X
3.
What is the value of x to the nearest tenth?
6
24

The apothecary system uses the minim as the basic unit of liquid measure and the grain as the basic unit of solid measure.

What is apothecary measurement?

What are the units of the apothecary system?

The grain, scruple (20 grains), dram (3 scruples), ounce (8 drams), and pound—a ancient scale of weight used in the British Isles for measuring and distributing pharmacological goods (12 ounces).

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The given trigonometric function consists of trigonometric values of common angles.

The values that represent the solution to [tex]cos(\frac{\pi }{4} -x)=\frac{\sqrt{2} }{2} .sinx[/tex], x ∈ [0, 2·π) are; [tex]x=({\frac{\pi }{2} or \frac{3.\pi }{2} )[/tex].

The given function is:  [tex]cos(\frac{\pi }{4} -x)=\frac{\sqrt{2} }{2} .sinx[/tex]

Where; x ∈ [0, 2·π).

We have; cos(A - B) = cos(A)·cos(B) - sin(A)·sin(B).

Which gives:

So, we obtain:
[tex]\frac{\sqrt{2} }{2} .cosx=\frac{\sqrt{2} }{2}.sinx-\frac{\sqrt{2} }{2} .sinx=0\\cosx=0\\cos\frac{\pi }{2} =0[/tex]

Therefore, the possible solutions (x-values) to cos x = 0 are:

[tex]0[/tex] ≤ [tex]\frac{n.\pi }{2}[/tex] ≤ [tex]2.\pi[/tex]

Where, n = 1, 3, 5, .., x ∈ [0, 2·π)

We get:  [tex]x=({\frac{\pi }{2} or \frac{3.\pi }{2} )[/tex].

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Answer:

8/11

Step-by-step explanation:

In the given scenario was cannot calculate P(B) directly. As it depends on what happened first, by itself we don’t know what was drawn first. Thus it becomes a conditional probability question:

P( B | A ) ← reads as the probability of “B” happening “given that” “A” has already happened — in this case the probability that the second marble drawn is a blue marble given that the first was a red marble.

Answers:

a) 49 square tiles - did the work on paper.

b) 83 circular tiles - did the work on paper.

c) C: could be even or odd - all patterns had both even and odd amounts of square and circular tiles.

Step-by-step explanation:

I did all the work on paper it took a while to do it. pls mark brainliest

Answer:

x+40

Step-by-step explanation:

Let's say the the "number" is x.

"Forty more than a number" would be x+40

[tex]\Large\texttt{Answer}[/tex]

[tex]\bold{40+n}[/tex]

[tex]\overline{\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad}[/tex]

[tex]\Large\texttt{Process}[/tex]

⇨ Letting n be the number

[tex]\bold n[/tex]

⇨ Add 40 to n (40 more)

[tex]\bold{40+n}[/tex] (or n+40; you can swap these numbers, they'll still add up to the same amount)

Hope that helped

Answer:

x= 5/2

Step-by-step explanation:

Answer:

-4 =x

Step-by-step explanation:

Brainly.com

We know

In a function

x represents the input and y represents output

So

x is time

So

f(30) represents distance traveled in 30mins

The area of the circle A and B is 86.54 inches and 124.62 mm

According to the statement

we have given that the radius of the circle A and b and we have to find the area of the given circle.

So, we know that the

The area enclosed by a circle of radius r is πr².

So, For area of the circle

For condition A :

diameter = 10.5 inches

then radius = 5.25

Area = πr²

Area = 3.14*27.56

Area = 86.54 inches

Now, For condition B :

radius = 6.3 mm

Area = πr²

Area = 3.14*39.69

Area = 124.62mm

So, The area of the circle A and B is 86.54 inches and 124.62 mm

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The key features of the above given functions are correctly matched to their corresponding definition.

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3/12, or 1/4 is the probability that it is blue.

What is probability?

Probability = number of successes / total number of outcomes

Total marbels in bag = 4+ 3 + 5 = 12  

A total of 12 marbles are in the bag.

3 blue marbles are in the bag.

Therefore, the probability of picking a blue is 3/12, or 1/4.

