Solving Equations. 2(a-3)=5a+3a

Answer:

X = 1 and below

Step-by-step explanation:

since X is less than 2.

the value of X will be 1 and below.

Answer:

Given distance=360 km.

Let the speed of the train be x km/hr.

Speed when increased by 5 km/hr =(x+5) km/hr

x

360

−

(x+5)

360

=1

x(x+5)

[360x+1800−360x]

=1

x

2

+5x−1800=0

x

2

+45x−40x−1800=0

x(x+45)−40(x+45)=0

(x−40)(x+45)=0

x=40,−45

The speed of the train is 40 km/hr.

Step-by-step explanation:

thanks... ☺️

Answer:

Below

Step-by-step explanation:

It's 66

To find a percentage of a number just multiply it by 0.whatever the percentage if that makes sense...

In this case you would do 55 x 1.2 = 66

Hope this helps!

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

\(\huge\boxed{\mathsf{120\% \ of\ 55}}\\\huge\boxed{= \dfrac{120}{100}\times55}\\\huge\boxed{= \dfrac{6}{5}\times\dfrac{55}{\bf 1}}\\\huge\boxed{= \dfrac{6\times55}{5\times 1}}\\\\\\\huge\boxed{6\times55=\bf 330}\\\boxed{5\times1=\bf 5}\\\\\\\huge\boxed{= \dfrac{330\div5}{5\div5}}\\\huge\boxed{=\dfrac{66}{1}}\\\huge\boxed{= \bf 66}\)

\(\huge\boxed{\textsf{Therefore, your ANSWER is: 66}}\huge\checkmark\)

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

~\(\huge\boxed{\frak{Amphitrite1040:)}}\)

Answer:

Yes,planner has met the minimum height, as minimum height was 9 feet and maximum height of arc is 9.6 feet

Step-by-step explanation:

The question is incomplete as all the details have not been given in the question.I have attached the complete question and its options at the bottom. Consult in for better understanding.

As we can see that at the mid value, for x=4, the value of f(x)=9.4

It means that the maximum height occurs at mid of the arc where it is height is 9.6 feet above the ground.

It means that the planner has met the minimum height, as minimum height was 9 feet and maximum height of arc is 9.6 feet

Answer:

B on Edge

Step-by-step explanation:

yes, because the width of the arch is 9.6 feet

proof:

CD= radius r

OC=OD= radius

OCD is equilateral triangle

∠DCO=∠COD=∠ODC=60  degrees

∠ACB=90  degrees

 (Angle in semicircle)

∠DOC=2∠DBC (half angle)

∠DBC=30  degrees

∠ECB+∠BCA=180  degrees

 (linear pair)

∠ECB=180−90=90  degrees

In △ECB

∠CEB+∠ECB+∠CBE=180  degrees

∠CEB+90+30=180

∠CEB=60  degrees

*This is the full proof and ask me questions in comments if you have anything you don't understand! Also I would appreciate if you give me brainlliest!!

Let's try to understand how we can solve this equation

Given equation,4f+2=6f-12

Now we will take the terms on one side and constants on the other.

=> 2+12=6f-4f

=> 14=2f

=>7=f

So, the value of f would be 7. Remember that while bringing value to another side, the sign of that value changes. If it is a positive sign then it is going to be transformed into a negative one and vice versa.

a) If 20 servers are available, they can serve approximately 114.29 tables in 20 minutes

b) To serve 160 tables in 20 minutes, the hotel would need approximately 35 servers

To answer these questions using the Service Capacity Excel template, we need to first determine the service rate (customers served per hour) and the arrival rate (customers arriving per hour).

Since it takes 4 minutes to get the meals and serve them to 10 guests (1018 seconds = 180 seconds = 3 minutes), the service time per table is 4 + 3 = 7 minutes. Therefore, the service rate is 60/7 tables per hour, or approximately 8.57 tables per hour per server. With 20 servers, the total service rate is 208.57 = 171.43 tables per hour.

Since we want to know how many tables can be served in 20 minutes, we need to convert this to an hourly arrival rate. There are 3 sets of 20 minutes in an hour, so the arrival rate is 160/3 = 53.33 tables per hour.

Using the Service Capacity Excel template, we enter the service rate of 171.43 tables per hour and the arrival rate of 53.33 tables per hour. We then select the "Number of servers" option and vary the number of servers until the utilization (or occupancy) is close to 100% (but not over). We find that the minimum number of servers needed to achieve this is 35. Therefore, the hotel needs 35 servers to be able to serve 160 tables in 20 minutes.

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Direct labor efficiency variance = $6,100 F.

Given that

Standard labor-hours per unit of output     8.5 hours

Standard labor rate                                     $12.30 per hour

Standard labor hours allowed                          6,800 hours (800 units *                                         8.5 hours allowed)

The following data pertain to operations concerning the product for the last month:

Actual hours worked  6,300 hours

Actual total labor cost  $74,970

Actual output                  800 units

We can determine the labor efficiency variance using the following equation:

1. Direct labor efficiency variance = (Standard hours allowed - Actual labor hours) * Standard rate

2. Direct labor efficiency variance = (6,800 hours - 6,300 hours) * $12.20

3. Direct labor efficiency variance = $6,100 F

The variance is favorable as the actual labor hours used are less than the standard hours allowed.

Hence the answer is Direct labor efficiency variance = $6,100 F.

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The required product of the function is \(8cos\frac{2\pi}{3}cos\frac{\pi}{3}+ 4i cos\frac{2\pi}{3}sin\frac{\pi}{3} + 2i sin\frac{2\pi}{3}cos\frac{\pi}{3} - 4i sin\frac{2\pi}{3}sin\frac{\pi}{3}\)

We are to find the product of the expression

\(a =4cos(\frac{2\pi}{3} )+isin(\frac{2\pi}{3})\\b=2cos(\frac{\pi}{3} )+isin(\frac{\pi}{3})\\\)

The product of the functions is expressed as;

\(ab = 4cos(\frac{2\pi}{3} )+isin(\frac{2\pi}{3})[2cos(\frac{\pi}{3} )+isin(\frac{\pi}{3}]\\ab=8cos\frac{2\pi}{3}cos\frac{\pi}{3}+ 4i cos\frac{2\pi}{3}sin\frac{\pi}{3} + 2i sin\frac{2\pi}{3}cos\frac{\pi}{3} + i^24i sin\frac{2\pi}{3}sin\frac{\pi}{3} \\ab=8cos\frac{2\pi}{3}cos\frac{\pi}{3}+ 4i cos\frac{2\pi}{3}sin\frac{\pi}{3} + 2i sin\frac{2\pi}{3}cos\frac{\pi}{3} - 4i sin\frac{2\pi}{3}sin\frac{\pi}{3}\)

Note that i² = -1

Hence the required product of the function is \(8cos\frac{2\pi}{3}cos\frac{\pi}{3}+ 4i cos\frac{2\pi}{3}sin\frac{\pi}{3} + 2i sin\frac{2\pi}{3}cos\frac{\pi}{3} - 4i sin\frac{2\pi}{3}sin\frac{\pi}{3}\)

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Answer:

D\(8[cos(\pi )+i sin(\pi )}\)

Step-by-step explanation:

Answer:

90.84

Step-by-step explanation:

49.7+41.14= 90.84

Answer:

the "^" symbol is called the exponent symbol

exponent is fast multiplication

in other words x^y means multiplying 'x' y times

Step-by-step explanation:

When the population standard deviation is unknown and the sample size is less than 30, we need to use the t-distribution to compute a confidence interval for the mean, and we should consult a t-table to find the appropriate t-value based on the degrees of freedom and the desired level of confidence.

When the population standard deviation is unknown and the sample size is less than 30, we need to use the t-distribution to compute a confidence interval for the mean.

The t-distribution is similar to the standard normal distribution, but with heavier tails, and it is used when the population standard deviation is unknown.

To compute the confidence interval for the mean using the t-distribution, we need to find the appropriate t-value from a t-table. The t-table provides critical values for different degrees of freedom and levels of confidence.

The degrees of freedom for a t-distribution with a sample size of n is (n-1). For example, if we have a sample size of 20, the degrees of freedom would be 19.

To find the appropriate t-value from the t-table, we need to know the degrees of freedom and the desired level of confidence. For example, if we have a sample size of 20 and want to calculate a 95% confidence interval, we would look for the t-value with 19 degrees of freedom and 0.025 (0.05/2) in the middle of the table. This t-value would be used in the formula to calculate the confidence interval for the mean.

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Answer:

y+3= 1/5 (x+2)

Step-by-step explanation:

The point slope form looks like this.

y - y1 = m (x - x1)

the m represent slope and (x1, y1) are the coordinates of the point that the line passes through.

