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If the volume of a cube is 125cm³, it's length is 5 cm² and it's total surface area is 150cm²

A Cube is a solid three-dimensional figure, which has 6 square faces, 8 vertices and 12 edges. It is also said to be a regular hexahedron.

The volume of a cube is expressed as;

V = l³

V = 125cm³

125 = l³

l³ = 5³

l = 5 cm

since cube as six surfaces , and the area of a surface = l²

The total surface area of a the cube = 6l²

= 6× 5²

= 6× 25

= 150cm²

therefore the length and total surface area of the cube is 5cm and 150 cm²

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Answer:

(i) \(\frac{27}{35}\)

(ii) \(\frac{8}{35}\)

Step-by-step explanation:

Probability refers to chances of occurrence of any event.

Probability is calculated by dividing number of favorable outcomes by total number of possible outcomes.

Total number possible of outcomes = 350

(i)

Number of favorable outcomes = \(65+95+110=270\)

Probability \(=\frac{270}{350}=\frac{27}{35}\)

(ii)

Exactly 3 heads is equivalent to no tails.

Number of favorable outcomes = \(80\)

Probability \(=\frac{80}{350}=\frac{8}{35}\)

A conclusion which can be inferred about an individual score that corresponds to a z-value of 1.0 is that: c.) it is likely to come from the healthy distribution.

A z-value is also referred to as a z-score or standard score and it can be defined as a measure of the distance between a raw score and the mean, when standard deviation units are used.

In Statistics, z-values can either be positive or negative and it can be calculated by using this formula:

\(Z=\frac{x\;-\;u}{\delta}\)

Where:

Since the individual score that corresponds to a z-value of 1.0, we can reasonably infer and logically conclude that an individual score is likely to come from the healthy distribution.

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Complete Question:

Scores of healthy adults on a neurological test form a normal distribution with mean = 100 and SD = 15. What conclusion can be inferred about an individual score that corresponds to a z value of 1.0?

a.) it falls in the general region of the population

distribution

b.) it falls in the common region of the distribution

c.) it is likely to come from the healthy distribution

d.) it is unlikely to come from the healthy distribution

For 420 minutes of calls will the costs of the two plans be equal.

We have,

The first plan has a $21 monthly fee and charges an additional $0.09 for each minute of calls.

The second plan has no monthly fee but charges $0.14 for each minutes.

So, the equation can be set as

0.14x = 0.09x +21

where x be the number of minutes.

0.14x - 0.09x = 21

0.05x = 21

x = 420 minutes

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Answer:

If the perimeter = 300m

let the ratio be in x

a/q.

3x + 5x + 7x. = 300m

15x = 300

x = 300/15

x = 20

hence angles are

60 , 100 and 140

hope it helps

Answer:

A ≈ 1500\(\sqrt{3}\) m²

Step-by-step explanation:

sum the parts of the ratio, 3 + 5 + 7 = 15 parts

Divide perimeter by 15 to find the value of one part of the ratio.

300 ÷ 15 = 20 m ← value of 1 part of the ratio , then

3 parts = 3 × 20 = 60 m

5 parts = 5 × 20 = 100 m

7 parts = 7 × 20 = 140 m

The 3 sides of the triangle are 60 m, 100 m , 140 m

To calculate the area (A) having all 3 sides use Hero's formula

A = \(\sqrt{s(s-a)(s-b)(s-c)}\)

where s is the semiperimeter and a, b , c the sides of the triangle

s = 300 m ÷ 2 = 150 m

let a = 60, b = 100 and c = 140 , then

A = \(\sqrt{150(150-60)(150-100)(150-140)}\)

   = \(\sqrt{150(90)(50)(10)}\)

   = \(\sqrt{6750000}\)

   = \(\sqrt{10000}\) × \(\sqrt{675}\)

   = 100 × \(\sqrt{25(27)}\)

    = 100 × 5\(\sqrt{27}\)    

    = 500 × \(\sqrt{9(3)}\)

   = 500 × 3\(\sqrt{3}\)

   = 1500\(\sqrt{3}\) m²

The required arc length of sector VW is 8\(\pi\).

Given that, in a circle U, radius  UV = 9 and  central angle of sector m∠VUW = 160°.

To find the arc length of sector VW, we can use the formula:

Arc length = (central angle / 360) x circumference of the circle.

First,  find the circumference of the circle by the  formula for the circumference of a circle is given by:

Circumference = 2 x \(\pi\) x radius.

Circumference = 2 x \(\pi\) x 9 = 18π.

