Sketch the triangle ABC and solve it using the law of cosines. Round off your answers to the nearest integer. b = 60, c = 30, ∠A = 70∘
Ams: a = 57, ∠B = 81∘, and ∠C = 29∘

The graph of the absolute function, p(x) = |x - 1|, has a minimum point (1, 0), and the points (-6, 7), and (6, 5), on the graph

Please find attached the graph of the absolute function created with MS Excel.

An absolute function is a function that nests an algebraic expression within an absolute value symbol.

The specified absolute function, p(x) = |x - 1|, indicates that the minimum value of the function, occurs where; p(x) = 0 = |x - 1|

Therefore; |x - 1| = 0, x = 1

When x = -6, we get; p(-6) = |(-6) - 1| = 7

When x = 6, we get; p(6) = |6 - 1| = 5

Therefore, the points on the graph are;

(-6, 7), (1, 0), and (6, 5)

Please find attached the graph of the absolute function created with MS Excel

The possible question, includes graph with the attached four options

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The claim that is being tested is: "the mean height of 12-year-old boys from high-income families is greater than 59.2 inches."

In order to test this claim, one could follow these steps:
1. Gather data: Collect a sample of 12-year-old boys from high-income families. 2. Calculate the sample mean: Compute the mean height of the boys in the sample. 3. Formulate a null hypothesis (H0): The mean height of 12-year-old boys from high-income families is equal to 59.2 inches.

4. Formulate an alternative hypothesis (H1): The mean height of 12-year-old boys from high-income families is greater than 59.2 inches. 5. Perform a hypothesis test: Using the appropriate statistical test, compare the sample mean to the population mean of 59.2 inches. 6. Draw conclusions: Based on the results of the hypothesis test, either reject the null hypothesis (supporting the alternative hypothesis) or fail to reject the null hypothesis (not enough evidence to support the alternative hypothesis).

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The claim that their mean height is greater than 59.2 in is the alternative hypothesis, which will be accepted or rejected based on the results of the data analysis.

The claim that he is testing is that the mean height of 12-year-old boys from high-income families is greater than 59.2 in. This claim is being tested by collecting data from a sample of 102 12-year-old boys and calculating their mean height. The hypothesis is that this mean height will be greater than 59.2 in, which is the assumed population mean height for all 12-year-old boys. The researcher is specifically interested in the height of boys from high-income families, so this is the subgroup that is being tested. The claim that their mean height is greater than 59.2 in is the alternative hypothesis, which will be accepted or rejected based on the results of the data analysis.

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Answer:

Let's denote the number of people in Team A as a, and the number of people in Team B as b. From the problem, we know that:

a/b = 3/4

Now, we also know that 4/5 of Team A and 24% (or 24/100 = 6/25) of Team B work full time. So, the number of people working full time from Team A is 4a/5 and from Team B is 6b/25.

The total number of people working for the company is a + b, and the total number of people working full time is 4a/5 + 6b/25.

We are asked to find the fraction of people working full time, which can be represented as:

(4a/5 + 6b/25) / (a + b)

Firstly, we need to have a common denominator for the fractions, so we can express 4a/5 as 20a/25:

[tex](20a/25 + 6b/25) / (a + b)[/tex]

Simplifying, we can write this as:

[tex](20a + 6b) / (25(a + b))[/tex]

Now, since we know a/b = 3/4, we can substitute a = 3b/4 in the above expression:

[tex](20*(3b/4) + 6b) / (25((3b/4) + b))[/tex]

Simplifying the above, we get:

[tex](15b + 6b) / (25((3b/4) + b)) = 21b / 25b[/tex]

So, the fraction of people working full time is 21/25.

The  product of the given matrices is [tex]AB=\left[\begin{array}{ccc}9\\18\end{array}\right][/tex]

Matrix multiplication is a binary operation that produces a matrix from two matricesThe given matrices are [tex]A=\left[\begin{array}{ccc}1\\2\end{array}\right][/tex] and [tex]B=\left[\begin{array}{ccc}4&5\end{array}\right][/tex]

To perform product of two matrices, we should make sure that the number of columns in the 1st matrix is equal to the rows in the 2nd matrix

AB=[tex]\left[\begin{array}{ccc}1\\2\end{array}\right].\left[\begin{array}{ccc}4&5\end{array}\right][/tex]

[tex]AB=\left[\begin{array}{ccc}4+5\\8+10\end{array}\right][/tex]

[tex]AB=\left[\begin{array}{ccc}9\\18\end{array}\right][/tex]

Hence, the  product of the given matrices is [tex]AB=\left[\begin{array}{ccc}9\\18\end{array}\right][/tex]

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The circumference of the circle is 25.12 inches. The Option C.

