Mr. Lucas contributed $1,576 to his
retirement account each month for
18 months. How much did he
contribute to his retirement account
in all?

Answer:

Angle A is 59.5 degrees

Step-by-step explanation:

i got you!

Answer:

∠ A ≈ 59.5°

Step-by-step explanation:

Using the sine ratio in the right triangle

sinA = \(\frac{opposite}{hypotenuse}\) = \(\frac{BC}{AB}\) = \(\frac{56}{65}\), then

A = \(sin^{-1}\) ( \(\frac{56}{65}\) ) ≈ 59.5° ( to 1 dec. place )

The radius of the circle is given as 9

To rewrite the equation of the circle from general form to standard form, we need to complete the square for both x and y terms.

x^2 - 18x + y^2 + 14y + 84 = 0 (Given)

To complete the square for x, we need to add and subtract the square of half the x coefficient (i.e., (18/2)^2 = 81) inside the parentheses:

x^2 - 18x + 81 + y^2 + 14y + 84 - 81 = 0

(x - 9)^2 + (y + 7)^2 - 81 = 0

(x - 9)^2 + (y + 7)^2 = 81

This is the standard form of the equation of a circle, where the center is located at (9, -7) and the radius is √81 = 9.

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The function f(x) = arcsin(\(x^2\)- 2x) is increasing for x > 1. To determine where the function f(x) = arcsin(\(x^2\) - 2x) is increasing, we need to find the intervals where its derivative, f'(x), is positive.

First, find the derivative of the inner function, g(x) = \(x^2\) - 2x:
g'(x) = 2x - 2
Now, find the derivative of the outer function, h(u) = arcsin(u), where u = g(x):
h'(u) = 1/√(1 - \(u^2\))
Using the chain rule, the derivative of f(x) is the product of the derivatives of the inner and outer functions:
f'(x) = h'(g(x)) * g'(x) = (1/√(1 - \((x^2 - 2x)^2)\)) * (2x - 2)
To find where f(x) is increasing, we need to determine where f'(x) > 0. Since the denominator of the fraction is always positive, we only need to focus on the numerator:
2x - 2 > 0
Solving for x, we get:
x > 1

The complete question is:-

Determine where f(x) = arcsin (\(x^{2}\) − 2x) is increasing.

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Answer:

Step-by-step explanation:

An input-output table's rule can be found by looking at the first input-output pair and figuring out what rules could be used to create that combination.

Find the proper rule by comparing it to a second input-output combination.

Verify your rule once more using a third input-output combination.

The roots of the given quadratic equation 3x² - 3x + 1 are x = [3 + √(-3)]/6 and x = [3 - √(-3)]/6 thus options (A) and (B) are correct.

An algebraic equation of the second degree in x is a quadratic equation. The quadratic equation is written as ax2 + bx + c = 0, where x is the variable, and a must not be zero.

As per the given equation,

3x² - 3x + 1

To find the roots of the above quadratic equation,

3x² - 3x + 1 = 0

x = [-(-3) ± √((-3)² - 4×3×1)]/(2×3)

x = [3 ± √(-3)]/6

x = [3 + √(-3)]/6 and x = [3 - √(-3)]/6

Hence "The roots of the given quadratic equation 3x² - 3x + 1 are x = [3 + √(-3)]/6 and x = [3 - √(-3)]/6".

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The equation of the circle that meets the specified requirements is x^2 + y^2 = 89, with the center at the origin and going through P(5, 8).

In its most basic form, an equation is a mathematical statement that indicates that two mathematical expressions are equal. 3x + 5 = 14, for example, is an equation in which 3x + 5 and 14 are two expressions separated by a 'equal' sign. A mathematical phrase with two equal sides separated by an equal sign is called an equation. An example of an equation is 4 + 6 = 10.

Here,

The equation of a circle with center at the origin (0,0) and passing through the point (x1,y1) can be found using the distance formula.

