Number 1 please help

Answer:

Engineer: 9.5 hr

Assistant: 4.5 hr

Step-by-step explanation:

To solve this problem, we can create and solve a system of equations.

Define the variables:

Given the engineer's time is billed at $40 per hour, and her assistant's is billed at $10 per hour, and a customer received a bill for $425 for a certain job:

Given the assistant worked 5 hours less than the engineer:

Therefore, the system of equations that represents the problem is:

\(\begin{cases}40x+10y=425\\ \quad \qquad \;\;\;y=x-5\end{cases}\)

Substitute the second equation into the first equation to eliminate y:

\(40x+10(x-5)=425\)

Solve the equation for x to find the number of hours the engineer worked:

\(\begin{aligned}40x+10(x-5)&=425\\40x+10x-50&=425\\50x-50&=425\\50x&=475\\x&=9.5\end{aligned}\)

Therefore, the engineer worked 9.5 hours.

Substitute the found value of x into the second equation and solve for y to find the number of hours the assistant worked:

\(\begin{aligned}y&=x-5\\y&=9.5-5\\y&=4.5\end{aligned}\)

Therefore, the assistant worked 4.5 hours.

The area of the triangle, when a = 2 and c = 3, is 1512 square centimeters.

We must apply the formula for the area of a triangle, which is provided by: to determine the triangle's area.

(1/2) * Base * Height = Area

We can enter the values of a = 2 and c = 3 into the formula given that the base length is 3ac2 and the height is 2 centimetres greater than the base length.

Base length =\(3ac^2 = 3 * 2 * (3^2) = 3 * 2 * 9 = 54\) centimeters

Height is calculated as Base Length + 2 (54 + 2 = 56 centimetres).

Using these values as a substitute in the formula, we obtain:

Area =\((1/2) * 54 * 56 = 1512\) square centimeters

centimetres square

It's crucial to understand that the calculation assumes the triangle is a right triangle with the specified base and height and that the given values of a and c are accurately used in the formula.

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The line perpendicular to the equation and has the same y-intercept with another is y = - 4 / 3 x + 4.

The equation of a line can be describe as follows:

y = mx + b

where

Therefore, lines that a perpendicular follows the rule below:

m₁m₂ = -1

Hence,

y + 6 = 3 / 4 (x - 2)

y + 6 = 3 / 4 x - 6 / 4

y =  3 / 4 x - 6 / 4 - 6

y = 3 / 4 x - 30 / 4

y = 3 / 4 x - 15 / 2

Hence,

3 / 4 m₂ = -1

m₂ = - 4 / 3

Therefore,

slope of the line is - 4 / 3

Let's find the y-intercept of the second line

4x + 5y -20 = 0

5y = -4x + 20

y = -4 / 5 x + 4

y-intercept  = 4

Therefore, the line perpendicular to the equation and has the same y-intercept with another is y = - 4 / 3 x + 4.

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Answer:c, the answer is c

Step-by-step explanation:

Answer:

5.04%

Step-by-step explanation:

To find the percent difference (which represents the tax percent/rate), we can first use the formula

(final value - inital value) / (inital value)

Our final value is 7.30, and our initial value is 6.95. Plugging this into the formula, we get

(7.3-6.95)/(6.95) = 0.0504

This is a decimal. To convert a decimal to a percent, we simply multiply the decimal by 100, getting

0.0504 * 100 = 5.04% as our answer

Answer:

it is called an irrational number

Step-by-step explanation:

I think that this is a fact answer, so I don't know how to explain it

The rule of (x, y) → (-x, y), which is reflection over y-axis.

Given that, ΔABC maps to triangle ΔA'B'C'.

When you reflect a point across the y-axis, the y-coordinate remains the same, but the x-coordinate is taken to be the additive inverse. The reflection of point (x, y) across the y-axis is (-x, y).

The coordinate points of ΔABC are A(-4, 3), B(-3, -3) and C(1, 2) and the coordinate points of ΔA'B'C' are A'(4, 3), B'(3, -3) and C'(-1, 2).