The Circumference, also perimeter of circle means the ratio of circumference to diameter of any circle.

The length of the segment represents radius of the circle which half length of diameter. So, the diameter is:

= 2 * 4 inches

= 8 inches.

The circumference is found using C = πd.

C = π*d

C = 3.14 * 8 inches

C = 25.12 inches.

Full question:

What is the circumference of the circle? Use 3.14 for π.

circle with a segment drawn from the center of the circle to a point on the circle labeled 4 inches

A. 157.75 inches

B. 50.24 inches

C. 25.12 inches

D. 12.56 inches.

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The factors of the given polynomial 18m²-8 are 2, (3m+2) and (3m-2).

The factors are the polynomials which are multiplied to produce the original polynomial.

Use the identity (a²-b²)=(a+b)(a-b)

1) 2a²-2b²

= 2(a²-b²)

= 2(a+b)(a-b)

2) 6x²-6y²

= 6(x²-y²)

= 6(x+y)(x-y)

3) 4x² - 4

= 4(x²-1)

= 4(x+1)(x-1)

4) ax²-ay²

= a(x²-y²)

= a(x+y)(x-y)

5) cm²-cn²

= c(m²-n²)

= c(m+n)(m-n)

6) st²-s

= s(t²-1)

= s(t+1)(t-1)

7) 2x²-18

= 2(x²-9)

= 2(x²-3²)

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

8) 2x²-32

= 2(x²-16)

= 2(x²-4²)

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

9) 3x²-27y²

= 3(x²-9y²)

= 3(x²-(3y)²)

= 3(x+3y)(x-3y)

10) 18m²-8

= 2(9m²-4)

= 2((3m)²-(2)²)

= 2(3m+2)(3m-2)

Therefore, the factors of the given polynomial 18m²-8 are 2, (3m+2) and (3m-2).

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Answer: D

Step-by-step explanation:

Team A has symmetric scores because the upper quartile (right part of the rectangle) is equal to lower quartile (left part of rectangle) in terms of size, so median (middle line in the rectangle) is equal to the mean. Team B has negative skewed scores because the upper quartile is smaller than lower quartile, so the median is greater than the mean.

Thus, the answer is D.

The sum of the measures of the exterior angles of the 14 sides polygon shown is 360 degrees.

The sum of the measures of the exterior angles of any polygon is always equal to 360 degrees.

This means that the exterior angles for the sides of this 14 sided polygon would be:

= 360 / 14

= 25. 71 degrees

Regardless of the polygon, so long as it is a regular polygon, the exterior angles will always add up to 360 degrees so the sum of exterior angles here is the same measure of 360 degrees.

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The correct solution to the inequality x^2 - 9x < -18 is x < 3 or x > 6.

To solve the inequality x^2 - 9x < -18, you can follow these steps:

Move all terms to one side of the inequality to form a quadratic expression: x^2 - 9x + 18 < 0.

Factorize the quadratic expression: (x - 6)(x - 3) < 0.

Determine the sign of the expression for different intervals of x. To do this, you can create a sign chart:

Interval | (x - 6) | (x - 3) | (x - 6)(x - 3) |

x < 3 | - | - | + |

3 < x < 6 | - | + | - |

x > 6 | + | + | + |

Analyze the sign chart to determine when the expression (x - 6)(x - 3) is less than zero (negative).

The expression is negative when x is between 3 and 6, i.e., 3 < x < 6.

Write the solution in interval notation:

x < 3 or x > 6

Therefore, the correct solution to the inequality x^2 - 9x < -18 is x < 3 or x > 6.

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Hope this image helps you out!

The value of the line integral is (-16/3)cos(6) + (16/9)sin(6). Evaluating this integral, you will get the value of the line integral for the given curve.

To evaluate the line integral ∫c x sin yds, where C is the line segment from (0,3) to (4,6), we first need to parameterize the curve. We can do this by letting x = t and y = 3 + (3/4)t, where t goes from 0 to 4. This gives us the parametric equations x = t and y = (3/4)t + 3.

