A survey of 225 students showed the mean number of hours spent studying per week was 20.6 and the standard deviations was 2.7

Answer:

  x = 18

Step-by-step explanation:

The parts of the triangles are proportional, so you can write ...

  2x/80 = 27/60

Multiply by 120:

  3x = 54

Divide by 3:

  x = 18

Answer:

8

Step-by-step explanation:

Let's set this up to see if we can simplify it a bit:

[tex](\frac{10^4*5^2}{10^3*5^3})^3[/tex]

Notice we have 4 tens on top and 3 on bottom, so we can eliminate the bottom 3 altogether and leave just one on top.  And we have 2 fives on the top and 3 on bottom, so we can eliminate the 2 on the top and leave one on the bottom.  Now that looks like this:

[tex](\frac{10}{5})^3[/tex]

10 divided by 5 is 2, and 2 cubed is 8

Final answer:

To find the value of the expression ((10⁴)(5²)/(10³)(5³))³, we simplify the powers of 10 and 5 and then raise the result to the power of 3, obtaining the final answer of 8.

Explanation:

To solve the expression ((10⁴)(5²)/(10³)(5³))³, we start by simplifying inside the parentheses. We use the properties of exponents to divide the powers of tens and fives separately:

So the inside of the parentheses simplifies to (10 * 1/5) which is 2. Then, we raise 2 to the power of 3 as indicated by the expression:

(2)^3 = 2*2*2 = 8

Therefore, the value of the expression ((10⁴)(5²)/(10³)(5³))³ is 8.

ANSWER

The pendulum's maximum displacement is 2cm.

EXPLANATION

The maximum value of the graph is the pendulum's maximum displacement.

The graph is a periodic function

The amplitude of the graph is 2.

The range of the graph is -2≤y≤2

The maximum value is 2.

The pendulum's maximum displacement is 2cm

The correct choice is B.

There are two possible ways for X=1: first light is green and second is red OR first light is red and second is green. The probabilities for these two options are to be summed: 0.6*0.4 + 0.4*0.6 to give the probability of exactly one light being green, namely 0.48.

P(X = 1) = 0.48

"Probability is a branch of mathematics which deals with finding out the likelihood of the occurrence of an event."

"It is a probability distribution that gives only two possible results in an experiment, either success or failure. "

[tex]P(x)=n_C_x\times (p)^{x}\times (q)^{n-x}[/tex], here n is the total number of outcomes, 'p' is the probability of success and 'q' is the probability of failure

For given example,

The probability that traffic lights on a certain road will be green is 0.6

This means, the probability  of success (p) = 0.6

So, the probability of failure (q) = 1 - p

q = 0.4

When a driver on that road approaches two traffic lights in a row, X is the number of traffic lights that are green.

here, n = 2, p = 0.6, q = 0.4, x = 1

Using the formula of Binomial distribution the required probability is,

[tex]P(x=1)=2_C_1\times (0.6)^{1}\times (0.4)^{2-1}\\\\P(x=1)=\frac{2!}{1!\times (2-1)!}\times 0.6\times 0.4^1\\\\P(x=1)=2\times 0.6\times 0.4\\\\\bold{P(x=1)=0.48}[/tex]

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Answer:

Explanation:

1) Write the model for the volume and base area of the rectangular sotorage container:

       base width, w = x

       base length, l = 2x

        B = (2x) (x) = 2x²

        height = h

        V = 2x² h = 10 ⇒ h = 10 / (2x²)

2) Total area, A

        S₁ = (x) . (h) = (x) . 10 / (2x²) = 10 / (2x) = 5 / x

        S₂ = S₁ = 5 / x

        S₃ = (2x) . (h) = (2x) . 10 / (2x²) = 10 / x

        S₄ = S₃ = 10 / x

3) Cost

        $ 10 (2x²) = 20x²

$6 (S₁ + S₂ + S₃ + S₄) = 6 (5/x + 5/x + 10/x + 10/x ) = 6 ( 30/x) = 180/x

4) Cheapest container

Minimum cost ⇒ find the minimum of the function 20x² + 180 / x, which formally is done by derivating the function and making the derivative equal to zero.

Solve to find the value of x that makes the first derivative equal to zero:

Replace x = 1.65 in the equations of costs to find the minimum cost:

That is the final answer, already rounded to the nearest cent: $163.54

The question is about the optimization of the costs for constructing a rectangular container with a specific volume of 10 m^3.  This is done by creating equations for volume and cost, and then optimizing the cost using calculus.

The subject of this question is Optimization in Calculus. Here, we trying to minimize the cost of a rectangular storage container with given constraints. First, we need to setup equations for the volume, V = length x width x height and cost, as given. Since the volume of the box is fixed at 10 m3 and given that the length is twice the width we have:

We solve for h in terms of w from the volume equation and substitute it in the cost, we can then take the derivative of the cost equation and solve it to get the width. Lastly, we plug the width value in the cost equation to get the minimal cost.

