Evaluate the expression for t = 9 and u = 2.
t + u =

After 4 hours of discharging, the volume left in the tank would be 500 liters. The correct option is C.

Initially, the tank has a water capacity of 1500 liters.

After three hours of discharging, half of the water is discharged, which means 1500/2 = 750 liters have been removed from the tank.

To find the volume left after 4 hours of discharging, we need to subtract the additional amount discharged in the fourth hour.

Since the discharge rate remains the same, we can calculate the amount discharged in one hour as 750/3 = 250 liters.

Therefore, in the fourth hour, 250 liters would be discharged. Subtracting this from the remaining water after three hours (750 liters), we get 750 - 250 = 500 liters.

Therefore, the correct answer is c. 500 liters.

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Answer:

Step-by-step explanation:

We divide the number by 8 and write the remainder in reverse order to get the equivalent octal number.

Answer:

Let's write down the base of each one:

- Decimal is base 10 (0 to 9)

- Octal is base 8 (0 to 7)

So, if we want to convert decimal to octal, we need to divide the decimal number by 8 and hold onto the remainder.

Then once your quotient becomes 0, from the last remainder to the first, write your numbers.

For example here is 437 base 10.

437 / 8 = 54 R 5

54 / 8 = 6 R 6

6 / 8 = 0 R 6

So, the answer is 665 base 8.

Answer:

j < 5

Step-by-step explanation:

=> 10 > j+5

Subtracting both sides by 5, we get

=> 10-5 > j

=> 5 > j

OR

=> j < 5

Step-by-step explanation:

☄ \( \underline {\underline{ \text{Given}}} : \)

☄ \( \underline{ \underline{ \text{To \: find}}}: \)

☄ \( \underline{ \underline{ \text{Solution}}} : \)

Part 1 : \( \boxed{\text{Area \:of \:a \:path \: running \:outside = 2d(l + b + 2d)}}\)

plug the known values and simplify :

⟹ \( \sf{2 \times 2.5(55 + 35 + 2 \times 2.5)}\)

⟹ \( \sf{5 \times 95}\)

⟹ \( \sf{475 \: {m}^{2} }\)

Part 2 : \( \boxed{ \sf{Total \: cost = Area \: of \: paths \: \times Rate}}\)

⟹ \( \sf{475 \times 120}\)

⟹\( \sf{Rs \: 57000}\)

\( \purple{ \boxed{ \boxed{ \sf{ \tt{⟿ \: Our \: final \: answer : (i) = 475 \: {m}^{2} \: and \: (ii ) = Rs \: 57000}}}}}\)

Hope I helped ! ♡

Have a wonderful day /night ツ

▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁

To find the number of three-letter initials with none of the letters repeated, we need to consider the number of choices for each position in the initials.

To determine the number of three-letter initials with none of the letters repeated, we can analyze each position in the initials. For the first letter, we have 26 choices since there are 26 letters in the English alphabet.

After selecting the first letter, for the second letter, we have 25 choices remaining since we cannot repeat the letter used in the first position. Similarly, for the third letter, we have 24 choices remaining since we cannot repeat either of the previous letters.

Therefore, the total number of three-letter initials with none of the letters repeated can be found by multiplying the number of choices for each position: 26 * 25 * 24 = 15,600. Hence, there are 15,600 different three-letter initials that people can have if none of the letters are repeated.

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The standard error of the mean is $128.125

Given:

a random sample is made of 256 middle managers concerning their annual incomes. the sample mean is computed to be $35,420. if the population standard deviation is $2,050.

n = 256

σ = 2050

standard error = standard deviation / sqrt of n

= 2050/\(\sqrt{256}\)

= 2050 / \(\sqrt{16*16}\)

= 2050 / \(\sqrt{16^2}\)

= 2050/16

= 1025/8

= 128.125

Therefore The standard error of the mean is $128.125.