The distance between a point (x1, y1) and the origin (0,0) is given by:

sqrt((x1-0)^2 + (y1-0)^2) = sqrt(x1^2 + y1^2)

Let's call the radius of the circle r. We know that the distance between the point (x1,y1) and the origin is equal to r. So, we can set up the equation:

sqrt(x1^2 + y1^2) = r

Substituting the values x1 = 5 and y1 = -8, we have:

sqrt(5^2 + (-8)^2) = r

Solving for r, we get:

r = sqrt(5^2 + (-8)^2) = sqrt(25 + 64) = sqrt(89)

Finally, we can write the equation of the circle in standard form using the center (0,0) and radius r:

(x - 0)^2 + (y - 0)^2 = r^2

x^2 + y^2 = r^2

x^2 + y^2 = 89

The  equation of the circle that satisfies the stated conditions that is center at the origin, passing through P(5, −8) is x^2 + y^2 = 89.

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Answer:

5

Step-by-step explanation:

Answer:

5

hope it helped you out

a)1 unit or less away from the x-plane. b) 1 unit or less away from the y-plane. c)1 unit or less away from the z-plane.

d)1 unit or less away from the w-plane.

a. The region on or the parabola in the ​x-plane and all points which are 1 unit or less away from the ​x-plane.
To find the region on or the parabola in the x-plane, we need to graph the equation of the parabola and determine the points that are 1 unit or less away from the x-plane.

b. The region on or the parabola in the ​y-plane and all points which are 1 unit or less away from the ​y-plane.
To find the region on or the parabola in the y-plane, we need to graph the equation of the parabola and determine the points that are 1 unit or less away from the y-plane.

c. The region on or the parabola in the z-plane and all points which are 1 unit or less away from the z-plane.
To find the region on or the parabola in the z-plane, we need to graph the equation of the parabola and determine the points that are 1 unit or less away from the z-plane.

d. The region on or the parabola in the w-plane and all points which are 1 unit or less away from the w-plane.
To find the region on or the parabola in the w-plane, we need to graph the equation of the parabola and determine the points that are 1 unit or less away from the w-plane.

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eighteen biscuits are made from each cup

Answer:

y = 7x -  6

Step-by-step explanation:

We are given the slope of 7 and the y-intercept of (0, -6).

We can easily write this in slope-intercept form.

\(y=mx+b\)

m - slope

b - y-intercept

Replace 'm' with '7' and 'b' with '-6'.

\(y=mx+b\rightarrow \boxed {y=7x-6}\)

Hope this helps.

Answer: A. 20 is the answer.

Step-by-step explanation:

x+40 = 3x

or, 40 = 3x-x

or, 2x = 40

or, x = 40/2

so, x = 20

The figure consist of four sides such that all four side form a closed figure then such figure is called quadilateral.

The quadilateral has four sides and all four side form a closed figure.

Answer

The height of the plane at that time is 1.1 miles

The distance of the plane's path is 10.1 miles

Explanation

The situation models a right angle triangle as shown below

Using trigonometric ratio,

tan 6° = opposite / adjacent

The opposite side of the triangle is the height of the plane. The distance traveled horizontally is the adjacent side. Therefore,

The height of the plane at that time ≈ 1.1 miles

The hypotenuse of the triangle formed is the distance of the plane path.

Therefore, this distance can be calculated using Pythagoras rule as follows:

The distance of the plane's path = 10.1 miles

The results using Fermat's little theorem are:

a. \(315 \mod 13 = 1\)

b. \(1518 \mod 17 = 1\)

c. \(4567 \mod 17 = 1\)

d. \(145102 \mod 101 = 1\)

Fermat's little theorem states that if p is a prime number and a is an integer not divisible by p, then \(a^{p-1} \equiv 1 \mod p\). We can use this theorem to find the results of the given congruences:

a. To find \(315 \mod 13\), we note that 13 is a prime number. Since 315 is not divisible by 13, we can apply Fermat's little theorem. We have \(315^{12} \equiv 1 \mod 13\). Simplifying this expression, we get \(315 \equiv 1 \mod 13\). Therefore, \(315 \mod 13 = 1\).

b. For \(1518 \mod 17\), we again use Fermat's little theorem. Since 17 is prime and 1518 is not divisible by 17, we have \(1518^{16} \equiv 1 \mod 17\). Simplifying this expression, we find \(1518 \equiv 1 \mod 17\). Hence, \(1518 \mod 17 = 1\).

c. Similarly, for \(4567 \mod 17\), we apply Fermat's little theorem. Since 17 is prime and 4567 is not divisible by 17, we have \(4567^{16} \equiv 1 \mod 17\). This simplifies to \(4567 \equiv 1 \mod 17\). Therefore, \(4567 \mod 17 = 1\).

d. Lastly, for \(145102 \mod 101\), we can once again use Fermat's little theorem. Since 101 is prime and 145102 is not divisible by 101, we have \(145102^{100} \equiv 1 \mod 101\). This simplifies to \(145102 \equiv 1 \mod 101\). Thus, \(145102 \mod 101 = 1\).