Answer:

One banana costs $1.66.

Step-by-step explanation:

You divide 5 by 3 and you get 1.66666666667, but its long so we have to shorten it. When you shorten the amount you get is 1.66.

Hope this helped! :D

Answer:

Just give me a few min ill be right back to help :)

Step-by-step explanation:

Connect the points where the first arc crosses the triangle's base and the second arc intersects the base of the triangle with the straightedge to create the triangle's third side, BC.

Generally, To accurately construct triangle ABC, you will need a straightedge (such as a ruler) and a protractor. Here are the steps to follow:

Use the straightedge to draw a straight line segment of length 8 cm, which will represent side AB. This line segment will be the base of the triangle.

Place the point of the protractor at one end of the line segment and draw an arc that intersects the other end of the line segment.

Measure the angle formed by the line segment and the arc using the protractor. The measure of this angle should be 70 degrees.

Without changing the position of the protractor, draw another arc that intersects the first arc and the base of the triangle.

Use the straightedge to connect the point where the second arc intersects the base of the triangle to the point where the first arc intersects the base of the triangle. This will form the third side of the triangle, AC.

Finally, use the straightedge to draw the third side of the triangle, BC, by connecting the point where the first arc intersects the base of the triangle to the point where the second arc intersects the base of the triangle.

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Performing a Chi-Square test is a statistical tool used to determine if there is a significant difference between observed and expected data. The test helps to analyze categorical data by comparing observed frequencies to the expected frequencies. The p-value in a Chi-Square test refers to the probability of obtaining the observed results by chance alone.

If a p-value lower than 0.01 is obtained in a Chi-Square test, it means that the results are statistically significant. In other words, there is strong evidence to reject the null hypothesis, which states that there is no significant difference between the observed and expected data. This means that the observed data is not due to chance alone, but rather to some other factor or factors.

The mean, or average, is not directly related to the Chi-Square test or the p-value. The Chi-Square test is specifically used to determine the significance of the observed data. However, the mean can be used as a measure of central tendency for continuous data, but it is not applicable to categorical data.

In conclusion, obtaining a p-value lower than 0.01 in a Chi-Square test means that there is strong evidence to reject the null hypothesis, and that the observed data is statistically significant.

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It is to be noted that the distance between P and ρ is: \(\approx\) 15.52

This solution is arrived at using the Line Segment theorem. See further explanation below.

The length of the line segment connecting two points in a plane is defined as the distance between two points. The method for calculating the distance between two locations is often written as

\(d = \sqrt{((x_{2} – x_{1})² + (y_{2} – y_{1})²).} \)

Hence, since we have ρ is to contain two points, we will solve as follows:

Distance between ρ and P where ρ is (0, -3) and (7,4)

we have to multiply the coordinates.

To multiply coordinates, you have to multiply the corresponding values.

That is

\(x_{1} \times x_{1} \)

and

\(y_{1} \times y_{1}\)

In this case:

x1 = 0

\(x_{1} = 0\)

also

\(x_{1} = 7\)

\(y_{1} = - 3\)

also

\(y_{1} = 4\)

Hence, for

\(x_{1} = 0 \times 7 = 0\)

for

\(y_{1} = - 3 \times 4 = 12\)

Hence, solving for the distance between P and ρ, we'd use coordinates of P as = (4, 3); and coordinates of ρ as = (0, -12)

Recall that distance is given as

\(d = \sqrt{((x_{2} – x_{1})² + (y_{2} – y_{1})²).} \)

Hence,

d = √((0-4)² + (-12-3))²)

\(d = \sqrt{{(( {0 - 4}^{2} }) + { (- 12 - 3)}^{2} } \)

Expand the brackets

\(d = \sqrt{ { - 4}^{2} + ( { - 15}^{2} } )\)

\(d = \sqrt{16 + 225} \)

\(d = \sqrt{441} \)

d = 15.5241746963

Approximately,

d = 15.52

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Answer:

no solutions

Step-by-step explanation:

(X-2)^2/3 + 13 = 5

Subtract 13 from each side

(X-2)^2/3 + 13-13 = 5-13

(x-2) ^2/3 = -8

Raise each to the 3/2 power

(x-2) ^2/3  ^3/2= -8^3/2

(x-2) = (-512) ^1/2

We cannot take the square root of a negative number and remain in the real number system