Here, A(-4, 3) → A'(4, 3), x-coordinate is negated and y-coordinate remains same.

Similarly, B(-3, -3) → B'(3, -3) and C(1, 2) → C'(-1, 2) follows the same pattern.

From this, it is clear that the coordinates of triangle ABC is reflected on y-axis.

Therefore, the rule of (x, y) → (-x, y), which is reflection over y-axis.

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The present value of the nominal rate of the annuity will be $535.

Annuity amount = 20

Number of annuities = 32

APR = 16%

PV of annuities = 357

Number of years to perpetuity = 8

Quarterly perpetuity = 25

PV of perpetuity at 9th year = 625

PV of perpetuity today = 178

Total PV = 357 + 178 = 535

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Answer:

Lets start with D:

It says, 0.43 but we're on the OPPOSITE of 0, so it can't be a positive number.

Same goes for C.

Now we are on to our last two.

B, is -2.5 and A, is -0.8

So, now we look at the point B and assume, because it says Select a reasonable value for Point B.

To me, point B looks to be about around -2.0

So, the reasonable value for this problem would be -2.25

Step-by-step explanation:

sin A = opposite/ Hypotenuse

Sin A = 5/7

Hello !

sin(A) = opposite/hypotenuse = 5/7

arcsin(5/7)  ≈ 45,58°

sin(A) = 5/7

the angle A ≈ 45,58°

Answer:

Step-by-step explanation:

x+9

Let x, be 4

4+9=13

given condition,

x+9<4x

4+9<4(4)

13<16

The answer is:

Work/explanation:

Our inequality is:

\(\sf{x+9 < 4x}\)

Flip it

\(\sf{4x > x+9}\)

Solve

\(\sf{4x-x > 9}\)

Combine like terms

\(\sf{3x > 9}\)

Divide each side by 3

\(\sf{x > 3}\)

Lucio is 64 meters from the starting point.

The square has four sides of equal length, so Lucio has walked half the length of one side.

To return to the starting point, he needs to walk the other half of the side, which is 64 meters.

The angle Lucio turns is irrelevant, as long as he turns 180 degrees in total.

With this in mind, it can be seen that based on the parameters and the conditions, Lucio is 64 meters from the starting point because the angle to which he turns is irrelevant.

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The question in English:

In a square Lucio walks in straight sections, starting from the flagpole, at one point he changes direction turning 150º to his left, advances 64 meters and stops. To return to the pole you have to turn 75º to the left. How far are you from the starting point?

Answer:

40 1/3

Step-by-step explanation:

7 1/3 x 5 1/2 =

121 /3 = 40 1/3

Answer:

When \(x=0\), the value of f(x) is 1.

Each time x increases by 1, f(x) is multiplied by 4.

Equation of function: \(f(x)=1\cdot 4^x\)

Step-by-step explanation:

The detailed explanation is attached below.

Answer:

Step-by-step explanation:

1/3= 1 hour

1/3= 1 hour

2/3 plus 2 tablespoons plus 1 teaspoon eaten.

I think I did the calculation correctly.

Answer:

-6

Step-by-step explanation:

Answer:

18

Step-by-step explanation:

3/5 x 30

(3 times 30)divided by 5

= 18 children are going.

Hope this helps:-)

Answer:

Step-by-step explanation:

4x-13

Answer:

4x - 13 there you go!!!

Step-by-step explanation:

The probability for the given case is 5/23.

Probability is the branch of Mathematics that deals with the measurement of the chance of occurrence of a random event.

The probability of any event always lie in the close interval of 0 and 1 [0,1].

Given that,

Total number of students is 29.

The students who play instrument are 23.

Those who play a sport are 9.

And, those who play both are 5.

Given problem is the case of conditional probability which can be solved by Bayes's theorem as,

P(A|B) = P(A ∩ B) / P(B)

Suppose, A be the event the students play instrument.

B be the event the students play a sport.

And, A ∩ B is the event they play th both.

