of the object can be found by plugging t = 0 into the parametric equations. This gives x = 5 sin(0) = 0 and y = 5 cos(0) = 5. Thus, the position of the object at t = 0 is (0, 5).

To determine the orientation of the motion (clockwise or counterclockwise), note that when t increases, x increases (since sine is positive in the first and second quadrants) while y decreases (since cosine is positive in the first and fourth quadrants). Therefore, the object moves in a clockwise direction.

To find the time it takes to complete one revolution around the circle, we need to consider the period of the trigonometric functions. The period of sine and cosine functions is 2π divided by the coefficient of t. In this case, the periods for x and y are 2π/26 and 2π/20, respectively.

Since the object's motion is described by both x and y, we need to find the least common multiple of these periods, which is 2π / gcd(26, 20). The gcd(26, 20) is 2, so the least common multiple of the periods is 2π / (2) = π. Therefore, it takes π seconds for the object to complete one revolution around the circle.

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Answer:

she will lose 12 pounds

Answer:

46

Step-by-step explanation:

a + 4(b - 3)

Substitute the values for a and b.

10 + 4(12 - 3)

Subtract inside the parenthesis.

10 + 4(9)

Multiply.

10 + 36

Add.

46

Answer:

10,000lbs

Step-by-step explanation:

There are 2000lbs in 1 ton

So

5 x 2000 = 10000lbs

Answer:

10,000 pounds is the the correct answer

Answer:

A. The sampling distribution follows a normal distribution

B. With 90% confidence the mean number of names that all people can remember when introduced to 40 people at a party is between 17.04 and 19.28

C. If many groups of 55 randomly selected people were surveyed, then a different confidence interval would be produced for each group. About 90 percent of these confidence intervals will contain the true population mean number of names remembered and about 10 percent will not contain the true population mean number of names remembered  

Step-by-step explanation:

The given parameters are;

The known population standard deviation of the number of names that people can recall after being introduced to 40 people in a party, σ = 6.34 names

The number of people randomly selected in the survey, n = 55 people

The average number of names correctly remembered, \(\overline x_1\) = 18.16

The standard deviation of the group surveyed, s = 4.28

A. Based on the Central Limit Theorem CLT, the sampling distribution follows a normal distribution

B. The 90% confidence interval is given as follows;

\(C.I.=\bar{x}\pm z_{\alpha /2}\cdot \dfrac{\sigma}{\sqrt{n}}\)

Where \(z_{\alpha /2}\) at 90% = 1.65, we have;

\(C.I.=18.16\pm 1.65 \times \dfrac{4.28}{\sqrt{55}}\)

C.I. ≈ 17.20 < μ < 19.11

With 90% confidence the mean number of names that all people can remember when introduced to 40 people at a party is between 17.04 and 19.28

C. The 90% confidence interval gives the certainty that if different groups of 55 randomly selected people were surveyed, then about 90 percent of the confidence intervals will contain the true population mean number of names remembered and about 10 percent will not contain the true population mean number of names remembered.

The price of the bond is $1,043.98 (rounded to 2 decimal places).

To calculate the price of a five-year bond that has a coupon rate of 7.0% paid annually and a current market rate of 4.50%, we need to use the formula for the present value of a bond. A bond's value is the present value of all future cash flows that the bond is expected to produce. Here's how to calculate it:

Present value = Coupon payment / (1 + r)^1 + Coupon payment / (1 + r)^2 + ... + Coupon payment + Face value / (1 + r)^n

where r is the current market rate, n is the number of years, and the face value is the amount that will be paid at maturity. Since the coupon rate is 7.0% and the face value is usually $1,000, the coupon payment per year is $70 ($1,000 x 7.0%).

Here's how to calculate the bond's value:

Present value = \($\frac{\$70 }{(1 + 0.045)^1} + \frac{\$70}{(1 + 0.045)^2 }+ \frac{\$70}{ (1 + 0.045)^3} + \frac{\$70}{ (1 + 0.045)^4 }+ \frac{\$70}{(1 + 0.045)^5} + \frac{\$1,000}{ (1 + 0.045)^5}\)

Present value = $1,043.98

Therefore, The bond costs $1,043.98 (rounded to two decimal places).