Now, let's find the arc length of sector VW using the central angle of 160 degrees:

Arc length = (160/360) x 18π

Arc length = (4/9) * 18\(\pi\) = 8\(\pi\).

Therefore, the arc length of sector VW is 8\(\pi\).

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Hello!

First, let's write the equation in Point-slope form.

y-y1=m(x-x1)

y-(-1)=2(x-(-3) (Point-Slope Form)

Now, convert it into Slope-Intercept form:

y+1=2(x+3)

y+2=2x+6

y=2x+6-2

y=2x+4 (slope-intercept form)

Hope everything is clear.

Let me know if you have any questions!

#KeepLearning

:-)

Answer:

1) 48

2)44

Step-by-step explanation:

Answer:  48 44 Are The Correct Answers

Step-by-step explanation:Hope This Helps

Answer:

4 bouquets

Step-by-step explanation:

She can make four bouquets, being that 4 is the greatest common factor of both 12 and 16

The equation of the sphere is

\(x^{2} +y^{2}+z^{2}+-10x-12y-10z+4=0\)

The standard form of the equation of the sphere is :

\((x-a)^{2}+(y-b)^{2}+(z-c^{2} )=r^{2}\)

Where A (a, b , c) is the center and r is the radius.

From the question we should first find the radius

r = \(\sqrt{(x-a)^{2}+(y-b)^{2}+(z-c)^{2}\)

Point = (x , y , z) = (8 , 3 , -3)

Center = (a, b , c)= (5 , 6 ,5)

Substituting it in the formula

r = \(\sqrt{(8-5)^{2}+(3-6)^{2}+(-3-5)^{2} }\)

By further calculation

r = \(\sqrt{9+9+64}\)

So, we get

r =\(\sqrt{82}\)

Substituting it in the standard form

\((x-5)^{2}+(y-6)^{2}+(z-5)^{2}=\sqrt{82}^{2}\)

\((x-5)^{2} +(y-6)^{2} +(z-5)^{2}=82\)

\(x^{2} +y^{2}+z^{2}+25+36+25-10x-12y-10z=82\)

\(x^{2} +y^{2}+z^{2}+-10x-12y-10z+86-82=0\)

\(x^{2} +y^{2}+z^{2}+-10x-12y-10z+4=0\)

Therefore, the equation of the sphere is

\(x^{2} +y^{2}+z^{2}+-10x-12y-10z+4=0\)

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There are 6 pairwise comparisons that need to be made in order to gain a complete understanding of which treatment effects differ significantly from others.

In order to determine which treatment effects differ significantly from others, we need to make pairwise comparisons between all possible pairs of treatment groups. Let's consider an example with four treatment groups labeled A, B, C, and D.

To determine which treatment effects differ significantly from others, we need to compare the mean scores of each treatment group with the mean scores of every other treatment group. This means we need to make the following pairwise comparisons:

A vs B

A vs C

A vs D

B vs C

B vs D

C vs D

Therefore, there are 6 pairwise comparisons that need to be made in order to gain a complete understanding of which treatment effects differ significantly from others.

It's worth noting that when making multiple pairwise comparisons, there is an increased risk of making a Type I error (i.e., rejecting the null hypothesis when it is actually true) due to the multiple testing problem. To control for this, researchers may choose to adjust the significance level or use methods such as the Bonferroni correction to adjust the p-values of the individual tests.

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Answer:

d Because I just took the test and got it right

Answer:

It depends on the type of function, but essentially the process is the same

Step-by-step explanation:

You gather up all of the y values and x values and plot them onto a coordinate grid. If you are using a calculator, go to the "y=" button and input the function and then hit "graph"

Answer:

Step-by-step explanation: Negatives because a number lower than 0 go like this -1 -2 -3 -4 -5 -6 -7 -8 -9 -10 see? so the answer is Negatives.

Answer:

To get the answer of this, we need to multiply 2/3 by 90 centimeters to get 2/3s of the total length. Sometimes it is easier to just think, "what is a third of 90?" and then double it, but the foolproof way to get the answer is to multiply the fraction by 90/1.

2/3 * 90/1 = 180/3. Divide out and the answer is:

60 centimeters

Step-by-step explanation:

Answer: Binder = 75c    notebook = 65c

Step-by-step explanation:

3b + 10n = 875

3b + 4n = 485

Subtracting gives:

6n = 390

390/6 = 65

n = 65

Substitute 65 into 3b + 4n = 485

3b + 260 = 485

3b = 485 - 260

3b = 260

b = 75

Answer:

4z-12

Step-by-step explanation:

the perimeter is the sum of all sides

so

\(P=(z+3)+(z-9)+(z+3)+(z-9)\\\\P=z+3+z-9+z+3+z-9\\\\P=4z+6-18\\\\P=4z-12\)

In a standard normal distribution, the mean is 0 and the standard deviation is 1.

Then, according to the normal table, the probability of gettin z < 0.18 is given by the area on the left of z = 0.18 in the graph related to the distribution. Then we have: P (z < 0.18) = 0.5714

Answer

1953. 64

Step-by-step explanation:

The original number, to the nearest tenth, is approximately 46.5. When the number 43 percent the rest of 20.

To find the original number when 43% of it is equal to 20, we can set up an equation and solve for the original number.

Let's denote the original number as x.

According to the problem, 43% of x is equal to 20. We can express this as an equation:

0.43x = 20

To find the value of x, we divide both sides of the equation by 0.43:

x = 20 / 0.43

x ≈ 46.51

Therefore, the original number, to the nearest tenth, is approximately 46.5.

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Answer:

The angle measures \(\frac\pi2\) radians, or 90°

Step-by-step explanation:

In radians, the measure of an angle is defined as the length of the arc divide by the radius of the circle of which that arc is part of. In our case

\(\angle XOY = \frac {\overarc{XY}}{OX} = \frac{16\pi}{32} = \frac\pi2\)

Answer:

angle XOY = \(\frac{\pi}{2}\) (in radians) or 90° (in degrees)

Step-by-step explanation:

So firstly we need to consider that the unit of measurement is radians, not degrees, as represented by the 'measures 16π cm'.

Next, since we have the length of arc XY given as 16π cm, we can apply the formula for the length of an arc, in radians, which is \(l=r\theta\).

I'm assuming that you know how to derive the formula for arc length since you are getting questions about arc length like this, but if not, then you can just search on the internet: "derivation for the formula of arc length in radians"

Therefore: we should let ∠XOY = ∅ and so,

\(l=16\pi\) and \(r=32\)

\(16\pi =32\theta\\\frac{16\pi}{32}=\theta\\ \frac{\pi}{2}=\theta\)

∴∠XOY = \(\frac{\pi}{2}\\\) radians

(Unless otherwise stated, return your answer in the same unit of measurement as the measurements in the question)

Answer:

X = all #'s

why?

6x+10+10x < 4(4x+3)

Combined liked terms

16x + 10 < 16x +12

you can see that there is X on both sides and the lowest one has a +10 and the highest has a +12 so it will always be greater by 2

Answer:

undeterminate (all real numbers are a solution)

Step-by-step explanation:

1) multiply 4 by 4x and 3

6x + 10 + 10x < 16x + 12

2) added up the terms with x

16x + 10 < 16x + 12

3) add at the two members -16x

10 < 12

4) notice the 10 is ever < 12, so the inhequality is undetermined

The inverse of f is a function which takes any value x and divides it by 4, then adds 7 to the result.

The inverse of a function is the opposite of the original function, meaning that it takes the output of the original function and turns it back into the input. In this case, the original function is f(x)=1/4x+7. To find the inverse, we need to solve for x in the equation, which can be done by subtracting 7 from both sides and then multiplying both sides by 4. This gives us x=(x+7)/4, which is the inverse of the original function. To put it simply, the inverse of f takes any output of the original function, adds 7 to it, and then divides it by 4 to get the original input.

example;

If f(x)=1/4x+7 and x=3, then

f(3) = (1/4)3 + 7

7.75

The inverse of f is f^-1(x) = (x + 7) / 4.

If f^-1(7.75) = (7.75 + 7) / 4, then

f^-1(7.75) = 14.75 / 4

3.6875

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Answer:

Step-by-step explanation:

If we consider a circle with a diameter of 7 cm... by superimposing a thread we may find that the circumference is approx. 22 cm.

Now, as we know that

2 pi r = c

d * pi =c

pi = c/d

Hence by dividing 22 by 7, we get 3.14 to two decimal places

[Note: The exact value of pi can never be found... as it is irrational. But for simplicity.. we take it as 3.14]

Answer:

y-1=7(x-0)

Step-by-step explanation:

The line perpendicular to y=-1/7+1 is y=7+1 because you find the reciprocal of the slope.

Then find one point on the line since the equation has a y intercept just use (0,1) and put that into point slope

Answer:

The solution to the system is (1, 6)

Step-by-step explanation:

Trust me its correct

pls mark me as brainliest

Answer:

8.40665 Step-by-step explanation:

Answer:

pretty sure it's the 2nd one

Step-by-step explanation: