CORE
SKILL
ADVANCED
If a is inversely related to the square of b, and a = 3 when bis
8, which of the following is another possible value for a and b?
(A) a = 4, b = 12
(B) a = 12, b = 4
(C) a = 8, b = 3
(D) a = 2, b = 4
(E) a = 6, b = 4

The volume of solid B is 1350 [tex]cm^{3}[/tex].

What is the volume ratio?

The side length ratio raised to the third power represents the volume ratio for the two solids.

If two solids are comparable, their volumes will have a ratio that is equal to the cube of their corresponding side ratios.

Given that both solids are similar.

The volume of solid A = 400 [tex]cm^{3}[/tex]

height of solid A = 10 cm

height of solid B = 15 cm

the volume of solid B = ?

Now,

volume of solid A/ volume of solid B = (height of solid A)^3/(height of solid B)^3

or, [tex]\frac{400}{x} = \frac{10^{3} }{15^{3} }[/tex]

or, [tex]x = \frac{400*15^{3} }{10^{3}}[/tex]

or, [tex]x = \frac{400*3375 }{1000}[/tex] = 1350

Hence, the volume of solid B is 1350 [tex]cm^{3}[/tex].

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The equation of given graph is y = |x - 3| + 5.

The graph of a absolute or modulus function is a V- shape graph. The function of absolute is f(x) = |x|. The general form of absolute function is f(x)=a |x - h| + k. Where (h,k) is the vertex of graph.

Here, we can see that graph is in the form of V shape, so the function will be absolute function. Now, we have to find the vertex of graph.

As seen from the graph the minimum point on the graph is located at the point (3, 5) and the value of a should be 1.

So, by putting the value of vertex in general equation we get the equation of the graph,

y = |x - 3| + 5

Therefore, the equation of given graph is y = |x - 3| + 5.

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To cover 10000 steps the time taken will be 115 minutes and he will cover at 9:55 AM.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that at 8 a.m., Sothy goes for a walk and plans to walk `10000` steps. At 8:23 a.m., his phone tells him that he has taken `2000` steps.

The time will be calculated as,

2000 steps ⇒ 23 minutes

1 Step ⇒ 23 / 2000 minutes

10000 steps ⇒ ( 23 x 10000) / 2000 minutes

10000 steps ⇒ 115 minutes

The time of covering 10000 steps will be at 9:55.

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To move at 100 km/hour at its end, the length of the minute hand that has an angular velocity of 2·π radians per hour, has to be approximately 15.92 kilometers

Angular velocity is the rate and direction of rotation of a body about an axis.

The required linear speed of the minute hand = 100 km/hour

The formula to convert angular speed to linear speed is presented as follows;

Which gives;

The angular speed of the minute hand = 2·π rad/hour

The required length of the minute hand is therefore;

[tex]r = \dfrac{100 \ km/hour}{2\cdot \pi/hour} = \dfrac{50}{\pi}\, km \approx 15.92 \, km[/tex]

The length of the minute hand that that give a motion of 100 km/hour at the end is approximately 15.92 km

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Answer: 41.18% or 7/17

Step-by-step explanation:

7 + 4 + 6 = 17

7/17 (fraction)

41.18%

The probability of not rolling a 5 is [tex]\frac{1}{6}[/tex]

For any event A, the probability of not getting A is given by

[tex]P(not A)= 1- P(A)[/tex]

A number cube with six sides numbered 1 through 6 is rolled.

Then we have,

The total number of possible outcomes [tex]= 6[/tex]

Also, it is given that, The probability of rolling a 5 is

P(rolling 5)=[tex]\frac{1}{6}[/tex].

Now, the probability of not rolling a 5 will be

[tex]P(\text{not rolling a 5})= 1- P(\text{rolling 5})[/tex]

[tex]=1-\frac{1}{6}[/tex]

[tex]=\frac{5}{6}[/tex]

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The coordinates of the midpoint M for the line segment AB are (-1/2, -2).