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Answer:

  S = 100,000 + 2,000n

Step-by-step explanation:

The salary went up $10,000 in 5 years, so the average raise seems to be $2000 per year. Of course, the initial salary is 100,000. Then ...

  S = 100,000 + 2,000n

Answer:

n=-3.1

Step-by-step explanation:

2n+3=-3.2

2n=-6.2

n=-3.1

2n+3 =-3.2

2n= -3.2-3

2n= -6.2

n= -3.1

The converse and the validity of the statement is:

The statement is given as:

If the diagonals of a parallelogram are congruent, then is the parallelogram is a rectangle

Considering the following statement

If a then b

Its converse is:

If b then a

So, the converse of the given statement is:

If a parallelogram is a rectangle, then the diagonals are congruent.

The diagonals of a rectangle are true.

Hence, the validity is true.

So, the true statement is (b)

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Answer:

16 3/4 or 16.75

Step-by-step explanation:

134/8=16 3/4or 16.75

a. On average, callers must wait 17.14 minutes before talking to the sales rep.

b. On average, there are 12.73 customers on hold.

c. The probability that a customer will be placed on hold is 0.9637 or 96.37%.

d. The sales rep's utilization rate is 95.24%.

e. Road Rambler should employ two sales reps to ensure no more than a 10% chance of customers being placed on hold.

a. The average time a caller must wait before talking to the sales rep is the sum of the average time between calls (4.29 minutes) and the average time it takes to service a call (4 minutes), which equals 8.29 minutes. Thus, the total average waiting time is 14.57 minutes per customer, resulting in 17.14 minutes of waiting time for each caller.

b. The average number of customers on hold is equal to the average time a customer spends waiting divided by the average time between calls, which is:

= 14.57/4.29

= 3.39

Therefore, the average number of customers on hold is 3.39 x 14 = 12.73.

c. The probability that a customer will be placed on hold is equal to the probability that there are more than zero customers in the system. Using the formula for the probability of zero customers in the system (0.0363), we can calculate that the probability of at least one customer in the system is:

= 1 - 0.0363

= 0.9637 or 96.37%.

d. The sales rep's utilization rate is the ratio of the average service time to the average time between calls, which is:

= 4/4.29

= 0.9524 or 95.24%.

e. To ensure that no more than a 10% chance of customers being placed on hold, the probability of zero customers in the system must be at least 0.1. Using the formula for the probability of zero customers in the system, we can solve for the required arrival rate:

λ = -ln(0.9)/4.29

λ = 0.1822 customers per minute.

This arrival rate requires two sales reps, assuming no idle time, to handle the calls.

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Quota sampling is a method used in research to ensure that a sample represents the target population accurately and is free from bias. In quota sampling, researchers determine in advance how many individuals from certain groups or characteristics they need to include in the survey.

The main goal of quota sampling is to ensure that every person in the target population has an equal chance of being selected for the sample. This is achieved by selecting individuals based on specific characteristics or demographics that are representative of the population being studied.

For example, let's say a researcher wants to conduct a survey about favorite ice cream flavors among teenagers. They may decide that they need an equal number of male and female participants and an equal representation from different age groups within the teenage population. The researcher would then set quotas for each of these groups and select participants accordingly.

It's important to note that quota sampling does not involve pre-planning or random selection. Instead, researchers use their judgment to select individuals who meet the predetermined quotas as they encounter them in the target population.

By using quota sampling, researchers can ensure that their sample is diverse and representative of the population they are studying. This method helps reduce bias and provides a more accurate understanding of the target population's opinions or behaviors.

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The distance between two points a and b on the real line is given by the absolute difference between the two points, which is calculated as the positive difference between the values of a and b regardless of their order.

The distance function, denoted as d(a, b), is a metric that satisfies the properties of non-negativity, symmetry, and the triangle inequality. It is used to quantify the distance between two points in one-dimensional space, and is an important concept in geometry, analysis, and other fields of mathematics. The distance formula can be extended to higher dimensions and is used in various applications such as optimization, clustering, and machine learning.

The distance between two points a and b on the real line is given by the absolute difference between the two points: d(a, b) = |a - b|

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A distribution of scores on a driver's license test forms is normally shaped. This is an example of a symmetrical distribution is TRUE.

A symmetrical distribution is a distribution where there is an equal number of data points on both sides of the center point, in which the mean, mode, and median of a data set are all similar.

A normal distribution is a bell-shaped distribution that is symmetrical, with most of the data falling near the mean and progressively less toward the tails. When data are symmetrical, the mean and median values are similar, and the standard deviation can be used to compute the proportions of data within a range of values surrounding the mean.

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Answer:

10√2

Step-by-step explanation:

√200=√2*100=10√2

Ans.is 10√2

the topic is Surds in math

(a) False. The set {x∈R^n | Ax=b} is not necessarily convex. It depends on the matrix A and the vector b. For example, if A is a non-convex matrix, then the set of solutions {x∈R^n | Ax=b} will also be non-convex.

(b) True. The set {(x₁,x₂) | x₂ ≤ 3x₁²} is convex. The inequality defines a downward parabolic region, and any line segment connecting two points within this region will lie entirely within the region. (c) False. Not all polygons on the R² plane are convex. For example, a polygon with a concave portion, such as a crescent shape, would not be convex.

(d) True. If S⊆R² is convex, then it must enclose a region of finite area. Convex sets do not have "holes" or disjoint parts, so they form a connected and bounded region. (e) False. If S₁⊆R² and S₂⊆R², and S₁∩S₂=ϕ (empty set), then S₁∪S₂ can be convex. If S₁ and S₂ are both convex sets that do not overlap, their union can still be a convex set. (f) True. If S₁⊆R² and S₂⊆R² are both closed sets, then their union S₁∪S₂ must also be closed. However, it may or may not be convex. The convexity of the union depends on the specific sets S₁ and S₂.

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"Study smart one triangle has vertices a,b, and c. another has vertices t, r, and i, are the 2 triangles similar?"

It is not possible to determine if the two triangles are similar based on the information provided.

In order for two triangles to be similar, they must have the same shape but not necessarily the same size. The sides of the two triangles must be in proportion and corresponding angles must be congruent.

Similarity between two triangles can be determined by using the criterion of AAA similarity or SAS similarity, which states that two triangles are similar if:

without knowing the measures of the angles and sides of the triangles, it is impossible to determine if the two triangles are similar.

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Answer:

105 pages

Step-by-step explanation:

We can solve this using ratios

Changing 3 hours to minutes

3 * 60 = 180 minutes

7 pages            x pages

---------------   = ----------------

12 minutes         180 minutes

Using cross products

180 * 7 = 12 x

Divide each side by 12

180*7/12 = x

105 =x

105 pages

Answer:If you can read 7 pages in 12 minutes then you will be able to read 105 pages in 3 hours.

Step-by-step explanation: you multiply 12x15 to get 180 since 180 is 3 hours in minutes then you multiply 7x15= 105. So you will read 105 pages every 3 hours.

100th Answer!!!!

Ans Measurement is the process of comparing and unknown physical quantity with a known or standard one.

Step-by-step explanation:

NO and PQ are congruent segments (have the same length), and both have the same midpoint M.

NO ≅ PQ, given.

NM ≅ ½ NO, definition of midpoint.

PM ≅ ½ PQ, definition of midpoint.

PM ≅ ½ NO, substitution.

PM ≅ NM, substitution.

Answer:

\(|JK|=3\sqrt{3}\)

Step-by-step explanation:

The diagram of the triangle is drawn and attached,

From trigonometric ratios,

\(cos \theta =\frac{Adjacent}{Hypotenuse} \\cos60^\circ =\frac{|JK|}{|JL|}\\ 0.5=\frac{|JK|}{6\sqrt{3} }\\$Cross multiply$\\|JK|=0.5*6\sqrt{3}\\|JK|=3\sqrt{3}\)

Answer:

the proof is in the picture

Step-by-step explanation:

Answer:

4 + 11 = 15

Step-by-step explanation:

brainliest plz

Your answer is B.

It states that 4 people signed up to go bowling, then 11 more people did.

So that means the equation would be \(\left[\begin{array}{ccc}4+11=15\end{array}\right]\)

If this helped please mark me as brainliest!

\(\left[\begin{array}{ccc}Thanks,\\JustSomeIdiot\end{array}\right]\)