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Answer:

The isosceles triangle has a perimeter of 7.5 m. 2.1 + 2x = 7.5 can be used to find the value of x if the shortest side, y, measures 2.1 m. This answer has been confirmed as correct and helpful

Step-by-step explanation:

Answer:

So.... u forgot to put the question.

Step-by-step explanation:

im not sure what u want but heres this : The isosceles triangle has a perimeter of 7.5 m. if the shortest side, y measures 2.1 m

The distance between the Woozy Wheel and the Roller Rail is 13 units.

To determine the distance between the Woozy Wheel and the Roller Rail, we can use the distance formula in the coordinate plane.

The coordinates of the Woozy Wheel are (-14, 1), and the coordinates of the Roller Rail are (-2, -4).

Using the distance formula, the distance (d) between two points (x₁, y₁) and (x₂, y₂) is given by:

d = √((x₂ - x₁)² + (y₂ - y₁)²)

Substituting the coordinates of the Woozy Wheel and the Roller Rail into the formula:

d = √((-2 - (-14))² + (-4 - 1)²)

= √(12² + (-5)²)

= √(144 + 25)

= √169

= 13

Therefore, the distance between the Woozy Wheel and the Roller Rail is 13 units.

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There is reason to doubt the expected ratio of 9:3:3:1.

To check whether there is a reason to doubt the expected ratio of 9:3:3:1, we can perform a chi-square goodness-of-fit test. The null hypothesis for this test is that the observed counts follow the expected ratio, and the alternative hypothesis is that they do not.

First, we need to calculate the expected counts based on the expected ratio:

Purple round: (9/16) * (280 + 95 + 62 + 23) = 267.75

Purple wrinkled: (3/16) * (280 + 95 + 62 + 23) = 89.25

Yellow round: (3/16) * (280 + 95 + 62 + 23) = 89.25

Yellow wrinkled: (1/16) * (280 + 95 + 62 + 23) = 29.25

Next, we can calculate the chi-square test statistic:

chi-square = Σ(observed count - expected count)^2 / expected count

Using the observed and expected counts above, we get:

chi-square = [(280 - 267.75)^2 / 267.75] + [(95 - 89.25)^2 / 89.25] + [(62 - 89.25)^2 / 89.25] + [(23 - 29.25)^2 / 29.25]

chi-square = 8.31

Finally, we need to compare the calculated chi-square value to the critical chi-square value with (4 - 1 = 3) degrees of freedom at a chosen significance level. For example, at a 5% significance level, the critical chi-square value with 3 degrees of freedom is 7.815.

Since the calculated chi-square value of 8.31 is greater than the critical chi-square value of 7.815, we reject the null hypothesis and conclude that there is reason to doubt the expected ratio of 9:3:3:1.

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Answer:

Ice Cube, Liquid Water, and Steam

Step-by-step explanation:

An example of a solid is a ice cube, the particles are compacted together and there's very little movement.

An example of a liquid is water, the particles are more spread around and the movement is more frequent.

An example of a gas is steam, the particles are anywhere, moving fast and sporadic.

Marina should have reversed the inequality in her final answer, reflecting the correct relationship between the magnitudes or absolute values of -2/3 and -5/8.

When comparing the absolute values of two numbers, the comparison is based on their magnitude or distance from zero, regardless of their sign.

In this case, Marina compared the decimal equivalents of -2/3 and -5/8, which are -0.666666... and -0.625, respectively. By calculating the decimal values, Marina attempted to compare the magnitudes of the numbers.

Marina correctly observed that |-0.666666...| = 0.666666... and |-0.625| = 0.625. However, she made an error in comparing the values by stating |-0.666666...| > |-0.625|.

To understand why the inequality needs to be reversed in her final answer (-2/3 < -5/8), let's examine the decimal values more closely.

When we write -0.666666... as a fraction, we have -2/3, and when we write -0.625 as a fraction, we have -5/8.

