The value 37 is a solution for the equation 3√√2 sece +7 = 1.
A. True
B. False

Answer:

4. 4155.3cm³

5. 783m³

6. 1962.44821094mm³

#4 Explanation:

First, you would separate the 2 shapes it consists of, a cylinder and a cone.

For the cone, you would use the equation (1/3)πr²h. Fill in the appropriate variables with the numbers from the formula. Pi, π, is a number itself so you leave it as it is.

r = radius = 8cm

h = height = 14cm

(1/3)(π)(8)²(14)

Put this equation into a calculator, it's important to include the parentheses or it might give you the incorrect answer, this is so that it separates the different values while multiplying. After inputting it, it should give you:

v = 938.289005872cm³

Then, you would have to find the volume of the cylinder, using the equation; πr²h.

The radius would be the same as the cone, and the height is as the problem states, 16cm.

Solve the problem after inputting the values:

π(8)²(16)= 3216.99087728cm³

Then, add the values to get the total volume.

938.289005872cm³ + 3216.99087728cm³ =

4155.27988315cm³

Round to nearest tenth: 4155.3cm³

#5 Explanation:

Again, you would separate the shapes into 2 separate ones.

The top one is a triangular prism and uses the equation (1/2)bh.

b = base = 9m

h = 12m

(1/2)(9)(12) = 54m³

The bottom shape is a rectangular prism, where we use the equation L×W×H.

Length = 9m

Width = 9m

Height = 9m

Substitute the numbers into the equation.

9×9×9 = 729m³

Add both of them together to get the total volume:

54m³ + 729m³ = 783m³

#6 Equation:
In this figure, we are looking for the outer shape, so we will have to subtract the smaller cone.

First, we find the total volume, and we will use the same equation, (1/3)πr²h.

radius = half of diameter = 20/2 = 10mm

h = 20mm

(1/3)π(10)²(20) = 2094.39510239mm³

Second, we find the volume of the smaller cone, using the same equation, (1/3)πr²h.

In order to find the diameter, we will have to subtract the 7 mm that are on either side of the cone, so 20 - 14 = 6, then divide it by 2 so we can get the necessary radius. 6/2 = 3

r = 3mm

h = 14mm

Substitute values into equation and use calculator to solve.

(1/3)π(3)²(14) = 131.946891451mm³

Subtract the value of the smaller cone from total volume in order to get the volume for this figure.

2094.39510239mm³ - 131.946891451mm³ =

1962.44821094mm³

Answer:

sin(100°) = 0.985

sin(-100°) = -0.985

Step-by-step explanation:

In a unit circle, each point (x, y) on the circumference corresponds to the coordinates (cos θ, sin θ), where θ represents the angle formed between the positive x-axis and the line segment connecting the origin to the point (x, y).

Therefore, sin(100°) equals the y-coordinate of the point (-0.174, 0.985), so:

\(\boxed{\sin(100^{\circ}) = 0.985}\)

Similarly, sin(-100°) equals the y-coordinate of the point (-0.174, -0.985), so:

\(\boxed{\sin(-100^{\circ}) = -0.985}\)

In the unit circle the value of sin (100) = 0.985 and the value of sin (-100) = -0.985, in three decimal places.

The value of the sine of the angles is calculated by applying the following formula as follows;

The value of sin (100) is calculated as follows;

sin(100°) corresponds to the y-coordinate of the point (-0.174, 0.985) as given on the coordinates of the unit circle.

sin (100) = 0.985

The value of sin (-100) is calculated as follows;

sin(100°) corresponds to the y-coordinate of the point (-0.174, -0.985), as given on the coordinates of the circle.

sin (-100) = -0.985

Thus, in the unit circle the value of sin (100) = 0.985 and the value of sin (-100) = -0.985, in three decimal places.

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Answer:

\(\huge\boxed{\sf 38}\)

Step-by-step explanation:

= a³ + b (6 + c)

Put a = 2, b = 3 and c = 4

= (2)³ + 3 (6 + 4)

= 8 + 3(10)

= 8 + 30

\(\rule[225]{225}{2}\)

Answer:

Step-by-step explanation:

the requied answer is 38.

according to the question the value of a=2,b=3,c=4.

here,

to find the value of   a³ + b (6 + c)we have to do it in steps:

step 1: solve the bracket (6+4) =10.

step 2:  solve the value of a³ =8.

now put these values ,

=8+3(10)

=38.