Next, we need to find ds, the length of the curve element. We can use the formula ds = sqrt(dx^2 + dy^2) to get ds = sqrt(1 + (3/4)^2)dt = sqrt(25/16)dt = (5/4)dt.

Now we can substitute in our parameterization and ds into the line integral to get ∫c x sin yds = ∫0^4 t sin((3/4)t + 3) (5/4)dt.

We can evaluate this integral using integration by parts. Let u = t and dv = sin((3/4)t + 3) (5/4)dt, then du/dt = 1 and v = (-4/3)cos((3/4)t + 3). The integral becomes:

∫0^4 t sin((3/4)t + 3) (5/4)dt = uv|0^4 - ∫0^4 v du/dt dt
= (-4/3)t cos((3/4)t + 3)|0^4 - ∫0^4 (-4/3)cos((3/4)t + 3) dt
= (-4/3)t cos((3/4)t + 3) + (16/9)sin((3/4)t + 3)|0^4
= (-16/3)cos(6) + (16/9)sin(6)

Therefore, the value of the line integral is (-16/3)cos(6) + (16/9)sin(6).

To evaluate the line integral ∫c x sin y ds, where C is the line segment from (0, 3) to (4, 6), you first need to parameterize the curve C.

A possible parameterization is r(t) = (1-t)(0, 3) + t(4, 6) = (4t, 3+3t), with t ∈ [0, 1]. Then, compute the derivative dr/dt = (4, 3).

Now, find the integrand by replacing x and y with the parameterized curve components: x sin y = (4t) sin(3 + 3t).

Next, find the magnitude of the derivative: |dr/dt| = √(4² + 3²) = 5.

Finally, compute the integral:

∫[0, 1] (4t sin(3 + 3t))(5) dt.

Evaluating this integral, you will get the value of the line integral for the given curve.

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The slope of the line that represent this relationship is 3.75.

In Mathematics and Geometry, the slope-intercept form of the equation of a straight line is given by this mathematical equation;

y = mx + c

Where:

Based on the information provided about the charges by this amusement park, we have the following system of equations;

51.25 = 7m + c  ....equation 1.

70 = 12m + c    ......equation 2.

By solving equation 1 and equation 2 simultaneously, we have the following:

70 = 12m + 51.25 - 7m

70 - 51.25 = 5m

18.75 = 5m

Slope, m = 18.75/5

Slope, m = 3.75

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the only critical number of g(y) is -1/4.

To find the critical numbers of the function g(y) = y - 2y^2 - 2y + 4, we need to find its derivative and set it equal to zero.

g'(y) = 1 - 4y - 2

Setting g'(y) = 0, we get:

1 - 4y - 2 = 0

-4y - 1 = 0

y = -1/4

what is number?

A number is a mathematical object used to represent a quantity or value. Numbers can be classified into different types based on their properties and the set of numbers they belong to. Some common types of numbers include:

Natural numbers: These are the counting numbers, such as 1, 2, 3, and so on.

Whole numbers: These are the natural numbers plus zero, such as 0, 1, 2, 3, and so on.

Integers: These are the whole numbers plus their negative counterparts, such as -3, -2, -1, 0, 1, 2, 3, and so on.

Rational numbers: These are numbers that can be expressed as a ratio of two integers, such as 1/2, 0.75, or -3/4.

Irrational numbers: These are numbers that cannot be expressed as a ratio of two integers, such as pi (3.14159...) or the square root of 2 (1.41421...).

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A) Yes, we can conclude that △ABD≅△ACD .

B) Rob says AB = AC and BD = CD. I agree.

C) The expression for the distance around the kite (perimeter) in centimeters is 4x + 30.

A) According to the principles of geometry, when two angles are marked alike, it means that they are equal.

Thus, ∠BAD ≅ ∠CAD; and

∠BDA ≅∠ADC

Since ∠BDA ≅∠ADC and

AD = DA (Based on the Reflexive postulate,

Then on the basis of the Angle  - Side - Angle theorem, △ABD≅△ACD.

B) AB = AC and BD = CD

This is because we have already proven that △ABD≅△ACD on the basis of A-S-A theorem.

C) Since both triangles are equal, the expression for their perimeter =

x + 15 + x + x + 15 + x

= 4x + 30

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Answer:

x + y = 22

3x + 5 = 35

3x = 30, so x = 10 and y = 12.

#3, the transformation can be represented by (x, -y)

Converting 4315425 quinary number into a decimal number​ results in 73,240.

A quinary number is a number that is in base 5.

A decimal number is a number in base 10.

The powers of 5 include (1, 5, 25, 125, 625, and so on).  We write these powers of 5 beside the quinary digits written from bottom to top and then multiply each digit by its associated power.

The sum of the products gives the decimal number of the quinary number.

Digit         Power       Multiplication

5                 1                  5 (5 x 1)

2                 5               10 (2 x 5)

4               25            100 (4 x 25)

1              125             125 (1 x 125)

5            625          3,125 (5 x 625)

3          3,125         9,375 (3 x 3,125)

4       15,625       62,500 (4 x 15,625)

Total                   73,240

Thus, 4315425 quinary is equal to 73,240 decimal.

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Answer:

(-5, 2)

Step-by-step explanation:

2x + 3y = -4

x + 9y = 13

We can solve this by substituting or using elimination.

Substituting:

2x + 3y = -4

-2x     = -2x     Subtract 2 from both sides.

3y = -2x - 4

3    =   3              Divide both sides by 3.

y = -2/3x - 4/3

x + 9(-2/3x - 4/3) = 13  Replace the y with -2/3x - 4/3.

x - 6x - 12 = 13     use the distributive property.

-5x - 12 = 13

     +12 = + 12           Add 12 to both sides.

-5x = 25

-5  = -5                  Divide both sides by -5.

x = -5

Now that we know what x is, we substitute -5 for the variable x in any of the two equations.

x + 9y = 13

-5 + 9y = 13  Replaced x with -5

+5       = +5   Add 5 to both sides.

9y = 18

Divide both sides by 9 to get:

y = 2

The other way to solve:

Elimination:

2x + 3y = -4

x + 9y = 13

Make the variable y cancel out.

-3(2x + 3y = -4)  use the distributive property.

-6x - 9y = 12

-6x - 9y = 12

x + 9y = 13

Add the equation.

-5x = 25

Divide both sides by -5.

x = -5

Plug in -5 for x.

2(-5) + 3y = -4

-10 + 3y = -4

+10     = +10   Add 10 to both sides.

3y = 6

Divide both sides by 3:

y = 2

We get the same answer in both strategies, you could use either one.

By using the formula of final amount, The future value is,

Future value = 29,640

We have to given that;

Present value = 12,000

Time = 8 years

And, interest rate = 12%

Now, For Calculate a future value for present value of 12,000 term of 8 years interest rate 12%, we can use the formula for present amount.

Since, We know that;

Future value = P (1 + r)ⁿ

Where, P is present amount.

r is interest rate.

n is number of years.

Hence, We can substitute all the given values, we get;

Future value = P (1 + r)ⁿ

Future value = 12,000 (1 + 12%)⁸

Future value = 12,000 (1 + 0.12)⁸

Future value = 12,000 (1.12)⁸

Future value = 12,000 x 2.47

Future value = 29,640

Therefore, The future value for present value of 12,000 term of 8 years interest rate 12% is,

Future value = 29,640

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The length of side x in the right triangle is approximately 38.2 units.

It looks like you have a right triangle problem where you need to solve for side x. The given information is the hypotenuse (Z) with a length of 56 units, an angle (M) of 43°, and side x which is opposite to angle M.
To solve for x, we can use the sine function in the context of the right triangle. The sine function is defined as:
sin(M) = opposite side (x) / hypotenuse (Z)
We are given the values for angle M (43°) and the hypotenuse (Z = 56 units). Plugging these values into the equation, we get:
sin(43°) = x / 56
Now, to solve for x, we will multiply both sides of the equation by 56:
x = 56 * sin(43°)
Next, use a calculator or trigonometric table to find the sine of 43°:
sin(43°) ≈ 0.682
Now, multiply this value by 56:
x ≈ 56 * 0.682
x ≈ 38.192
Finally, round your answer to the nearest tenth:
x ≈ 38.2
So, the length of side x in the right triangle is approximately 38.2 units.

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The probability of getting a head on the coin or a prime number on the spinner is 2/3.

The probability of getting a head on the coin toss is 1/2, and the probability of landing on a prime number on the spinner is 1/6. By adding up the probabilities in the column corresponding to a head or any prime number, we find the overall probability.