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keeping in mind that the points are A(-8 , 6) and C(2 , 5), so

[tex]\textit{internal division of a segment using a fraction}\\\\ A(\stackrel{x_1}{-8}~,~\stackrel{y_1}{6})\qquad C(\stackrel{x_2}{2}~,~\stackrel{y_2}{5})~\hspace{8em} \frac{2}{5}\textit{ of the way from A to C} \\\\[-0.35em] ~\dotfill\\\\ (\stackrel{x_2}{2}-\stackrel{x_1}{(-8)}~~,~~ \stackrel{y_2}{5}-\stackrel{y_1}{6})\qquad \implies \qquad \stackrel{\stackrel{\textit{component form of}}{\textit{segment AC}}}{\left( 10 ~~,~~ -1 \right)} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\left( \stackrel{x_1}{-8}~~+~~\frac{2}{5}(10)~~,~~\stackrel{y_1}{6}~~+~~\frac{2}{5}(-1) \right)\implies \left(-8+4~~,~~6-\frac{2}{5} \right) \\\\[-0.35em] ~\dotfill\\\\ ~\hfill B\left(-4~~,~~5\frac{3}{5} \right)~\hfill[/tex]

Using the normal distribution, the probability that a worker selected at random makes between $500 and $550 is: 2.15%.

The z-score of a measure X of a normally distributed variable with mean mu and standard deviation sigma is given by:

Z = (X - mu)/sigma

The mean and the standard deviation are given as follows:

mu = 400, sigma = 50

The probability is the p-value of Z when X = 550 subtracted by the p-value of Z when X = 500, hence:

X = 550:

Z = (X - mu)/sigma

Z = (550 - 400)/50

Z = 3

Z = 3 has a p-value of 0.9987.

X = 500:

Z = (X - mu)/sigma

Z = (500 - 400)/50

Z = 2

Z = 2 has a p-value of 0.9772.

0.9987 - 0.9772 = 0.0215 = 2.15% probability.

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Answer:

6 2/5 hrs or   6.4 hours total

Step-by-step explanation:

In two hours, Bob completes  2/10  = 1/5 of the job

           Ellen completes  2/ 8   = 1/4  

Find amount left

   1 - 1/5 -1/4 =  1 - 4/20 - 5/20 = 11/20 left

Ellen will need   8hrs * 11/20 = 88/20 = 4 2/5 hours to finish the job

2 hours to start + 4 2/5 hours to finish = 6 2/5 hours total

[tex]\huge\underline{\underline{\boxed{\mathbb {SOLUTION:}}}}[/tex]

▪ [tex] \sf{Area\text{ ABCD=}\frac{1}{2}\times AC\times BD}[/tex]

▪ [tex] \sf{Area = 72 yd^2}[/tex]

▪ [tex] \sf{BD = 6yd}[/tex]

[tex]\leadsto[/tex] Substitute the values:

[tex]\longrightarrow \sf{72 = \dfrac{1}{2} \times AC \times 16}[/tex]

[tex]\leadsto[/tex] Solve for AC:

[tex]\longrightarrow \sf{72=8\times AC}[/tex]

[tex]\longrightarrow \sf{ \dfrac{72}{8}=\dfrac{8\times AC}{8}}[/tex]

[tex]\longrightarrow \sf{AC=9}[/tex]

[tex]\huge\underline{\underline{\boxed{\mathbb {ANSWER:}}}}[/tex]

[tex]\large \bm{AC= \: 9 yd}[/tex]

BD = 16 yd

Area of ABCD = 72 yd²

AC = ?

Area of rhombus, using diagonal:

[tex] \frac{1}{2} \times d1 \times d2[/tex]

Therefore:

[tex] \frac{1}{2} \times 16 \times ac = 72[/tex]

Then:

[tex] \frac{16ac}{2} = 72[/tex]

Cross multiply the above into:

[tex]16ac \times 1 = 72 \times 2 = 144 \\ 16ac = 144[/tex]

Divide by the coefficient of AC:

[tex] \frac{16ac}{16} = \frac{144}{16} [/tex]

Final answer is 9 yd

Assuming that the variable h is the same for each figure, the figures from the least to the greatest is:

The value of h is the same for all the shape so assume the value of h is 2 units.