I think you might be referring to the definite integral,

\(\displaystyle \int_{-1}^2|x-1|\,\mathrm dx\)

Recall the definition of absolute value:

\(|x| = \begin{cases}x&\text{if }x\ge0\\-x&\text{if }x<0\end{cases}\)

Then \(|x-1|=x-1\) if \(x\ge1\), and \(|x-1|=1-x\) is \(x<1\). So spliting up the integral at x = 1, we have

\(\displaystyle \int_{-1}^2|x-1|\,\mathrm dx = \int_{-1}^1(1-x)\,\mathrm dx + \int_1^2(x-1)\,\mathrm dx\)

The rest is simple:

\(\displaystyle \int_{-1}^2|x-1|\,\mathrm dx = \left(x-\dfrac{x^2}2\right)\bigg|_{-1}^1 + \left(\dfrac{x^2}2-x\right)\bigg|_1^2 \\\\ = \left(\left(1-\frac12\right)-\left(-1-\frac12\right)\right) + \left(\left(2-2\right)-\left(\frac12-1\right)\right) \\\\ = \boxed{\frac52}\)

Número de horas que trabajó uno de los cocineros = 8

Número de horas que trabajó uno de los camareros = 8

Número de horas que trabajó uno de los cocineros = 8

Número de horas que trabajó uno de los camareros = 8

Número de horas que trabajó uno de los cocineros = 6

Número de horas que trabajó uno de los camareros = 6

Número de horas que trabajó uno de los cocineros = 3

Número de horas que trabajó uno de los camareros = 4

Relación de horas trabajadas :

\( = \tt 8 : 8 : 8 : 8 : 6 : 6 : 3 : 4\)

Proporción de las propinas que obtendrán :

\(= \tt 8 : 8 : 8 : 8 : 6 : 6 : 3 : 4\)

Total de propinas ganadas en un día = $ 18,156

Dinero que consiguió cada uno de ellos :

\( = \tt \frac{8}{51} \times 18156\)

\( = \tt \frac{8 \times 18156}{51} \)

\( = \tt \frac{145248}{51} \)

\( \color{plum} = \tt \$ \: 2848\)

Por lo tanto, 2 cocineros y 2 camareros habrían obtenido $2848 cada uno.

Dinero que recibirá el segundo par de cocineros y camareros :

\( = \tt \frac{6}{51} \times 18156\)

\( = \tt \frac{6 \times 18156}{51} \)

\( = \tt \frac{108936}{51} \)

\( \color{plum} = \tt \$ \: 2136\)

Por lo tanto, el segundo par de cocineros y camareros recibe $2136 cada uno.

Consejos que recibirá uno de los cocineros :

\( = \tt \frac{3}{51} \times 18156\)

\( = \tt \frac{3 \times 18156}{51} \)

\( = \tt \frac{54468}{51} \)

\( \color{plum} = \tt \$ \: 1068\)

Por lo tanto, uno de los cocineros recibe $1068 como propina.

Otro cocinero obtiene :

\( = \tt \frac{4}{51} \times 18156\)

\( = \tt \frac{4 \times 18156}{51} \)

\( = \tt \frac{72624}{51} \)

\( \color{plum} = \tt \$ \: 1424\)

Por lo tanto, otro cocinero recibe $1424 como propina.

▪︎El cocinero que trabajó durante 8 horas recibe $ 2848 como propina.

▪︎El mesero que trabajó durante 8 horas recibe $ 2848 como propina.

▪︎El cocinero que trabajó durante 8 horas recibe $ 2848 como propina.

▪︎El mesero que trabajó durante 8 horas recibe $ 2848 como propina.

▪︎El cocinero que trabajó durante 6 horas recibe $ 2136 como propina.

▪︎El mesero que trabajó durante 6 horas recibe $ 2136 como propina.

▪︎El cocinero que trabajó durante 3 horas recibe $ 1068 como propina.

▪︎El cocinero que trabajó durante 4 horas recibe $ 1424 como propina.

Step-by-step explanation:

x = number of cards

the production costs (PC) per day are

PC(x) = 264 + 1.1x

the sales (S) are

S(x) = 5.1x

the profit (P) per day is sales minus costs

P(x) = S(x) - PC(x) = 5.1x - (264 + 1.1x) =

= 5.1x - 264 - 1.1x = 4x - 264

we need to find the value of x, so that P(x) = 52.

52 = 4x - 264

316 = 4x

x = 316/4 = 79

79 cards must be delivered daily to make a profit of $52.

By using the concept of normal distribution of probability, it can be inferred that

x = 50 gives the least amount of variability in the sampling distribution of the sample mean

Fourth option is correct

What is normal distribution of probability?

Normal distribution of probability is a continuous type probability distribution whose probability density function is given by-

f(x) = \(\frac{1}{\sigma \sqrt{2 \pi}}e^{-\frac{z^2}{2}}\)

where z = \(\frac{x - \mu}{\sigma}\), \(\mu\) is the mean and \(\sigma\) is the standard deviation.

Here,

mean = 50

Standard deviation =22

If x = 50

z = \(\frac{50 - 50}{22}\) = 0

This means x = 50 is already on mean. There is no question of variability here.

So x = 50 gives the least amount of variability in the sampling distribution of the sample mean

Fourth option is correct

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Answer:

3.5: 0.75 is the aswee

Step-by-step explanation:

I just turned into improper then decimal

pls give me brainliest

Answer:

\(\displaystyle\)\(\displaystyle f'(1)=-\frac{9}{e^3}\)

Step-by-step explanation:

Use Quotient Rule to find f'(x)

\(\displaystyle f(x)=\frac{3x^2+2}{e^{3x}}\\\\f'(x)=\frac{e^{3x}(6x)-(3x^2+2)(3e^{3x})}{(e^{3x})^2}\\\\f'(x)=\frac{6xe^{3x}-(9x^2+6)(e^{3x})}{e^{6x}}\\\\f'(x)=\frac{6x-(9x^2+6)}{e^{3x}}\\\\f'(x)=\frac{-9x^2+6x-6}{e^{3x}}\)

Find f'(1) using f'(x)

\(\displaystyle f'(1)=\frac{-9(1)^2+6(1)-6}{e^{3(1)}}\\\\f'(1)=\frac{-9+6-6}{e^3}\\\\f'(1)=\frac{-9}{e^3}\)

Answer:

\(f'(1)=-\dfrac{9}{e^{3}}\)

Step-by-step explanation:

Given rational function:

\(f(x)=\dfrac{3x^2+2}{e^{3x}}\)

To find the value of f'(1), we first need to differentiate the rational function to find f'(x). To do this, we can use the quotient rule.

\(\boxed{\begin{minipage}{5.5 cm}\underline{Quotient Rule for Differentiation}\\\\If $f(x)=\dfrac{g(x)}{h(x)}$ then:\\\\\\$f'(x)=\dfrac{h(x) g'(x)-g(x)h'(x)}{(h(x))^2}$\\\end{minipage}}\)

\(\textsf{Let}\;g(x)=3x^2+2 \implies g'(x)=6x\)

\(\textsf{Let}\;h(x)=e^{3x} \implies h'(x)=3e^{3x}\)

Therefore:

\(f'(x)=\dfrac{e^{3x} \cdot 6x -(3x^2+2) \cdot 3e^{3x}}{\left(e^{3x}\right)^2}\)

\(f'(x)=\dfrac{6x -(3x^2+2) \cdot 3}{e^{3x}}\)

\(f'(x)=\dfrac{6x -9x^2-6}{e^{3x}}\)

To find f'(1), substitute x = 1 into f'(x):

\(f'(1)=\dfrac{6(1) -9(1)^2-6}{e^{3(1)}}\)

\(f'(1)=\dfrac{6 -9-6}{e^{3}}\)

\(f'(1)=-\dfrac{9}{e^{3}}\)

Answer: y = 3x - 1

Step-by-step explanation:

y = 3x + c

-1 = 3(0) + c

-1 = 0 + c

-1 - 0 = c

-1 = c

y = 3x - 1

Answer:

-18 and -12

Or, 18 and 12

Step-by-step explanation:

Let the integers be 'a' & 'a + 6'.

Their product = 216

=> a x (a + 6) = 216

=> a² + 6a = 216

=> a² + 6a - 216 = 0

=> a² + (18 - 12)a - 216 = 0

=> a² + 18a - 12a - 216 = 0

=> a(a + 18) - 12(a + 18) = 0

=> (a + 18)(a - 12) = 0

=> a = - 18 or a = 12

Integers are: -18 and -18+6 = -12

Or, 12 and 12 + 6 = 18

We have

First, we will factorize the square term

Then we simplify

We simplify

As we can see the simplification given is TRUE

ANSWER

TRUE

Answer:

6 3/8 inches

Step-by-step explanation:

let 'x' = distance in 1 hr, 25 minutes (which is 85 minutes)

(3/8 ÷ 5) = x ÷ 85

cross-multiply:

5x = 255/8

40x = 255

x = 6 3/8

Answer:AC is equal to 88

Step-by-step explanation:

C=11

A=8

B=2

The length of one side of the equilateral triangle in terms of x is 6x.

To find the length of one side of the equilateral triangle in terms of x, we need to consider the perimeter of both the rectangle and the equilateral triangle.

The perimeter of a rectangle is given by the formula:

Perimeter of rectangle = 2(length + width)

In this case, the length of the rectangle is 7x cm, and the width is 2x cm. Substituting these values into the formula, we have:

Perimeter of rectangle = 2(7x + 2x) = 2(9x) = 18x

We are told that the equilateral triangle has the same perimeter as the rectangle.

Since an equilateral triangle has all sides equal, the perimeter can be calculated by multiplying the length of one side by 3.

Therefore, we have:

Perimeter of equilateral triangle = 3(side length)

Since the perimeter of the equilateral triangle is equal to the perimeter of the rectangle (18x), we can set up the equation:

3(side length) = 18x

Dividing both sides of the equation by 3, we get:

side length = 6x

Hence, the length of one side of the equilateral triangle in terms of x is 6x.

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The complete question may be like: A rectangle measures 2x cm by 7x cm. An equilateral triangle has the same perimeter as the rectangle. What is the length of one side of the triangle in terms of x?

Answer:

c) 1:3

Step-by-step explanation:

Since 16 watermelons cost $48, the cost of 1 watermelon is 48 / 16 = $3.

Hence 1 : 3

Answer:

Inverse Property of Addition

Step-by-step explanation:

The polar form of the rectangular coordinates (-√√2, -√2) is (2√(1 + √2), 15π/28)

To convert the rectangular coordinates (-√√2, -√2) into polar form, we first need to find the value of r (the radius) and θ (the angle).

r = √((-√√2)^2 + (-√2)^2) = √(2 + 2√2) = 2√(1 + √2)

To find the value of θ, we can use the following formula:

θ = atan(y/x)

where atan is the inverse tangent function, and (x, y) are the rectangular coordinates.

θ = atan(-√2/(-√√2)) = atan(√2) = π/4 radians

However, we need to express the angle in terms of 7 over the interval 0 ≤ θ < 2π/7, with a positive value of r.

To do this, we can add a multiple of 2π/7 to the value of θ until we get an angle in the desired interval.

θ = π/4 + 2π/7 = (7π + 8π)/28 = 15π/28 radians

So the polar form of the rectangular coordinates (-√√2, -√2) is:

(2√(1 + √2), 15π/28)

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The Least common multiple (LCM)  The time at which both bells will ring together is 10:45 am, and the Subsequent times will be 11:30 am, 12:15 pm, 1:00 pm, and so on, with an interval of 45 minutes between each occurrence.

The time at which both bells will ring together, we need to find the least common multiple (LCM) of the intervals at which each bell rings.

The first bell rings every 45 minutes, and the second bell rings every minute. We want to find the point at which both intervals align, meaning they both divide evenly into the same amount of time.

To find the LCM, we can list the multiples of each interval until we find a common multiple.

Multiples of 45 minutes: 45, 90, 135, 180, 225, 270, 315, 360, 405, ...

Multiples of 1 minute: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, ...

From the lists above, we can observe that the least common multiple occurs when both intervals coincide at the same time, which is 45 minutes.

Thus, the two bells will ring together every 45 minutes.

If we consider the initial adjustment time of 10:00 am, the first time both bells will ring together is at 10:45 am. After that, they will continue to ring together every 45 minutes throughout the day.

Therefore, the time at which both bells will ring together is 10:45 am, and the subsequent times will be 11:30 am, 12:15 pm, 1:00 pm, and so on, with an interval of 45 minutes between each occurrence.

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The  width of the river, RS, is 102 ft.

To find the width of the river, we can use the concept of similar triangles.

Let's analyze the given information and the diagram provided:

We have a right triangle TRS, where RS is the width of the river, and RT is the distance Karl walks along the edge of the river.

Karl then turns 90° and walks until his location (point U), point S, and point Q are collinear, forming a right triangle SUQ.

We are given that TU = 68 ft and that the distance Karl walks from S to U is 28 ft.

Now, let's consider the similar triangles TRS and SUQ:

Since TRS and SUQ are similar, their corresponding sides are proportional.

The ratio of the length of the corresponding sides is:

RS / TU = RT / SU

Substituting the given values, we have:

RS / 68 ft = 42 ft / 28 ft

To solve for RS, we can cross-multiply and solve for RS:

RS \(\times\) 28 ft = 68 ft \(\times\) 42 ft

RS = (68 ft \(\times\) 42 ft) / 28 ft

RS = 102 ft.

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The full question: A bottle contains 2 liters of water. The bottle leaks 80 milliliters of water every 3 minutes. Will the bottle be empty in 1 hour? Explain why or why not. (1 liter = 1,000)


The bottle will NOT be empty in an hour. However, it will leak 26.6 milliliters in a minute, so 1.596m in an hour.

Hope that helps!

To find the equation of a line that passes through the points (5, -3) and (-2, -4) in standard form, we can use the point-slope form of a linear equation and then convert it to standard form.

Determine the slope (m) of the line using the formula:

   m = (y2 - y1) / (x2 - x1)

For the given points (5, -3) and (-2, -4), we have:

   m = (-4 - (-3)) / (-2 - 5) = (-4 + 3) / (-2 - 5) = -1 / (-7) = 1/7

Use the point-slope form of a linear equation:

   y - y1 = m(x - x1)

Using the point (5, -3), we have:

   y - (-3) = (1/7)(x - 5)

Simplifying:

   y + 3 = (1/7)(x - 5)

Convert the equation to standard form:

Multiply both sides of the equation by 7 to eliminate the fraction:

   7y + 21 = x - 5

Rearrange the equation to have the x and y terms on the same side:

   x - 7y = 26

The equation of the line in standard form that passes through the points (5, -3) and (-2, -4) is x - 7y = 26.

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a) To calculate SSTr, we need to first find the overall mean of the samples and then use it to calculate the sum of squares due to treatments (SSTr).

The overall mean of the samples can be found by adding up all the sample means and dividing by the number of samples:

Overall mean = (650 + 750 + 700 + 650) / 4 = 687.5

Next, we can calculate SSTr using the formula:

SSTr = n * (sample mean - overall mean)^2

where n is the number of observations in each sample. In this case, n = 5 for each sample.

So for the first sample, SSTr = 5 * (650 - 687.5)^2 = 5362.5

For the second sample, SSTr = 5 * (750 - 687.5)^2 = 14062.5

For the third sample, SSTr = 5 * (700 - 687.5)^2 = 3062.5

For the fourth sample, SSTr = 5 * (650 - 687.5)^2 = 5362.5

Therefore, the total SSTr is:

SSTr = 5362.5 + 14062.5 + 3062.5 + 5362.5 = 27750

b) The degrees of freedom (df) for SSTr is k-1 where k is the number of groups/populations, and df for SSE is N-k where N is the total number of observations.

df(SSTr) = k - 1 = 5 - 1 = 4

df(SSE) = N - k = 20 - 5 = 15

The mean square for treatments (MSTr) is calculated as:

MSTr = SSTr / df(SSTr) = 12 / 4 = 3

The mean square for error (MSE) is calculated as:

MSE = SSE / df(SSE) = (20 - 5) / 15 = 1

Finally, we can calculate the F-test statistic as:

F = MSTr / MSE = 3 / 1 = 3

Therefore, the MSTr is 3, the MSE is 1, and the F-test statistic is 3.

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Answer:

it is the mode.

Step-by-step explanation:

i. e 5 is the most occuring number in the set of data listed above

Answer:

Step-by-step explanation:

1.

Domain is the set of x-values

As per graph the domain is

2.

g(f(x)) is, replacing x with f(x) = 4x

Answer:

No

Step-by-step explanation:

To form a proporion, both would need to be a multiple of the same thing, whcih they aren't

Answer:

c c c c c c c c c c c c c c c c c c c c

Answer:

10 units²

Step-by-step explanation:

The shape is a triangle.

The area can be found by multiplying the base (in units) with height (in units) divided by 2.

base = 4 units

height = 5 units

\(\frac{4 \times 5}{2}\)

\(\frac{20}{2} =10\)