Therefore, the results using Fermat's little theorem are:

a. \(315 \mod 13 = 1\)

b. \(1518 \mod 17 = 1\)

c. \(4567 \mod 17 = 1\)

d. \(145102 \mod 101 = 1\)

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2005 is 10 years after 1995.

\(392(10)+5400=\boxed{\$8690}\)

(a) The probability tree diagram summarizes the possible outcomes of Spinner A and Spinner B. Spinner A can land on either 2 or 3, and Spinner B can also land on 2 or 3. The outcomes are represented by (A, B) pairs.

(b) Probability of A=2, B≠2: 1/2. Favorable outcomes: (2,3), (2,2). Total outcomes: 4.

(a) The probability tree diagram for the given scenario can be completed as follows:

```

                   Spinner A

               /             \

             2                3

      Spinner B         Spinner B

       /     \          /      \

     2        2        2        3

   (2, 2)  (2, 3)  (3, 2)  (3, 3)

```

In the probability tree diagram, the branches represent the possible outcomes of each spinner, and the numbers in parentheses denote the outcome of each spin (Spinner A, Spinner B).

(b) To calculate the probability that Spinner A lands on 2 and Spinner B does not land on 2, we need to find the probability of the outcome (2, not 2) from the probability tree diagram.

From the diagram, we can see that there are two favorable outcomes: (2, 3) and (2, 2), where Spinner A lands on 2, but Spinner B does not land on 2.

The total number of possible outcomes is four, as there are four possible combinations of Spinner A and Spinner B outcomes: (2, 2), (2, 3), (3, 2), (3, 3).

Therefore, the probability of Spinner A landing on 2 and Spinner B not landing on 2 is:

Probability = Number of favorable outcomes / Total number of possible outcomes

Probability = 2 / 4 = 1/2

Hence, the probability that Spinner A lands on 2 and Spinner B does not land on 2 is 1/2.

In summary, the probability that Spinner A lands on 2 and Spinner B does not land on 2 is 1/2, which can be obtained by analyzing the probability tree diagram and calculating the ratio of favorable outcomes to the total number of possible outcomes.

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The distance from Dan's house to Samuel's house is 4 km

The distance from Dan to Samuel house, Dan to Cindy house and Samuel to Cindy house forms a right angled triangle.

Distance from Dan to Samuel house = x, Distance from Dan to Cindy house = 3 km and Distance from Cindy to Samuel house = 5 km

Pythagoras theorem shows the relationship between the lengths of a right angled triangle.

Using Pythagoras theorem:

5² = x² + 3²

25 = x² + 9

x² = 16

x = 4 km

Hence the distance from Dan's house to Samuel's house is 4 km

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Answer: Yes

Step-by-step explanation:

Yes area should be right because you are finidng how much it covers which would be area. A way I used to remember it was you looking for the AREA it covers so that awnser is area! Hope that helped!

Answer:

Yes

Step-by-step explanation:

Yes, that is exactly what Sarah did wrong. Apparently, she tried to divide both the numerator and denominator in this problem by 2 (half) but divided the numerator incorrectly. 26 divided by 2 would equal 13 but Sarah mistakenly calculated it as 14 which would give her a totally different value when divided by the new denominator. If were to have divided correctly it would give her \(\frac{13}{4}\) which is the same as \(\frac{26}{8}\)

Answer:

0.7890176%

Step-by-step explanation:

First, there is a 64% chance of failing a test.

Then there are 54 cards in a deck. There are two colors, red and black. There are two red aces and two black aces. You have a 50% chance that the card is red. Then there are 27 cards of each color. Since there are 2 aces in those 27, there is a 2/27 or ~7.4%.

Lastly there are 6 sides on a die. Each side has the same chance of landing. So this gets you 16.66%

Now we need to multiply each chance of something happening by one another

64% × 7.4% = 0.04736%

4.736% × 16.66% = 0.7890176%

So there is a 0.7890176% of all of these happening

The probability that you will fail a test, draw a red ace, and then roll a 6 is  0.7890176%

We have given that,

First, there is a 64% chance of failing a test.

We have to determine the probability

Probability is an event is to occur, or how likely it is that a proposition is true. The probability of an event is a number between 0 and 1, where, roughly speaking, 0 indicates the impossibility of the event and 1 indicates certainty.

Then there are 54 cards in a deck. There are two colors, red and black. There are two red aces and two black aces.

You have a 50% chance that the card is red. Then there are 27 cards of each color. Since there are 2 aces in those 27, there is a 2/27 or ~7.4%.

Lastly there are 6 sides on a die. Each side has the same chance of landing. So this gets you 16.66%

Now we need to multiply each chance of something happening by one another

64% × 7.4% = 0.04736%

4.736% × 16.66% = 0.7890176%

So there is a 0.7890176% of all of these happening

Therefore the probability that you will fail a test, draw a red ace, and then roll a 6 is  0.7890176%.

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Answer:

85

Step-by-step explanation:

The sum of the angles of a triangle are 180 degrees

A + B+ C = 180

A +72+ 23 = 180

Combine like terms

A + 95  = 180

Subtract  95  from each side

A +95-95 = 180-95

A =85

Answer:

x + 8

Step-by-step explanation:

Expand the brackets.

-4(x-2) + 5x

-4x + 8 + 5x

x + 8

Different geometries exist because the concept of "geometry" refers to a branch of mathematics that studies the properties and relationships of points, lines, shapes, and spaces.

Geometry is indeed a branch of mathematics that deals with the study of spatial relationships and properties. It explores the nature of points, lines, angles, shapes, and their interconnections. The concept of "geometry" can be seen as a broad term encompassing various systems and frameworks within which these relationships are studied.

Different geometries arise from different sets of axioms and assumptions. Euclidean geometry, named after the Greek mathematician Euclid, is the most familiar and widely studied geometry. It assumes certain basic axioms, including the parallel postulate, and follows a set of logical deductions to establish the properties of flat, two-dimensional space and three-dimensional space.

However, there are also non-Euclidean geometries that depart from these assumptions. For example, in spherical geometry, the curvature of a sphere introduces different properties compared to flat Euclidean space. Hyperbolic geometry, on the other hand, exhibits different properties from both Euclidean and spherical geometries, with its own set of axioms and structures.

In summary, the existence of different geometries arises from the fact that geometry is a branch of mathematics concerned with studying spatial relationships and structures. Different geometries result from variations in axioms and assumptions, leading to distinct sets of properties and rules that govern points, lines, shapes, and spaces.

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Answer:

61/84

Step-by-step explanation:

i just finished doing that problem

Answer: 61/84

Step-by-step explanation:

82

84

−

3

12

=

82

84

+

−3

12

=

41

42

+

−1

4

=

82

84

+

−21

84

=

82+−21

84

=

61

84

Answer:

268,770 AU i think im not to sure

Step-by-step explanation:

Answer:

15

hope this helps

have a good day :)

Step-by-step explanation:

ANSWER:

YOUR ANSWER IS C,15

EXPLAINATION:16 - 1 = 15, Range = 15

Answer:1/4

Step-by-step explanation:

Answer:

$67.50

Step-by-step explanation:

Method 1

original rate = $12.50 per hour

therefore, money earned in 15 hours = 15 x 12.50 = $187.50

new rate = 12.50 + 4.50 = $17 per hour

therefore, money earned in 15 hours = 15 x 17 = $255.00

255 - 187.50 = $67.50

Therefore, Kate earns $67.50 more after the raise.

Method 2

As the raise is an additional $4.50 per hour, simply multiple 4.50 by 15 to calculate the extra money Kate earns:

4.5 x 15 = 67.50

The average value of a necklace at Julie's shop is $4.90. For further explanation;-

Julie the jeweler has two gold necklaces worth $105, seven silver necklaces valued at $100, twenty-seven plated necklaces valued at $55, and twenty-two beaded necklaces worth $25. The average value of a necklace at Julie's shop can be calculated by finding the sum of the values of all the necklaces and dividing it by the total number of necklaces.

The total value of all the necklaces is $105 + $100 + $55 + $25 = $285. The total number of necklaces is 2 + 7 + 27 + 22 = 58.

Therefore, the average value of a necklace is $285 / 58 = $4.90. This answer should be rounded to the nearest cent, giving an average value of $4.90 per necklace at Julie's shop.

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