The volume of a cylinder is:

= πr²h

First cylinder area:

= 22/7 x 3 x 2

= 56.54867 units

The second cylinder area:

= 22/7 x 6 x 2

= 226.19467 units

The volume of a cone is:

= πr²h/3

First cone volume:

= 22/7 x 3 x 2/3

= 18.84956 units

Second cone volume:

= 22/7 x 6 x 2/3

= 75.39822 units

The order is therefore:

Cone with radius of 3 units < Cylinder with radius of 3 units < Cone with radius of 6 units < Cylinder with radius of 6 units

In conclusion, the shapes with the larger radius of 6 units will have more volume.

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Answer: The gas would not have remained liquid

Step-by-step explanation:

Since the freezing point of gasoline starts at -40°F, and the temperature that day was -49°F, we can conclude that the gasoline would not have remained liquid

When calculating a nation’s digital power, the term that is used to refer to the demonstrated capabilities of a nation-state in cyber offense or defense is Cyberwarfare.

Cyberwarfare  can be regarded as the use of cyber attacks against a nation-state so as to produce significant harm.

It should be noted that Cyber Warfare is set of actions  which is been carried out by  nation or organization so as to be able to launch an attack on institutions' computer network systems.

The interests or reasons for cyberwarfares based on the Cybersecurity as well as Infrastructure Security Agency are;

In order to achieve the goals behind the cyberwarfare programs, it is usually designed to focus on spectrum of objectives which will bring harm to national interests.

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The value of integration of y=16-[tex]x^{2}[/tex] from x=-1 to x=1 is 94/3.

Given the equation y=16-[tex]x^{2}[/tex] and the limit of the integral be x=-1,x=1.

We are required to find the value of integration of y=16-[tex]x^{2}[/tex] from x=-1 to x=1.

Equation is relationship between two or more variables that are expressed in equal to form.Equation of two variables look like ax+by=c.It may be linear equation, quadratic equation, or many more depending on the power of variable.

Integration is basically opposite of differentiation.

y=16-[tex]x^{2}[/tex]

Find the integration of 16-[tex]x^{2}[/tex].

=16x-[tex]x^{3}/3[/tex]

Now find the value of integration from x=-1 to x=1.

=16(1)-[tex](1)^{3}/3[/tex]-16(-1)-[tex](-1)^{3}/3[/tex]

=16(1)-1/3+16-1/3

=32-2/3

=(96-2)/3

=94/3

Hence the value of integration of y=16-[tex]x^{2}[/tex] from x=-1 to x=1 is 94/3.

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Answer:

3

Step-by-step explanation:

- 4x³y² + 6

the x is raised to the power of 3 , that is exponent of x is 3

For given power series [tex]\sum_{n=0}^{\infty} \frac{(-1)^nx^n}{2^n}[/tex] the radius of convergence is 2.

For given question,

We have been given a power series [tex]\sum_{n=0}^{\infty} \frac{(-1)^nx^n}{2^n}[/tex]

We need to find the radius of convergence of the power series.

We use ratio test to find the radius of convergence of the power series.

Let [tex]a_n=\frac{(-1)^nx^n}{2^n}[/tex]

[tex]\Rightarrow a_{n+1}=\frac{(-1)^{n+1}x^{n+1}}{2^{n+1}}[/tex]

Consider,

[tex]\lim_{n \to \infty}|\frac{a_{n+1}}{a_n} |\\\\= \lim_{n \to \infty} |\frac{\frac{(-1)^{n+1}x^{n+1}}{2^{n+1}}}{ \frac{(-1)^nx^n}{2^n} } |\\\\=\lim_{n \to \infty} |\frac{(-1)^{n+1}x^{n+1}}{2^{n+1}}\times \frac{2^n}{(-1)^nx^n} |\\\\=\lim_{n \to \infty} |\frac{(-1)x}{2} |\\\\=\lim_{n \to \infty}|\frac{-x}{2} |\\\\=\frac{x}{2}[/tex]

By Ratio test, given power series converges at [tex]|\frac{x}{2} | < 1[/tex]

⇒ |x| < 2

So, the radius of convergence is 2.