Overall probability:

P(head or prime) = P(H) + P(2) + P(3) + P(5)

= 1/2 + 1/6 + 1/6 + 1/6

= 1/2 + 3/6

= 4/6

= 2/3

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The length of RU in triangle is,

⇒ RU = 16

We have o given that;

In triangle;

ST = 37

UT = 35

RS = 20

Hence, By using definition of Pythagoras theorem we get;

In triangle STU;

⇒ ST² = SU² + UT²

⇒ 37² = SU² + 35²

⇒ 1369 = SU² + 1225

⇒ SU² = 144

⇒ SU = 12

Hence, In triangle RSU;

⇒ RS² = SU² + RU²

⇒ 20² = 12² + RU²

⇒ 400 - 144 = RU²

⇒ RU² = 256

⇒ RU = 16

Thus, The length of RU in triangle is,

⇒ RU = 16

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False. It can be concluded that the faster a motor vehicle is traveling at the time of a crash, the more severe the injuries to the driver are

While the information states that there is a moderate positive correlation between the speed of the motor vehicle and the severity of injuries, correlation does not imply causation. Therefore, it cannot be concluded that the faster a motor vehicle is traveling at the time of a crash, the more severe the injuries to the driver are. Correlation simply indicates that there is a relationship between the two variables, but other factors may also be influencing the severity of injuries.

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Answer: What is the least number of gumballs jack has to buy to be certain he gets 6 gumballs of the same color?

Step-by-step explanation:

To be certain he gets 6 gumballs of the same color, Jack must buy at least 16 gumballs.

This is because he could buy 5 gumballs of each color (for a total of 15 gumballs) and still not have 6 gumballs of the same color. However, if he buys one more gumball, he will have at least 6 gumballs of one color.

Therefore, the least number of gumballs Jack has to buy to be certain he gets 6 gumballs of the same color is 16.

{Hope This Helps! :)}

Answer:

150

Step-by-step explanation:

The restaurant should expect to serve 180 customers in week 10.

The number of customers served in the restaurant follows a repeating pattern of 180, 170, 200, 180, 210, 180, 210, 170, 200, 180. Therefore, the number of customers served in week 10 will be 180.

The number of customers served in the restaurant follows a repeating pattern of 180, 170, 200, 180, 210, 180, 210, 170, 200, 180. This means that after 10 weeks, the number of customers served will be the same as it was in week 1. Since week 1 had 180 customers served, week 10 will also have 180 customers served.

As you can see, the number of customers served in week 10 is the same as the number of customers served in week 1. Therefore, the restaurant should expect to serve 180 customers in week 10.

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A distance-time graph below shows a car travelling then the Speed of the car is 8.88 miles per hour

Speed is the time rate at which an object is moving along a path,

A distance-time graph below shows a car travelling

We know that speed is distance by time

From the graph the distance is 80 and time is 9

Speed= 80/9

=8.88 miles per hour

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The probability that a randomly selected adult consumes more than 40.0 hamburgers in a year is approximately 0.85.

In order to find the probability that randomly selected adult eats more than 40.0 hamburgers in a year, we use the normal distribution and z-scores.

First, we need to standardize the value of 40.0 using the formula : z = (x - μ)/σ,

Where : x = value we want to standardize (40.0 hamburgers), μ = mean number of hamburgers eaten (48.5 hamburgers), σ = standard-deviation (8.3 hamburgers),

Substituting the values,

We get:

z = (40.0 - 48.5)/8.3,

z = -1.024

Next, we find the area under the normal-curve to the right of z = -1.024. This represents the probability of randomly selecting an adult who eats more than 40.0 hamburgers.

We know that area to left of z = -1.024 is approximately 0.15. We need the area to right, so, we subtract this value from 1,

P(x > 40.0) = 1 - P(x ≤ 40.0)

P(x > 40.0) = 1 - 0.15

P(x > 40.0) ≈ 0.85,

Therefore, the required probability is 0.85.

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The value of x in the triangle is,

x = 9.4 cm

We have to given that;

A triangle is shown in figure.

Now, By trigonometry formula we get;

cos 20° = Base / Hypotenuse

cos 20° = x / 10

0.94 = x / 10

x = 0.94 × 10

x = 9.4 cm

Thus, The value of x in the triangle is,

x = 9.4 cm

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