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Answer: D.

Step-by-step explanation:

Answer:

Answer one: the parent function has been translated to the left

Answer tw: the parent function has been translated down

Answer three: the parent function has been compressed

Answer:

x = 2

Step-by-step explanation:

Answer:

x = 2

Step-by-step explanation:

use the Vertex form, Y=a(x-h)^2+k, to determine the values of a, h, and k.

a=2

h=2

k=5

since the values of a are positive the parabola opens up

Find the vertex (h,k)

(2,5)

Find p from the vertex and the focus

1/8

find the focus

(2,41/8)

Find the axis of symmetry by finding the line that passes though the Vertex and the focus

x=2

Or also a line that goes through the middle but that is just my opinion!

2:6 so simplify it 1:3. This means the scale ratio is 1:3 for the figures. To find w, sub in the 3 from the smaller figure to the ratio so 3×3=9, 3:9 w=9

Answer:

w = 9

Step-by-step explanation:

Since the 2 polygons are similar then the ratios of corresponding sides are equal, that is

[tex]\frac{2}{6}[/tex] = [tex]\frac{3}{w}[/tex] ( cross- multiply )

2w = 18 ( divide both sides by 2 )

w = 9

X=93 degrees

Y=74 degrees

       10√2

and this simplifies to a = -----------

                                               2Answer:

Step-by-step explanation:

The cosine function links the angle (45°), the side a and the hypotenuse (10):

                     a

cos 45° = ------------

                     10                    

                                              1

and so a = 10 cos 45° = 10(------)  =  10√2 / 2  = a

                                             √2

Speed is distance/time so

[(d/20)+(d/24)]/2= 24d+20d/24•20•2=44d/20•24•2=22d/20•24=11d/240

Answer:

C

Step-by-step explanation:

The volume of the cone can be calculated using formula

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

where h is the height of the cone, r is the base radius.

In your case, h=24 un., r=7 un. So

[tex]V=\dfrac{1}{3}\cdot \pi \cdot 7^2\cdot 24=49\cdot 8\pi=392\pi \ un^3.[/tex]

ANSWER

C.

[tex] 392\pi \: {units}^{3} [/tex]

EXPLANATION

The volume of a cone is calculated using the formula:

[tex]V= \frac{1}{3} \pi {r}^{2} h[/tex]

The radius of the cylinder is

r=7 units.

The height is 24 units.

We substitute these values into the formula to obtain:

[tex]V= \frac{1}{3} \times \pi \times {(7)}^{2} \times 24[/tex]

[tex]V = 392\pi \: {units}^{3} [/tex]

Answer:

x=18

Step-by-step explanation:

The two triangles are similar. The ratio of the sides are the same.

20/20=40/(40+x)

Cross multiply and solve. Hint: the easiest way to solve is to simplify, then solve.

Answer:

k.lkkkkkkkkkkkkk

200 ft because 8x25 is 200

Answer:

Option D.

Step-by-step explanation:

Given that (x-3) is a factor of  P(x)=x^3-7x^2+15x-9. If we divide the P(x) by (x-3) we will get a second grade polynomial, which is easier to factorize.

Dividing x^3-7x^2+15x-9 by (x-3), the answer is: x^2 - 4x + 3 with a remainder of zero.

Now, to factorize x^2-4x+3 we just need to find two numbers that equal -4 when added and 3 when multiplied. These two numbers are -1 and -3.

So the complete factorization of P(x) is: (x-3)(x-1)(x-3)

Which is option D.

Answer: D. (x-3)(x-3)(x-1)

Step-by-step explanation:

ANSWER

[tex]x ^{2} = - 4(y - 1).[/tex]

EXPLANATION

Since the parabola has the (0, 0) and the directrix at y=2.

The equation is of the form

[tex] {(x - h)}^{2} = - 4p(y - k)[/tex]

where (h,k) is the vertex.

The vertex is half way between the directrix and the focus.

The vertex will be at (0,1)

and is the distance from the vertex to the focus which is 1.

[tex]{(x - 0)}^{2} = - 4(1)(y - 1)[/tex]

[tex]x ^{2} = - 4(y - 1)[/tex]

[tex]\bf \textit{volume of a sphere}\\\\ V=\cfrac{4\pi r^3}{3}~~ \begin{cases} r=radius\\ \cline{1-1} V=14137 \end{cases}\implies 14137=\cfrac{4\pi r^3}{3}\implies 42411=4\pi r^3 \\\\\\ \cfrac{42411}{4\pi }=r^3\implies \sqrt[3]{\cfrac{42411}{4\pi }}=r\implies 14.99994\approx r\implies \stackrel{\textit{rounded up}}{15=r}[/tex]

A destructive earthquake happens once per year.

The exponential equation would be f(x) = 1-e^-x

The probability of going 3 months out of a year would be

P(X≥3/12)  ( divide 3 months by 12 months per year).

Now x equals 3/12

Now you have

P = 1-(1-e^-3/12)

= e^-1/4

= 0.7788

The probability that at least 3 months elapse would be 0.7788

(Round answer as needed).

The probability that at least 3 months elapse before the first earthquake of destructive magnitude occurs is; 0.7788

We are told that a destructive earthquake happens once per year.

Thus, the exponential equation in this scenario is;

f(x) = 1 - e⁻ˣ

Thus, the probability that at least 3 months elapse before the first earthquake of destructive magnitude occurs is given as;

P(X ≥ ³/₁₂)  since 12 months make a year

This will be;

P(X ≥ ³/₁₂) = 1 - (1 - e^(⁻³/₁₂))

P(X ≥ ³/₁₂) = e^-1/4

P(X ≥ ³/₁₂)= 0.7788

In conclusion, the probability that at least 3 months elapse would be 0.7788

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[tex]\boxed{d=2\sqrt{107}}[/tex]

For a rectangular prism whose side lengths are [tex]a,\:b\:and\:c[/tex] the internal diagonal can be calculated as:

[tex]d=\sqrt{a^{2}+b^{2}+c^{2}}[/tex]

So here, we know that:

[tex]a=l=18 \\ \\ b=w=10 \\ \\ c=h=2[/tex]

So:

[tex]d=\sqrt{l^{2}+w^{2}+h^{2}} \\ \\ d=\sqrt{18^{2}+10^{2}+2^{2}} \\ \\ d=\sqrt{324+100+4} \\ \\ d=\sqrt{428} \\ \\ \boxed{d=2\sqrt{107}}[/tex]

Answer : The value of diagonal of the rectangular solid is, 20.69 unit.

Step-by-step explanation :

First we have to calculate the side AC.

Using Pythagoras theorem in ΔABC :

[tex](Hypotenuse)^2=(Perpendicular)^2+(Base)^2[/tex]

[tex](AC)^2=(AB)^2+(BC)^2[/tex]

Given:

Side AB = l = 18

Side BC = w =  10

Now put all the values in the above expression, we get the value of side AC.

[tex](AC)^2=(18)^2+(10)^2[/tex]

[tex]AC=\sqrt{(18)^2+(10)^2}[/tex]

[tex]AC=\sqrt{324+100}[/tex]

[tex]AC=\sqrt{424}[/tex]

Now we have to calculate the side AD (diagonal).

Using Pythagoras theorem in ΔACD :

[tex](Hypotenuse)^2=(Perpendicular)^2+(Base)^2[/tex]

[tex](AD)^2=(AC)^2+(CD)^2[/tex]

Given:

Side AC = [tex]\sqrt{424}[/tex]

Side CD = h =  2

Now put all the values in the above expression, we get the value of side AD.

[tex](AD)^2=(\sqrt{424})^2+(2)^2[/tex]

[tex]AD=\sqrt{(\sqrt{424})^2+(2)^2}[/tex]

[tex]AD=\sqrt{424+4}[/tex]

[tex]AD=\sqrt{428}[/tex]

[tex]AD=20.69[/tex]

Thus, the value of diagonal of the rectangular solid is, 20.69 unit.

Answer:

A is the closest one

Step-by-step explanation:

Remark

The general formula is

V = V_2 cones + V_cylinder.

Formula

That turns out to be

V = 2*(1/3)*pi*r^2*h1 +  pi*r^2*h

Givens

r = 7 feet

h = 22 feet

h1 = 12 feet

pi = 3.14

Solution

V = 2*(1/3)*3.14 * 7^2*12  +   3.14* 7^2 * 22

V = 1231.5 ft^3 + 3384.92

V = 4616.42

Answer:

4618.1 ft3

Step-by-step explanation:

That's the exact correct answer :)

Answer:

Option A. 5.8 miles

Step-by-step explanation:

It is given in the question that angle SCD = 45°  and ∠ SAD = 35°

Distance between Cooper and Drew = 10 miles

Let distance between Ship and Cooper is = x miles

Now we apply Sine rule in the Δ SCD

[tex]\frac{sin100}{10}=\frac{sin35}{x}[/tex]

[tex]\frac{0.9848}{10}=\frac{0.5736}{x}[/tex]

By cross multiplication

(0.9848)x = 10(0.5736)

[tex]x=\frac{5.736}{0.9848}=5.82[/tex] miles

Option A. 5.8 miles is the correct option.

Answer:

  D. a constant function divided by the sum of a constant function and an exponential function

Step-by-step explanation:

It's all about the meaning of the math symbols used to create the function. The exponential function is called that because the variable (t) is in the exponent of the expression.