Now, when comparing fractions, a larger magnitude corresponds to a smaller value. In other words, the fraction with the smaller numerator or the larger denominator has a smaller value.

In this case, we can observe that -2/3 has a smaller numerator compared to -5/8, indicating a larger magnitude. Thus, -2/3 is actually greater than -5/8 in terms of their magnitudes or absolute values.

To correctly represent this comparison, the inequality should be reversed, resulting in the correct statement: -2/3 > -5/8.

Therefore, Marina should have reversed the inequality in her final answer, reflecting the correct relationship between the magnitudes or absolute values of -2/3 and -5/8.

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For k = -4, y = x^(-4) is a solution to the differential equation x²y'y''-4yy'=6x⁵.


To find the value of k for which y = x^k is a solution to the differential equation x²y'y''-4yy'=6x⁵, we need to first rewrite the differential equation in terms of y and its derivatives. To do this, we can apply the product rule to the left side of the equation, giving us: (x²y')(y'') + (x²y'')(y') - 4(yy')(1) = 6x⁵.

Next, we can substitute y = x^k into this equation to find the value of k. When we do this, we can see that the left side of the equation simplifies to: x²k(k-1)(x^k) + (x²)(k)(x^(k-1)) - 4(x^k)(1) = 6x⁵.

Solving this equation for k yields: k(k-1)x^k + kx^(k-1) - 4x^k = 6x⁵. We can then simplify this equation further by dividing both sides of the equation by x^k, giving us: k(k-1) + kx^(-1) - 4 = 6x⁴.

Finally, we can solve this equation for k to obtain the value of k for which y = x^k is a solution to the differential equation x²y'y''-4yy'=6x⁵. When we do this, we find that k = -4. Therefore, y = x^(-4) is a solution to the differential equation x²y'y''-4yy'=6x⁵.

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Answer:

I think it is complement. Not so sure so sorry If i get it wrong I haven't done this in 2 or 3 years

Step-by-step explanation:

Step-by-step explanation:

= ( 3x + 5 ) ( 4x² + 8x + 40 )

= 3x ( 4x² + 8x + 40 ) + 5 ( 4x² + 8x + 40 )

= 12x³ + 24x²+ 120x + 20x² + 40x + 200

= 12x³ + 24x² + 20x² + 120x + 40x + 200

= 12x³ + 44x² + 160x + 200

Answer:

12x^3 +44x^2 +160x +200

Step-by-step explanation:

Distribute:

(3x+5)(4x^2 +8x+40)

3x(4x^2 +8x+40) +5(4x^2 +8x+40)

Then it would be:

(12x^3 +24x^2 +120x) + (20x^2 + 40x +200)

therefore the soloution is:

12x^3 +44x^2 +160x +200

The transformation given as A(-8,7) → A'(-8,-7) represents a reflection over x-axis .

In the reflection of the point (x,y) over x-axis transformation ,the x-coordinate of each point remains the same, but the y-coordinate is negated (changes sign).

Let's consider the coordinates of point A that is  (-8, 7).

The transformation takes this point to A' (-8, -7).

We can see that the x-coordinate of the point remains the same which is -8. but , the y-coordinate changes from 7 to -7.

We know that in a reflection over the x-axis, the x-coordinate remains the same while the y-coordinate changes sign.

Therefore , the transformation that takes A to A' is a reflection over the x-axis.

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The given question is incomplete , the complete question is

Identify the Transformation given as A(-8,7) → A'(-8,-7)?

Answer:

x = 4, y = 5

Step-by-step explanation:

\(2x-y=3\\4x-2y=6\)

so:

\(4x - 2y = 6\\+ 5x + 2y = 30\\9x= 36\\x=4\)

Substitute this into 2x - y = 3:

\(8-y=3\\y = 5\)

The area of the prism is 6in^2.

The prism is one of the shapes that we have in geometry. There are several types of prism such as;

Now  we know that;

Volume of a prism = base area * height

In this case;

Base area = ?

Volume = 36 in³

Height = 6in

Base area = Volume /height

Base area = 36 in³/ 6in

Base area = 6in^2

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The number of rice balls Justin can make with 700 grams of rice is 7.

How many rice balls can Justin make?

In order to determine the rice balls he can make, divide the grams of rice he has by the grams needed to make one rice ball. Division is the process of grouping a number into equal parts using another number.

Rice balls he can make = 700 grams / 100 grams = 7

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Answer:

7 rice balls

Step-by-step explanation:

The length of time for one individual to be served at a cafeteria follows an exponential distribution with a mean of 4 minutes.

In an exponential distribution, the probability density function (PDF) is given by:

f(x) = (1/μ) * e^(-x/μ)

Where μ is the mean of the distribution. In this case, the mean is 4 minutes. Therefore, the PDF for the length of time for one individual to be served at the cafeteria can be expressed as:

f(x) = (1/4) * e^(-x/4)

The exponential distribution is commonly used to model the time between events in a Poisson process. In this case, it represents the time it takes for an individual to be served at the cafeteria, with an average of 4 minutes.

The exponential distribution is characterized by the property of memorylessness, which means that the probability of an event occurring in the next interval of time is independent of how much time has already elapsed. In the context of the cafeteria, this property implies that the probability of an individual being served in the next minute is the same, regardless of how much time has already passed.

It's important to note that the exponential distribution is only valid for non-negative values of x, as it represents a continuous random variable. The distribution is skewed to the right, with a longer tail on the positive side. The mean (μ) and standard deviation (σ) of the exponential distribution are equal and can be calculated as 1/λ, where λ is the rate parameter of the distribution.

In summary, the length of time for one individual to be served at the cafeteria follows an exponential distribution with a mean of 4 minutes. The probability density function (PDF) for this distribution is given by f(x) = (1/4) * e^(-x/4), where x represents the time in minutes.

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Answer:

(3x+4)(2x-5)

Step-by-step explanation:

You have 6x^2 - 7x-20, you add and take 8x so now you have

6x^2 - 7x +8x -8x -20 now you take 6x^2  and the +8x and factorize

6x^2 +8x = 2x( 3x +4 )

and you have -7x -8x-20 = -15x -20 factorize

-5(3x +4 ) add all up.

2x(3x +4) -5(3x +4) and you have

(3x+4)(2x-5)

Answer: 300cal ≤ y ≤ 1200 cal

Step-by-step explanation:

Let's define x as the number of cookies that you eat, and y as the number of calories you consume in those cookies.

"if you eat no fewer than 2 cookies..."

This is written as:

2 ≤ x

This means that x can be equal to 2, or larger than 2.

"...and no more than 8 cookies"

This is written as:

x ≤ 8

This means that x can be smaller than 8 or equal to 8.

If we combine those two, we have:

2 ≤ x ≤ 8

And we know that each cookie contains 150 calories, and rememer that these numbers represent number of cookies, then the numbers of calories will be:

2*150 cal  ≤ y ≤ 8*150 cal

300cal ≤ y ≤ 1200 cal.

33-9=24

\(\\ \sf\longmapsto \dfrac{24}{9}=\dfrac{40}{-x+30}\)

\(\\ \sf\longmapsto 24(-x+30)=320\)

\(\\ \sf\longmapsto -24x+720=320\)

\(\\ \sf\longmapsto -24x=320-720=-400\)

\(\\ \sf\longmapsto x=\dfrac{-400}{-24}\)

\(\\ \sf\longmapsto x=16.6\)

_________

\( \: \)

Answer in the picture.

Answer:

  x = 45

Step-by-step explanation:

  0.4 + x(10%) = 4.9 . . . . . . given

  x(10%) = 4.5 . . . . . . . . . subtract 0.4

  x = 45 . . . . . . . . . . . . multiply by 10

_____

10 × 10% = 100% = 1