There are no solutions

Answer:

No real solutions

Imaginary/complex solutions:

x = 2 +/- 16sqrt(2)i

Step-by-step explanation:

(X-2)^2/3 + 13 = 5

(X-2)^2/3 = -8

(X - 2)² = (-8)³

X - 2 = +/- sqrt(-512)

No real solution

x = 2 +/- 16sqrt(2)i

(2 +/- 16sqrt(2)i - 2)^⅔ + 13 = 5

[(+/- 16sqrt(2)i)²]^⅓ + 13 = 5

(-512)^⅓ + 13 = 5

-8 + 13 = 5

5 = 5

Since the distanc function is given by

in order to find the distance at 8 seconds, we need to substitute t=8 into this function, that is,

By taking into account that g=32 ft/sec^2, we have

which gives

Therefore, the answer is 1024 ft, which corresponds to the last option.

Answer:

-7//40

Step-by-step explanation:

Answer:

7

Step-by-step explanation:

5 + 7 = 12

8 + 7 = 15

12/15 simplified into 4/5

Answer:

k=1 or k=-15

Step-by-step explanation:

The first step is simplifying:

\(k^{2}+18k-15=4k\)

\(k^{2}+14k=15\)

Now, take half the k term and square it ( \((\frac{14}{2})^{2}=7^{2}=49\)), and add the result to both sides.

\(k^{2}+14k+49=64\)

Now, we know  \(k^{2}+14k+49=(k+7)^{2}\), so let's rewrite our equation as:

\((k+7)^{2}=64\)

Now we solve:

\((k+7)^{2}=64\)

\(k+7=\sqrt{64}\)

So k+7=8 or k+7=-8

Therefore k=1 or k=-15

Answer:

Step-by-step explanation:

(((10•(x3))•y)+((30•(x2))•(y2)))-(22•52xy3)

STEP

2

:

Equation at the end of step

2

:

 (((10•(x3))•y)+((2•3•5x2)•y2))-(22•52xy3)

STEP

3

:

Equation at the end of step

3

:

 (((2•5x3) • y) +  (2•3•5x2y2)) -  (22•52xy3)

STEP

4

:

STEP

5

:

Pulling out like terms

5.1     Pull out like factors :

  10x3y + 30x2y2 - 100xy3  =   10xy • (x2 + 3xy - 10y2)

Trying to factor a multi variable polynomial :

5.2    Factoring    x2 + 3xy - 10y2

Try to factor this multi-variable trinomial using trial and error

Found a factorization  :  (x + 5y)•(x - 2y)

Final result :

 10xy • (x + 5y) • (x - 2y)

The probability to take 5 classes is 0.1, while the probability to take at least one class is 0.6, the probability to take 2 or 3 classes is 0.23 and the expectation of the distribution is 1.37.

The distribution given is

X                  PIX)

0                  0.4

1                   0.25

2                  0.15

3                  0.08

4                  0.02

5                  ???  

1.

We know that the sum of all the probabilities in a probability distribution is always equal to 1.

Let the probability of X = 5 be p

Hence,

0.4 + 0.25 + 0.15 + 0.08 + 0.02 + p = 1

or, 0.9 + p = 1

or, p = 1 - 0.9

or, p = 0.1

Hence the probability to take 5 classes is 0.1.

2.

We need to find P(X ≥ 1)

= 1 - P(X = 0)

From the distribution we know that P(X = 0) is 0.4

Therefore, P(X ≥ 1)

= 1 - 0.4

= 0.6

Hence, the probability to take at least one class is 0.6

3.

The probability to take 2 or 3 classes in a semester

= P( X = 2)  +  P(X = 3)

= 0.15  +  0.08

= 0.23

4.

The expectation of any distribution

= ∑xp(x)

where,

x is the random variable

p(x) is the probability of the random variable

Therefore,

E(X) = 0 X 0.4  +  1 X 0.25  +  2 X 0.15  +  3 X 0.08  +  4 X 0.02  +  5 X 0.1

= 0  +  0.25  +  0.30+  0.24  +  0.08  +  0.50

= 1.37

Therefore the expectation is 1.37

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The variable "N" in time value of money (TVM) calculations typically represents the number of periods at which the interest is applied.

In TVM calculations, "N" refers to the number of compounding periods or the number of times interest is applied. It represents the time duration or the number of periods over which the cash flows occur or the investment grows. The value of "N" can be measured in years, months, quarters, or any other unit of time, depending on the specific situation.