As per the stated values;

Th end points of the line segment AB are given as;

A(−5, 1) = (x1, y1)

B(4,−5) = (x2, y2)

The formula for the evaluation of the coordinates of the mid point is-

Mid point - M(x, y)

x = (x1 + x2)/ 2

x = (-5 + 4) /2

x = -1/2

y = (y1 + y2)/2

y = (1 - 5)/2

y = -2

Thus, the coordinates of the midpoint M for the line segment AB are (-1/2, -2).

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Answer: -62.5

PLEASE GIVE BRAINLIEST THANK YOU!!!

Step-by-step explanation:

Answer:

14.7

Step-by-step explanation:

Answer:

6[tex]\sqrt{6}[/tex]

or

≈14.7

Step-by-step explanation:

√6 x √6 x√6 can someone help​

√6 x √6 x√6 =

6[tex]\sqrt{6}[/tex]

or

≈14.7

The angle C = 103.85° using the sine rule and rounded to the nearest hundredth.

In trigonometry, the sine rule is an equation relating the lengths of the sides of any triangle to the sines of its angles.

Considering the ∆ABC, the sine rule states that;

(a/sinA) = (b/sinB) = (c/sinC)

so

25/sin120° = 20/sinB

sinB = (20 × sin120°)/25 {cross multiplication}

sinB = 0.6928

B = sin^(-1)[0.6928)] {sine inverse}

B = 43. 85°

Sum of interior angles in ∆ABC is 180° so;

C = 180° - (120° + 43.85°)

C = 180° - 76.15°

C = 103.85°

With the application of the sine rule, we can conclude that the value of the angle C is 103.85° rounded to the nearest hundredth.

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The zero of the function f(x) = 2x² - 8 is ± 2.

Zeros of the function

Zero of the function means the values of x when f(x) is equal to 0. Which  means that when f(x) = 0, x is a zero of the function.

Given,

Here we have the function f(x) = 2x² - 8.

Here we need to find the zero of the function.

As per the definition of the zeros of the function,

We have to apply the value of f(x) = 0, then we get,

2x² - 8 = 0

Now, we need the value of x only, so we have to move the other numbers to the other side , then we get,

2x² = 8

Now, move the number 2 to the right hand side then it will be dividing the number 8,

x² = 8/2

x² = 4

x = √4

Therefore, the value of x is ± 2.

So, the zeros of the function is either +2 or -2.

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As per the given percentage, Sherry want to invest $2,000 amount in mutual fund and $13,200 amount in bonds.

Percentage:

Percentage means the number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, "%".

Given,

Sherry has 15,200 dollars to invest in mutual funds and in bonds. Sherry has selected a mutual fund that earns 1% a year and a bond that earns 4% a year.

Here we need to find if she wants to earn 548 at the end of the first year, how much does she need to invest in each type of account.

It is given that the total amount is 15200.

So, let us consider x be the amount invested in mutual funds then 15200 - x be the amount invested in bonds.

Therefore, it can be written in the following matrix,

[tex]\begin{bmatrix}x & 15200-x\end{bmatrix}[/tex]

Now, we have know that the total interest amount after 1 year is 548,

So, it can be written like the following expression

amount invested x percentage = final amount

Therefore,

[tex]\begin{bmatrix}x & 15200-x\end{bmatrix}\times\begin{bmatrix}\frac{1}{100} \\\frac{4}{100}\end{bmatrix}=548[/tex]

It can be simplified as,

[tex]\begin{bmatrix}x\times(\frac{1}{100})+(15200-x)\times(\frac{4}{100}) \end{bmatrix}=[548][/tex]

=> x/100 + 60800-4x/100 = 548

=> x + 60800 - 4x = 54800

=> -3x = 54800 - 60800

=> -3x = -6000

=> x = 2000

=> 15200 - 2000 = 13200

Therefore, she invests $2,000 in mutual funds and $13, 200 in bonds.