The "numerator" is the part of the expression above the "divided by" line. The "denominator" is the part below that line. When describing a fraction like this, we say, "<the numerator> divided by <the denominator>."

The numerator is a number with no math symbols or variables: it is a constant. The same is true of the left term of the denominator.

The plus sign between the denominator terms indicate these terms are added together. The result of that addition is called a "sum." The terms either side of the plus symbol are those that the symbol is indicating the sum of.

So, we can describe the expression as ...

  a constant function divided by the sum of a constant function and an exponential function

The logistic equation is a model of population growth, correctly described as a constant function divided by the sum of a constant function and an exponential function. This matches option D from the choices provided.

The logistic equation is a model of population growth where the growth rate decreases as the population approaches its carrying capacity. The equation structure is generally given as a constant function divided by the sum of a constant function and an exponential function. Thus, the correct description from the options provided would be D. A constant function divided by the sum of a constant function and an exponential function.

As an example, the basic form of a logistic function is P(t) = c / (1 + ae-bt). Here c is the constant function representing the maximum achievable population and ae-bt is an exponential function that models the population growth over time 't'.

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C) no solution

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Answer: Option C

C) No solution

Step-by-step explanation:

To graph both lines identify the cut points with the axes

For [tex]2x = -y + 7[/tex]

The intersection with the x axis is:

[tex]2x = -(0) +7\\\\x = 3.5[/tex]

The intersection with the y axis is:

[tex]2 (0) = -y +7\\\\y = 7[/tex]

Draw a line that cuts the y-axis in 7 and the x-axis in 3.5

For [tex]2y = -4x + 10[/tex]

The intersection with the x axis is:

[tex]2 (0) = -4x +10\\\\4x = 10\\\\x = 2.5[/tex]

The intersection with the y axis is:

[tex]2y = -4 (0) +10\\\\y = 5[/tex]

Draw a line that cuts the y-axis in 5 and the x-axis in 2.5

The intersection of both lines will be the solution of the system. Observe the attached image

The lines are parallel, so they never intercept. Therefore the system has no solution

The first line of music shows a glide reflection from all the lines.

A glide reflection is one of the types of reflection in 2-dimensional geometry.

It is a symmetry figure that consists of a reflection over a line and then translates along the line.

In this figure, the first option shows the exact symmetry operation and reflection. but the second and third line doesn't represent a glide reflection.

In the second option, the reflection does not take place, the music lines are the same before and after.

In the third option, the music lines are just interchanged which doesn't prove the glid reflection.

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k = coefficient of similarity for lengths

k ^ 2 = coefficient of similarity for surfaces

k ^ 3 = coefficient of similarity for volumes

[tex]\displaystyle\bf\\ \text{Coefficient of similarity for lengths}=~k=\frac{1}{4}\\\\\implies~\text{Coefficient of similarity for surfaces}=k^2=\left(\frac{1}{4}\right)^{\b2}=\boxed{\bf\frac{1}{16}}[/tex]

When both the radius and slant height of a right cone are multiplied by 1/4, the effect on the surface area is that it is multiplied by 1/16.

In the case of a right cone, the total surface area is given by the formula πr(r + l), where r is the radius and l is the slant height. If both the radius and slant height are multiplied by 1/4, then the new surface area becomes π(1/4r)((1/4r)+(1/4l)) = π(1/16)r(r+l). This tells us our new surface area is 1/16 of the original surface area.

Therefore, the correct effect on the surface area when both the radius and slant height of a right cone are multiplied by 1/4 is that the surface area is multiplied by 1/16.

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Answer:

102 students

Step-by-step explanation:

Note that 65% and 71% are both 1 standard deviation from the mean (71%).  According to the empirical rule, 68% of scores lie within 1 std. dev. of the mean.

68% of 150 students would be 0.68(150 students) = 102 students

68% of 150 students would be 0.68 (150 students) is, 102 students.

According to the question:

65% and 71% are both 1 standard deviation from the mean (71%).

According to the empirical rule, 68% of scores lie within 1 std. dev. of the mean.

68% of 150 students would be 0.68(150 students) = 102 students.

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Answer:

Step-by-step explanation:

The length of EA is the difference between AD (6) and ED (5), so is ...

  6 - 5 = 1

That is, the distance ED is 5 times the distance EA.

The two triangles are similar, so the distance BC will be 5 times the distance BA:

  BC = 5·AB

  BC = 5·2 = 10 . . . . . substitute for length AB

  x +4 = 10 . . . . . . . . . substitute for length BC

  x = 10 -4 = 6 . . . . . . subtract 4

We already know BC = 10. Of course AC = AB + BC = 2+10 = 12.

The lengths of interest are x=6, BC=10, AC=12.

Answer:

75%

Step-by-step explanation:

3/4=0.75

Percent: 75%

Your answer would be 75%