For example, if an investment pays interest annually for 5 years, then "N" would be 5. If the interest is compounded quarterly for 10 years, then "N" would be 40 (4 compounding periods per year for 10 years).

Understanding the value of "N" is essential for calculating present value, future value, annuities, and other financial calculations in TVM, as it determines the frequency and timing of cash flows and the compounding effect over time.

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SOLUTION

Step 1:

A store pays $ 127. 53 for a Jedi outfit.

Assuming the store marks up the price 15 %.

We are asked to find the amount of mark-up? ( nearest hundredth)

Step 2 :

The amount of the mark - up ( to the nearest hundredth ) = $ 19. 13

Answer:

D.

Step-by-step explanation:

Choices A., B., and C. are always true.

Choice D. is true only for rectangles with congruent sides, which are squares.

Answer: D.

Answer:

A

Step-by-step explanation:

If you were to dilate a point by a scale factor of 2, then if you have the point (-4,0), both the x value and the y value would be multiplied by 2, giving a coordinate of (-8,0). If you do this to the other point, you get (0,4).

Now graph it out, and you get a parallel line that is not right on top, eliminating answer B. It's not C because it is parallel, not intersecting. And it's not D because they are related, they're parallel.

Hope this helps!

Answer:

  no, the vertex of Function A is 6 units lower

Step-by-step explanation:

The vertex of Function A can be found several ways:

__

To put the equation in vertex form, we can consider separately the variabel terms and the constant. Once we have the variable terms separated, we can "complete the square" and then simplify the result to vertex form. The vertex form of a quadratic is ...

  y = a(x -h)² +k . . . . for vertical scale factor 'a' and vertex (h, k)

We have ...

  y = 2x² +12x +10

  y = 2(x² +6x) +10

We complete the square by adding the square of half the x-coefficient inside parentheses. We subtract the same quantity outside parentheses, so we don't change the equation any.

  y = 2(x² +6x +9) +10 -2(9)

  y = 2(x +3)² -8 . . . . . . simplify to vertex form

The vertex of Function A is (-3, -8), which is (-2 -(-8)) = 6 units lower than the vertex of Function B in the graph. Bob is incorrect.

__

The axis of symmetry of quadratic expression ax² +bx +c is x=-b/(2a). For the given Function A, the axis of symmetry is ...

  x = -12/(2(2)) = -3

The height of the vertex is the y-value for that x-value:

  y = 2(-3)² +12(-3) +10 = 18 -36 +10 = -8

This is lower than the vertex of the graphed function, which is at y=-2. Bob is incorrect.

__

The graph of Function A is the solid red curve in the attached. The graph of Function B is added as the dashed blue curve for reference. The graph clearly shows the vertex of Function A is lower than that of Function B. Bob is incorrect.

_____

Additional comment

Modern graphing calculators make the graphing option the quickest and easiest way to find the vertex of the function. The only "work" is to type the equation into the calculator.

Given the above prompt on hypothesis testing, we can state that specifically, cars with manual transmissions have a significantly higher average city mileage than those with automatic transmissions.

To determine if there is strong evidence of a difference between the average fuel efficiency of cars with manual and automatic transmissions in terms of their average city mileage, we can conduct a two-sample t-test assuming unequal variances. The null hypothesis is that there is no difference in the average city mileage between the two types of transmissions, and the alternative hypothesis is that there is a difference.

The t-test statistic is calculated as follows:

t = (x1 - x2) / sqrt((s1^2/n1) + (s2^2/n2))

where x1 and x2 are the sample means, s1 and s2 are the sample standard deviations, and n1 and n2 are the sample sizes.

Plugging in the values from the given statistics, we get:

t = (16.12 - 19.85) / sqrt((3.85^2/26) + (4.51^2/26))

t = -3.31

Using a significance level of 0.05 and 50 degrees of freedom (approximated by n1+n2-2), the critical t-value is ±2.01.

Since the calculated t-value (-3.31) is less than the critical t-value, we can reject the null hypothesis and conclude that there is strong evidence of a difference between the average fuel efficiency of cars with manual and automatic transmissions in terms of their average city mileage.

Specifically, cars with manual transmissions have a significantly higher average city mileage than those with automatic transmissions.

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Full Question:

Although part of your question is missing, you might be referring to this full question: See attached image.