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Answer:

$180

Step-by-step explanation:

[tex]P\times{(1-0.20)}=144[/tex]

[tex]P\times{0.80}=144[/tex]

[tex]P=\frac{144}{0.80}[/tex]

[tex]P=180[/tex]

The equation of the line passing through (-5, 1) and is parallel to y = -2/5x -5 in standard form is 5y + 2x = -5

The equation of a line can be represented in standard form or slope intercept form as follows;

Slope intercept form,

y = mx + b

where

Line are parallel when they have the same slope.

Therefore, the slope of the equation has a slope of - 2 / 5 x.

The line passes through (-5, 1).

Hence, let's find y-intercept.

y = - 2 / 5 x + b

1 = - 2 / 5 (-5) + b

1  - 2 = b

b = -1

Therefore, y = -2 / 5x - 1.

The equation in standard form should be in the form Ax + By = C.

Hence,

y + 2 / 5 x  = -1

5y + 2x = -5

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The margin of error with 80% confidence interval is 2.099

Given that,

A straightforward random sample of 25 observations is taken from a population that is normally distributed and has a standard deviation of 8.2.

To find : The margin of error with 80% confidence

Margin of Error : The margin of error is a statistic that describes how much random sampling error there is in survey results. One should have less faith that a poll's findings would accurately reflect those of a population census the higher the margin of error.

Here we have

n=25,σ=8.2

For 80% confidence interval, the critical value of z is 1.28. So requried margin of error is

ME=[tex]Z_{c}\cdot \frac{\sigma}{\sqrt{n}}[/tex]=1.28[tex]\cdot \frac{8.2}{\sqrt{25}}[/tex]=2.0992

Thus, with 80% confidence, the error margin is 2.099.

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The matrix

[tex]MN = \left[\begin{array}{ccc}-2&1&0\\17&2&-3\\11&12&-5\end{array}\right][/tex]

The given matrix is

[tex]M = \left[\begin{array}{ccc}1&0\\-4&3\\2&5\end{array}\right][/tex]

[tex]N = \left[\begin{array}{ccc}-2&1&0\\3&2&-1\\\end{array}\right][/tex]

The Order of M = (3×2)

The Order of N = (2×3)

Since the number of columns of M is equal to the number of rows, the multiplication of M and N is possible,

The order of the matrix formed is MN = ( 3 × 3 )

So,

[tex]MN = \left[\begin{array}{ccc}-2+0&1+0&0+0\\8+9&-4+6&0-3\\-4+15&2+10&0-5\end{array}\right] \\\\MN = \left[\begin{array}{ccc}-2&1&0\\17&2&-3\\11&12&-5\end{array}\right][/tex]

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Answer: 3

I used PEMDAS in this explanation: Parenthesis, Exponents, Multiplication, Division, Addition, Subtraction. Also known as the order of operations

Step-by-step explanation:

-5 + (5+3) :

First, add 5+3 =8

-5+8

When adding a negative to a positive, first, switch the -5 and 8 around like so.

8 + (-5)

then turn the -5 into it's opposite and subtract ---> 5

8-5=3

Unworded explanation:

-5 + (5+3) :

-5 + 8

8 + (-5)

8-5 = 3

Answer:

Step-by-step explanation:

Answer: [tex]x=\frac{-A+\left(A^2-34560\right)^{\frac{1}{2}}}{270},\:x=\frac{-A-\left(A^2-34560\right)^{\frac{1}{2}}}{270}[/tex]

Step-by-step explanation:

64+Ax+135x^2

135x^2+Ax+64=0

[tex]x_{1,\:2}=\frac{-A\pm \sqrt{A^2-4\cdot \:135\cdot \:64}}{2\cdot \:135}[/tex]

[tex]x_{1,\:2}=\frac{-A\pm \left(A^2-34560\right)^{\frac{1}{2}}}{2\cdot \:135}[/tex]

[tex]x_1=\frac{-A+\left(A^2-34560\right)^{\frac{1}{2}}}{2\cdot \:135},\:x_2=\frac{-A-\left(A^2-34560\right)^{\frac{1}{2}}}{2\cdot \:135}[/tex]

[tex]x=\frac{-A+\left(A^2-34560\right)^{\frac{1}{2}}}{270},\:x=\frac{-A-\left(A^2-34560\right)^{\frac{1}{2}}}{270}[/tex]

The alternative hypothesis and null are:

H₀ : p = 0.31 vs H₁ : p > 0.31

Given that;

A sample of 900 computer chips revealed that 34% of the chips do not fail in the first 1000 hours of their use. the company's promotional literature states that 31% of the chips do not fail in the first 1000 hours of their use. the quality control manager wants to test the claim that the actual percentage that do not fail is different from the stated percentage.

To get decision rule for rejecting the null hypothesis, h0, at the 0.10 level;

n = 900

P = 0.34

p = 0.31

α = 0.10

Claim: More than 31% do not malfunction within the first 1000 hours of operation.

The null and alternative hypothesis must be stated.

This is a right-tailed test because the claim is directional to the right side (> type).

Therefore, the alternative hypothesis and null are:

H₀ : p = 0.31 vs H₁ : p > 0.31

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The distance yet to be covered by Ashlee is 6.8 miles.

Ashlee is riding her bike to the beach. The beach is 17 miles from her home. She has already travelled 3/5 of the total distance. We need to find out how much farther she has to cycle.

Let the distance left to be covered by Ashlee be represented by the variable "D". The distance already covered by Ashlee on her cycle is calculated below.

d = (3/5)×17

d = 10.2

So she has already covered a distance of 10.2 miles. The distance yet to be covered is the difference between the total distance and the distance covered.

D = 17 - 10.2

D = 6.8

Hence, the distance yet to be covered by Ashlee is 6.8 miles.

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The simplified expressions for the questions will be, 1) 3w, 2) 8x, 3) 10p, 4) 8b.

The simplification of an algebraic expression generally means breaking the equation into a smaller form for easier calculation with the help of formulas or using the rule of BODMAS.

Here, all the questions can be solved by using the BODMAS rule.

1) 7w + 2w - 6w

= (7w + 2w) - 6w

= 9w - 6w

= 3w.

2) 9x - 3x + 2x

= (9x + 2x) -3x

= 11x - 3x

= 8x.

3) 8p + 3p - p

= (8p + 3p) - p

= 11p - p

= 10p.

4) 6b - 3b + 5b

= (6b +5b) - 3b

= 11b -3b

= 8b.

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Step-by-step explanation:

[tex]7w + 2w - 6w \\ 9w - 6w \\ = 3w[/tex]

[tex]9x - 3x + 2x \\ 6x + 2x \\ = 8x[/tex]

[tex]8p + 3p - p \\ 11p - p \\ = 10p[/tex]

[tex]6b - 3b + 5b \\ 3b + 5b \\ = 8b[/tex]

The perpendicular bisector of the line segment with endpoints (6, -5) and (-2, -9) is 7x,2y = 6.

Therefore,

The coordinates of the end points:

(6, -5) and (-2, -9)

((6, -5) +(-2, -9))/2

= ((6,-9)/2, (-2, -5)/2)

= (1.5, 3.5)

The difference in endpoint coordinates will be;

(Δx, Δy) = (9-(-5), (-2)-6) = (14, 8)

Then the ratio of these values, so we need to divide both by the common factor of 2:

(Δx, Δy) = (7, 2)

A line perpendicular to this segment through the point (h, k) can be written as;

Δx·x +Δy·y = Δx·h +Δy·k

7x ,2y = 7(2) 2(4)

7x, 2y = 6 .

Hence the standard form equation for the perpendicular bisector will be;  7x ,2y = 6 .

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A number line which shows -4, -1, 1, and 2 correctly plotted on a graph is shown in the image attached below.

In Mathematics, a number line can be defined as a type of graph with a graduated straight line which comprises both positive and negative numbers that are placed at equal intervals along its length.

This ultimately implies that, a number line primarily increases in numerical value towards the right from zero (0) and decreases in numerical value towards the left from zero (0). Therefore, the numerical values -4 and -1 would be plotted on the left hand side of zero (0) while the numerical values 1 and 2 would be plotted on the right hand side of zero (0) using a number line.

In this scenario, a number line would be used for the comparison of two or more numbers such as -4, -1, 1, and 2, and this is plotted in the graph shown in the image attached below.

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The probability that Rupert picked 2 green balls is 1/21.

What is probability?

The area of mathematics known as probability deals with numerical descriptions of how likely it is for an event to happen or for a claim to be true. It's value ranges from 0 to 1.  

Main Body:

total balls = 7  , green balls =2

1st try:  

probability of getting green ball = 2/7

As there is no replacement so now,

total balls = 6  , green balls = 1

2nd try:  

probability of getting green ball = 1/6

total probability = (2/7)*(1/6)

                          = 1/21

Hence the answer is 1/21.

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The number of books each classroom received = 185

In this question, we have been given two libraries donated books to a local school. One library donated 786 books and the other library donated 1,245 books. The school divided the books evenly among 11 classrooms.

We need to find the number of books each classroom received.

Total number of books received:

786 + 1245 = 2031

The school divided the books evenly among 11 classrooms.

Let x be the number of books each classroom received.

By unitary method,

x = 2031 /11

x ≈ 185

Therefore, the number of books each classroom received = 185

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Answer:

Here ,

sigma x=50+60+65+70+70+80+90=485

N=7

now,

Mean =sigma x÷N

=485÷7

=69.28

The probability that the coin lands on heads is D = (3±√3)/6

Probability is a branch of mathematics that studies the likelihood of a random event occurring. For example, when a coin is tossed into the air, the possible outcomes are Head and Tail.

Let x be the probability of flipping heads. As a result, the probability of flipping tails is 1- x.

The probability of flipping two heads and two tails is equal to the number of ways to flip it multiplied by the product of the probabilities

(4+2)x2(1-x)2 = 1/6

6x2(1-x)2 = 1/6

x2(1-x)2 = 1/36

x(1-x) = ±1/6

As for the desired probability x, both x and 1 - x are nonnegative, we only need to consider the positive root, hence

x(1-x) = 1/6

6x2 – 6x +1 = 1/6

Using the quadratic formula, we can determine that the roots of this equation are

(3±√3)/6

Therefore the probability that the coin lands on heads is D = (3±√3)/6

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The vertex of the graph is (2, -1), the axis of symmetry of the graph is x = 2 and the parabola opens downward

The vertex

The graph represents the given parameter

From the graph, we can see that:

The maximum point on the graph is located at

(2, -1)

The vertex of a graph is the maximum or the minimum  of the graph

This means that

Vertex = (2, -1)

The axis of symmetry

The graph represents the given parameter

In (a), we have

Vertex = (2, -1)

Remove the y-coordinate

x = 2

The axis of symmetry of a graph is the x coordinate of the vertex

This means that the axis of symmetry is x = 2

From the graph, we can see that the parabola opens downward

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Answer:

The object has fallen [tex] \boxed{\sf 289} [/tex] feet from ts intial position.

Step-by-step Explanation:

Given:

Formula:

[tex] \rm v = \sqrt{2gh} [/tex]

Where,

v = velocity (in feet per second)

h = Height fallen (in feet)

g = acceleration due gravity (in feet per second squared) = approximately 32 ft/s²

To find:

How far an object has fallen if its velocity (v) is 136 ft/s

Solution:

By substituting the value of g & v in the formula we get:

[tex]\rm \implies 136 = \sqrt{2 \times 32 \times h} \\ \\ \rm \implies 136 = \sqrt{64h} \\ \\ \rm \implies 64h = {136}^{2} \\ \\ \rm \implies h = \dfrac{ {136}^{2} }{64} \\ \\ \rm \implies h = \dfrac{18496}{64} \\ \\ \rm \implies h = 289 \: ft[/tex]