Therefore, for given power series [tex]\sum_{n=0}^{\infty} \frac{(-1)^nx^n}{2^n}[/tex] the radius of convergence is 2.

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Answer:

The answer is A. V=pi r³

Step-by-step explanation:

:)

The expression for the volume of the pyramid in terms of the radius r of the cone is [tex]\pi r^3[/tex]. So, option A is correct.

The cone is a three-dimensional figure with a vertex and a flat base.

The volume of a pyramid is given by the formula:

[tex]V = \dfrac{1}{3} \times base\ area \times height.[/tex]

Given that:

The base area of the pyramid = B

The height is 3r

The base area of the pyramid is the same as that of the cone.

The base of the cone = [tex]\pi r^2[/tex]

The volume of the pyramid is calculated as:

[tex]V = \dfrac{1}{3} \times \pi r^2 \times 3r[/tex]

V =[tex]\pi r^3[/tex]

Therefore, the volume of the pyramid is [tex]\pi r^3[/tex]. So, option A is correct.

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Answer:

-2

Step-by-step explanation:

See attachment

Answer:

Yes, they are proportional.

Step-by-step explanation:

The ratio for Veronica's trail mix is 3:7

The ratio for Casey's trail mix is 27:63 <--- Simplify this number

27:63 simplified is 3:7, which means these ratios are proportional.

hope this helps :)

Answer:

 29.9 cm³

Step-by-step explanation:

You want to know the volume represented by 1/3 of a cone that is 7 cm high and has a radius of 3.5 cm.

The volume of a cone is given by ...

  V = 1/3πr²h

The volume of the cone of interest is ...

  V = 1/3π(3.5 cm)²(7 cm) ≈ 89.797 cm³

1/3 of the volume is the amount of water that sloshed out of the cone. That volume is ...

  1/3(89.797 cm³) ≈ 29.9 cm³

They sloshed out about 29.9 cm³ before they drank the water.

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The length of line segment AB by observation if the diagram in the task content is; 14.

It follows from the task content that the line segment MN can be considered as parallel to line segment AB. This follows from the fact that the vertices of triangle MNO are midpoints of the line segments of triangle ABC.

Consequently, it can be concluded that line segment AB is twice the length of line segment MN and hence, BC = 2 × 7 = 14.

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The apothem is 15 inches, the perimeter is calculated to be 99.41 while the area is given as 745.59

The side of the octagon is given by x inches

the interior side of the angles can be gotten by:

8-2 * 180 / 8 sides

= 135

We have to find the value of the angles

<abc = 180 - 135 = 45 degree

<acb = 180 - 135 = 45 degrees

x² = 2AB²

AB = x/√2

30 =  x/√2 + x +  x/√2

x = 30 / 1 + √2

The apothem = 30 / 2

= 15

perimeter = 8x

= 8(30 / 1 + √2)

= 99.4 inches

area = 0.5 x 15 x 99.4

= 745.59

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Answer:

Short leg = 10

Longer leg = 10[tex]\sqrt{3}[/tex]

Hypotenuse = 20

Step-by-step explanation:

The given is a special right triangle, its angle measures are as follows:

30-60-90 and the side lengths will follow as:

x, x[tex]\sqrt{3}[/tex], 2x respectively.

The length of hypotenuse (sees angle measure 90) is represented with 2x and it's given as 20

We can conclude x = 10 from this

So the length of short leg is 10

Then the length of longer leg is 10[tex]\sqrt{3}[/tex]

The length of hypotenuse is already given as 20

Answer:

y = (3/4)x + 1/2

Step-by-step explanation:

the slope-intercept form is in general

y = ax + b

with a being the slope, and b the y-intercept (the y-value when x = 0).

because we got the slope and a point we can start with the point-slope form and then transform the equation.

the point-slope form is in general

y - y1 = a(x - x1)

a is again the slope (the same value), and (x1, y1) is a point on the line.

so,

y - 2 = 3/4 × (x - 2) = (3/4)x - 3/2

y = (3/4)x - 3/2 + 2 = (3/4)x - 3/2 + 4/2 = (3/4)x + 1/2

Answer:

D 34.8

Step-by-step explanation:

[tex]\frac{31+36+28+52+27}{5}[/tex]