Then A|B implies the event when a student play instrument given he plays sport.

Apply the rule of probability in the equation for Bayes's theorem to get,

P(A|B) = (5/29) / (23/29)

          = 5/23

Hence, the probability that a student plays an instrument given that they play a sport is 5/23.

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Answer:

Step-by-step explanation:

Given:

fair coin is flipped n times

sequence is balanced when there are equal number of heads and tails

To find:

In terms of n, what is the expected number of times the sequence is balanced within n flips

Solution:

Let C(n,r) be the binomial co-efficient. The sample space has \(2^{n}\)

Suppose that n is even because there are equal number of heads and tails and the number of heads and tails is not equal when n is odd.

As the result can be either head or tail so the probability of getting head is 1/2. So the number of these sequences with n/2 head is C(n,n/2) since we choose n/2 out of n to be assigned heads.

As every string sequence is equal chance of occurring so the probability is

C(n,n/2) / \(2^{n}\)

If the train travels at an average speed of 50 Km/h, it would be late by 10 minutes.

Speed is simply referred to as distance traveled per unit time.

It is expressed as:

Speed = distance / time

Given that the train running between two stations 50 Km apart arrives on time if it travels at an average speed of 60 km/h.

The time taken by the train to travel 50 km at an average speed of 60 km/h can be calculated using the formula:

Speed = distance / time

time = distance / speed

time = 50 km / 60 km/h

time = 5/6 hour

Next, if the train travels at an average speed of 50 km/h, the time taken to cover the same distance of 50 km would be:

Speed = distance / time

time = distance / speed

time = 50 km / 50 km/h

time = 1 hour

Now, the difference in time between the two scenarios would be:

time difference = 1 hour - 5/6 hour

time = 1/6 hour

Convert to minutes

time = 1/6 × 60

time = 10 minutes

Therefore, the train would be late by 10 minutes.

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Answer:

0.391+8.42=8.811

8.811 in dollars is 10.42 United States Dollars

Step-by-step explanation:

Your answer is 10.42 c:

Answer:

Step-by-step explanation:

y = 3*\(\sqrt{15}\)

Answer:

3,952 ft

Step-by-step explanation:

Use the sine function since you need to find the hypotenuse but know the opposite side of the angle, since sine is equal to opposite/hypotenuse.

sin8°=\(\frac{550}{c}\)

csin8°=550

c=550/sin8°

c= 3,952

The ODE's general solution has real solution and complex eigen functions. Typical trajectories are sinusoidal curves.

The general solution of the ODE involves complex eigenfunctions, which are solutions of the form e^(ikx), where k is a real number and i is the imaginary unit. By combining these complex eigenfunctions with real coefficients, a general real solution can be obtained. Typically, these solutions will take the form of sinusoidal curves, with the amplitude and period determined by the coefficients of the eigenfunctions. The coefficients can be determined using initial conditions, allowing for more specific trajectories to be determined. For example, if the initial condition is known, then the coefficients of the eigenfunctions can be determined using Fourier analysis, allowing for the trajectory of the system to be determined.

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Answer:

$8518.40

Step-by-step explanation:

FV = PV(1+r)^n

FV = future value

PV = present value

r = rate

n = # of years

Value in 2 yrs = 11,000 x (1 - 0.12)^2 = 8518.4

If 18 out of the 24 girls scored, it means that 6 missed. Therefore, the ratio of missed to total tried​ is:

Simplified,

Meaning that 1 out of every 4 girls that shot during the drill missed.

Answer:

8

Step-by-step explanation:

5 = 40

1 = x

Then we multiply by the rule of crisscrossing

5 x X = 40 x 1

5x = 40 then divide both by 5

X = 8

Answer:

D. 60.3

Step-by-step explanation:

Finding the mean,

M = (sum of values of data)/(number of data)

now, number of data = 9,

calculating the mean,

M = (54 + 68 + 68 + 54 + 59 + 58 + 68 + 57 + 57)/9

M = 543/9

M = 60.333

M = 60.3