gary increased his income by 30 percent after changing jobs. if his previous income was 25,000 per year, what was his income after the job chan ge

The value of x obtained using the inverse trigonometric ratios for tangent  is x ≈ 51.1°

The tangent of an angle, θ, tan(θ) in a right triangle is the ratio of the length of the side adjacent to the angle to the length of the side opposite to the angle.

Mathematically; tan(θ) = Opposite/Adjacent

The details in the question includes;

The shape of the figure = A right triangle

The length of the side adjacent to the angle, ON x = 7.5

Length of the side opposite to the angle, NM x = 9.3

The measure of the angle x° can be found using the trigonometric ratio for tangent as follows;

tan(x) = NM/ON

Therefore;

tan(x) = 9.3/7.5

x° = arctan(9.3/7.5) ≈ 51.1°

x ≈ 51.1°

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\(\huge\text{Hey there!}\)

\(\mathsf{3x + 99x = 1,224}\\\\\large\textbf{COMBINE the LIKE TERMS}\\\\\mathsf{(3x + 99x) = 1,224}\\\mathsf{3x + 99x = 1,224}\\\mathsf{\bold{102x} = 1,224}\\\\\large\textbf{DIVIDE 102 to BOTH SIDES}\\\\\mathsf{\dfrac{102x}{102} = \dfrac{1,224}{102}}\\\\\large\textbf{SIMPLIFY IT!}\\\\\mathsf{x = \dfrac{1,224}{102}}\\\\\mathsf{x = 12}\\\\\\\huge\text{Therefore, your answer should be: \boxed{\mathsf{x = 12}}}\huge\checkmark\)

\(\huge\text{Good luck on your assignment \& enjoy your day!}\)

Just from a quick search, the motto of Zootopia is "anyone can be anything"

The probability she pulls out a purple piece of candy would be 0.22.

In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.

Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations and other aspects of logical syntax.

Given is Sam's fathers collection.

We can write the equations for upstream and downstream as -

x - y = 7/2

x + y = 21/10

Solving the equations graphically -

{x} = 2.8

{y} = 0.7
In still water, the speed would be -

S = 3 - 0.7

S = 2.3 Km/h

Distance peddled upstream -

D = 2.8 x 3.5 = 9.8 Km

Therefore, the speed in still water would be 2.3 Km/h and the distance peddled upstream would be 9.8 Km.

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Answer:

56

Step-by-step explanation:

simple ratio: 7/95 = x/760

first, calculate 7/95 which is 0.0736

next, multiply that by 760, which would be 56

According to the concept of algebraic expression and arithmetic, the correct answers are A) Number of adults = N - 25. B) Number of adults when N = 124: 124 - 25 = 99

A) Let's denote the number of children as N. Since there are 25 fewer adults than children, the number of adults can be expressed as N - 25.

B) If there are 124 children, we substitute N with 124 in the expression from part A. Thus, the number of adults would be 124 - 25 = 99.

To arrive at these answers, we used the given information that there are "N" children and 25 fewer adults than children. By substituting the value of N, we determined the number of adults in terms of N and then calculated the specific number of adults when N is equal to 124.

Note: The given question is incomplete. The complete question is:

Some adults and children are watching a musical. there are 'N' number of children. There are 25 fewer adults than children.

A) find the number of adults in terms of 'N'.

B) if there are 124 children how many adults are there?​

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a.The Industry Average Salary is $55,680. b.The Firm A's Average Salary is $51,718.40 .c. Firm B's average salary is approximately 112.27% of Firm A's average salary.

a. To determine the industry average salary, we can use the information that the industry average salary is 96% of Firm B's average salary. Firm B's average salary is $58,000. Therefore, we can calculate the industry average salary as follows:

Industry Average Salary = 96% of Firm B's Average Salary

= 0.96 * $58,000

= $55,680

b. Firm A's average salary is stated as 93% of the industry average salary. To calculate Firm A's average salary, we can multiply the industry average salary by 93%:

Firm A's Average Salary = 93% of Industry Average Salary

= 0.93 * $55,680

= $51,718.40

c. To express Firm B's average salary as a percentage of Firm A's average salary, we can divide Firm B's average salary by Firm A's average salary and multiply by 100:

Percentage = (Firm B's Average Salary / Firm A's Average Salary) * 100

= ($58,000 / $51,718.40) * 100

≈ 112.27%

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The Propositions are resulting

(a) ∀x∃y(x = y²) is False

(b) ∀x∃y(x² = y) is True.

(c) ∃x∀y(xy = 0) is True.

(d) ∀x∃y(x + y = 1) is True.

(a) ∀x∃y(x = y²)

This proposition states that for every x, there exists a y such that x is equal to y². To determine the truth value, we need to check if this statement holds true for every value of x.

If we take any positive value for x, we can find a corresponding value of y that satisfies the equation.

For example, if x = 4, then y = 2 satisfies the equation since 4 = 2². Similarly, if x = 9, then y = 3 satisfies the equation since 9 = 3².

Therefore, the proposition (a) is false.

(b) ∀x∃y(x² = y)

For any given positive or negative value of x, we can find a corresponding value of y that satisfies the equation.

For example, if x = 4, then y = 2 satisfies the equation since 4² = 2. Similarly, if x = -4, then y = -2 satisfies the equation since (-4)² = -2.

Therefore, the proposition (b) is true.

(c) ∃x∀y(xy = 0)

The equation xy = 0 can only be satisfied if x = 0, regardless of the value of y. Therefore, there exists an x (x = 0) that makes the equation true for every y.

Therefore, the proposition (c) is true.

(d) ∀x∃y(x + y = 1)

To determine the truth value, we need to check if this statement holds true for every value of x.

If we take any value of x, we can find a corresponding value of y that satisfies the equation.

For example, if x = 2, then y = -1 satisfies the equation since 2 + (-1) = 1. Similarly, if x = 0, then y = 1 satisfies the equation since 0 + 1 = 1.

Therefore, the proposition (d) is true.

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Answer:

1. 8t

2. 510 + 6t

3. 510 - 2t

Step-by-step explanation:

1. Since the hare moves at a speed of 8 metres per second, the distance it moves from the starting line is d = speed × time = 8t

2. Since the rabbit moves at a speed of 6 metres per second, and gets a head start of 510 metres, the distance it moves from the starting line is d = 510 m + speed × time = 510 + 6t

3. The distance the tortoise is ahead of the hare is thus, distance moved by rabbit - distance moved by hare in time, t.

d' = 510 + 6t - 8t

= 510 - 2t  

im so sorry i dk.............

Answer:

D. 41 races

Step-by-step explanation:

We can use the equation:

Number of races per year = Total number of races / Number of years

In this case, the total number of races is 287 and the number of years is 7.

Plugging in the values:

Number of races per year = 287 / 7

Number of races per year = 41

So, Laurie won 41 races each year. The answer is D) 41 races

Answer:

your answer is fifteen

∠G+∠H+∠J=180 and ∠K+∠L+∠M=180 from the angle sum property of triangle, ∠H=∠L (3rd Angle Theorem) and ∆GHJ≅∆KLM from ASA congruency theorem.

In the given question we have to prove ∆GHJ congrurnce ∆KLM.

Given that: ∠G≅∠K, ∠J≅∠M, \(\over{HJ}\) ≅ \(\over{LM}\).

As given that;

∠G≅∠K

∠J≅∠M

\(\over{HJ}\) ≅ \(\over{LM}\)

So from the angle sum property of triangle

∠G+∠H+∠J=180................(1)

∠K+∠L+∠M=180.................(2)

Now equation equation 1 and 2

∠G+∠H+∠J=∠K+∠L+∠M

As we know that ∠G=∠K, ∠J=∠M

So now the expression is

∠G+∠H+∠J=∠G+∠L+∠J

After solving ∠H=∠L (3rd Angle Theorem)

Since, ∠H=∠L, HJ=LM and ∠G=∠K, so from the theorem Angle Side Angle(ASA) congruency,

∆GHJ≅∆KLM

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326 divided by 0.24 to the nearest hundredth is 1358.33

To divide 326 by 0.24 and round the result to the nearest hundredth, we can perform the following calculation:

326 ÷ 0.24 = 1358.3333

Rounding to the nearest hundredth means we need to look at the third decimal place.

So 326 divided by 0.24 to the nearest hundredth is 1358.33.

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Answer:

The total compound interest is $37,147.24.

Step-by-step explanation:

I could be wrong

Answer:

√38

Step-by-step explanation:

√38

step 1: Check which squared numbers can be multiplied by another number to get 38.

Start with these numbers: 4, 9, 16, and 25

Step 2: Testing out the numbers

√25 × __ = 25 can't be divided by 38

√16 × ___ = 16 can't be divided by 38

√9 × ____ = 9 can't be divided by 38

√4 × ____= 4 can't be divided by 38

Step 3: Answer

After trying the square root numbers that could possibly work with √38 none work; which means √38 can't be simplified. So the answer is √38

I hope this helps!

Answer: 0.7

Step-by-step explanation:

Answer:

0.7 is the decimal

Answer:

5/34

Step-by-step explanation:

change 10:68 into 10/68, then divide by 2/2 to get 5/34.

Answer: To find the distance of a chord from the center of a circle, we need to use the following formula:

Distance from center = sqrt(r^2 - (c/2)^2)

Where r is the radius of the circle and c is the length of the chord.

In this case, the radius of the circle is 3.7cm and the length of the chord is 7cm.

So, substituting these values in the formula, we get:

Distance from center = sqrt(3.7^2 - (7/2)^2)

= sqrt(13.69 - 12.25)

= sqrt(1.44)

= 1.2 cm

Therefore, the distance of the chord from the center of the circle is 1.2 cm.

Step-by-step explanation:

Answer:

x=5

y=2

Step-by-step explanation:

5x + 3y= 31

-6x - 3y = -36  (multiple  by -3)

-x=-5

x=5

2(5)+y=12   or         25 + 3y= 31

10+y=12                  3y=6

y=2                          y=2

Answer:

x = 5, y = 2

Step-by-step explanation:

I'll use substitution on this one, which makes me choose one of the equation and solve for x. (5x + 3y = 31 was chosen)

5x + 3y = 31

Subtracct 3y from both sides

5x = -3y + 31

Divide both sides by 5

x = 1/5 (-3y + 31)

Multiply 1/5 by -3y + 31

x = -3/5y + 31/5

Substitute -3/5y + 31/5 for x in the other equation (2x + y = 12)

2 (-3/5y + 31/5) + y = 12

Multiply -3/5y + 31/5 by 2.

-6/5y + 62/5 + y = 12

Add -6/5y to y

-1/5y + 62/5 = 12

Subtract 62/5 from both sides

-1/5y = -2/5

Multiply both sides by -5

y = 2

Now head back to the previous equation, except substitute y for 2.

x = -3/5 * 2 + 31/5

Multiply -3/5 by 2.

x = (-6 + 31)/5

Add -6 and 31

x = 25/5

Divide 25 by 5.

x = 5

Formulate 5 and 2 for x and y in the equation.

5(5) + 3(2) = 31

2(5) + 2 = 12

25 + 6 = 31; true

10 + 2 = 12; true

x is 5 and y is 2.

Answer: 2 feet.

Step-by-step explanation: 16 - 14 = 2. That would be 14 inches. 2 feet.

Answer:

A

Step-by-step explanation:

The compound amount after 3 years is $2275.22.

In this case, you are given:

Principle = $2,000

rate = 0.0353

time = 3

You need to find A, the compound amount after 3 years.

To do this, you need to plug in the values of P, r and t into the formula and use a calculator:

A=P×e^rt

A=2000×(e)^0.0353×3

A≈2275.22

Therefore, by the compound interest the answer will be $2275.22.

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Answer:

{-5, -1, 2}

Step-by-step explanation:

domain is the inputs or x numbers

Answer:

ŷ = -1.618X + 215.636

191

Step-by-step explanation:

From the graph:

The data below could be obtained to produce the best fit line :

Week, x :

0

1

2

3

4

5

6

7

8

9

10

Weight :

216

214

213

210

210

207

206

202

203

202

200

Using a linear regression calculator. The best fit line obtained is :

ŷ = -1.618X + 215.636 ; which shows decrease in weight has the number of weeks grow.

Carters weight 15 Weeks into his diet :

X = 15

ŷ = -1.618(15) + 215.636

= 191.366

= 191 (nearest whole number)

Answer: C) 165

Step-by-step explanation:

\(\displaystyle\\C_{11}^3=\\\\\frac{11!}{(11-3)!3!} =\\\\\\\frac{8!*9*10*11}{8!*1*2*3} =\\\\\\\frac{9*10*11}{2*3} =\\\\3*5*11=\\\\15*11=\\\\165\)

Answer:

Step-by-step explanation:

Answer:

P(B,B) = 3/68

P(R,B) = 2/17

P(R,R) = 7/17

Step-by-step explanation:

P(B,B) = 4/17 · 3/16 = 3/68

P(R,B) = 8/17 · 4/16 = 2/17

P(R,R) = 8/17 · 7/16 = 7/17

Answer:

all are 17.67%

Step-by-step explanation: