Help me with this please!!

Answer:

[tex]1234567x = [/tex]

The object compresses the spring up to 0.8577m.

Potential Energy is the energy possessed by an object at rest.

The object is falling from the rest and it is assumed that the friction on the ramp is zero and the air resistance is also considered to be zero so only the gravitational force acts and the total potential energy gets converted to Kinetic Energy.

The total amount of potential energy at the top of the ramp is given by

Ep=mgh

Ep=3 * 9.81 *5

Ep=147.15 Joules

This is equal to kinetic energy.

From the formula for elastic potential energy

The distance up to which the spring is compressed is determined

The force constant = 400N/m

147.15 =(1/2)k(x²)

294.3=(400)(x²)

0.73575=x²

x=0.8577 m

So, the object compresses the spring up to 0.8577m.

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Answer:

1000 times

Step-by-step explanation:

To find out how many times 0.1 can fit into 100, we can just divide 100 by 0.1.

But, we first find out how many times can 1 fit into 100.

No. of times 1 fit into 100 = 100 / 1 = 100 times

Now we know 1 is 10 times of 0.1, so we multiply the above by 10,

so 100 * 10 = 1000 times.

Therefore 0.1 can fit into 100 a 1000 times.

Answer:

1000

Step-by-step explanation:

100 divide by 0.1 the answer is 1000

The required probability is given by 0.012 for the director chooses 4 boy kittens and 3 girl kittens

A TV studio has brought in 6 boy kittens and 8 girl kittens for a cat food commercial.

Probability, can be define as the ratio of favorable events to the n number of total events

The director is going to choose 7 of these kittens at random to be in the commercial. the director chooses 4 boy kittens and 3 girl kittens.

Here, probability of to choose 7 of these kittens at random
= c(14,7)

probability to chooses 4 boy kittens and 3 girl kittens
= c(6,4) x c(8,3)

Required probability = [tex]\frac{c(6, 4) * c(8, 3)}{c(14, 7)}[/tex] = 0.012

Thus, The required  required probability is given by 0.012 for the director chooses 4 boy kittens and 3 girl kittens.

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For convenience sake, I will let [tex]y=f(x)=9e^{x}\sin x[/tex]

First, we evaluate the function at the endpoints of the interval.

[tex]f(0)=9e^{0}\sin(0)=0\\\\f(\pi)=9e^{\pi}\sin(\pi)=0[/tex]

Then, we need to find the critical points.

We can start by taking the derivative using the power rule.

[tex]f'(x)=9e^{x} \frac{d}{dx} \sin x+9\sin x \frac{d}{dx} e^{x}=9e^{x}(\cos x+\sin x)[/tex]

Setting this equal to 0,

[tex]9e^x (\cos x+\sin x)=0[/tex]

Since [tex]9e^x > 0[/tex], we can divide both sides by [tex]9e^x[/tex].

[tex]\cos x+\sin x=0\\\\\sin x=-\cos x\\\\\tan x=-1\\\\x=\frac{3\pi}{4}[/tex]

[tex]f\left(\frac{3\pi}{4} \right)=9e^{3\pi/4}\sin \left(\frac{3\pi}{4} \right)=\frac{9\sqrt{2}e^{3\pi/4}}{2}[/tex]

So, the absolute minimum is [tex]\boxed{\left(\frac{3\pi}{4}, \frac{9\sqrt{2}e^{3\pi/4}}{\sqrt{2}} \right)}[/tex] and the absolute minima are [tex]\boxed{(0,0), (\pi, 0)}[/tex]

The form which should be used when you know the slope of a line and one of the points on the line is: d. point-slope form.

The point-slope form can be defined as an equation which is used when the slope of a line and one of the points on this line is known.

Mathematically, the point-slope form of a line is given by:

y - y₁ = m(x - x₁)

Where:

In conclusion, you should use the point-slope form when you know the slope of a line and one of the points on the line is given.

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Answer:

b

Step-by-step explanation:

Answer:

Option A) [tex]\bf{ x^{\frac{2}{7}}*y^{-\frac{3}{5}}}[/tex]

Step-by-step explanation:

we have

[tex]\sf{\dfrac{\sqrt[7]{x^{2}}}{\sqrt[5]{y^{3}}}}[/tex]

we know that

[tex]\sf{\sqrt[7]{x^{2}}=x^{\frac{2}{7}}}[/tex]

[tex]\sf{\sqrt[5]{y^{3}}=y^{\frac{3}{5}}}[/tex]

substitute in the expression

[tex]\sf{\dfrac{x^{\frac{2}{7}}}{y^{\frac{3}{5}}}=x^{\frac{2}{7}}*y^{-\frac{3}{5}}}[/tex]

The probability that the hacker guesses the password in first go is

[tex]\dfrac{1}{5^5}[/tex]

While statistics examines the frequency of previous events, probability deals with estimating the possibility of future events.

The primary goal of the theoretical branch of mathematics known as the probability is the investigation of the consequences of mathematical concepts. At its core, statistics is a field of mathematics that seeks to explain observations in the actual world.

Both topics are significant, pertinent, and helpful. However, they are distinct, and appreciating this difference is essential to correctly assessing the applicability of mathematical evidence.

Since sample space has 5⁵ possibilities.
The event space has only one possibility which is to successfully hack the password perfectly.
Hence, the probability is

[tex]\dfrac{1}{5^5}[/tex]

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An adult with a weight of 75 kilograms have an equivalent weight of 165.60 pounds.

Herein we have an application of unit conversions between weight units, from kilograms to pounds. Unit conversions follow this direct proportional formula:

y = k · x

Where:

x - Weight in kilograms

y - Weight in pounds

k - Conversion ratio

If we know that x = 75 kg and k = 2.208 lb/kg, then the weight of the adult in pounds is:

y = (2.208 lb/kg) · (75 kg)

y = 165.6 lb

An adult with a weight of 75 kilograms have an equivalent weight of 165.60 pounds.

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Answer: 11.4

Step-by-step explanation:

Using the distance formula,

[tex]AC=\sqrt{(-3-1)^2 + (-1-2)^2}}=5\\\\AB=\sqrt{(-3-0)^2 +(-1-3)^2}=5\\\\BC=\sqrt{(1-0)^2 + (2-3)^2}=\sqrt{2} \approx 1.4\\\\\implies P \approx 5+5+1.4=\boxed{11.4}[/tex]

Answer:

At Less In Number 20

Step-by-step explanation:

1234567891011121314151617181920

Answer:

y > 2/3x + 3

Step-by-step explanation:

It is first option because > because shaded above the line and 2/3x is rise/run so 2/3.

+3 is because y-intercept is 3

The system of linear inequalities represented by the graph is the option;

y ≥  (1/3)·x + 3 and 3·x - y > 2

An inequality is a relation which makes a non-equal comparison between two numbers or mathematical expressions.

here, we have,

The system of linear inequalities are given by the in the question, that

describes the inequalities.

The points on the given graph are;

(3, 4), and (-3, 2)

The slope is; (2 - 4)÷((-3) - 3) = 1/3

The equation is;

y - 4 = (1/3)·(x - 3)

y = (1/3)·x - 1 + 4 = (1/3)·x + 3

Therefore;

The graph is y ≥  (1/3)·x + 3

Point on the second graph are;

(0, -2) and (2, 4)

The slope is; (4 - (-2)) ÷ (2 - 0) = 3

The equation is; y - (-2) = 3·(x - 0)

y = 3·x - 2

The inequality is; y < 3·x -2

Which gives;

2 < 3·x - y

Therefore;

3·x - y > 2

The correct option is the first option;

y ≥  (1/3)·x + 3 and 3·x - y > 2

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Answer:

[tex]-\frac{8\sqrt{2}+2}{15}.[/tex]

Step-by-step explanation:

1) sin(a+b)=sin(a)cos(b)+sin(b)cos(a);

2) if sin(a)=-0.4, then cos(a)=0.8; if cos(b)=1/3, then sin(b)=-√8/3;

3) finally, sin(a+b)=-0.4*1/3-√8/3*0.8=

[tex]=-\frac{8\sqrt{2}+2}{15}.[/tex]

Answer: 4, 2, 8

Step-by-step explanation:

4 + 2 + 8 = 14

14 = 14

2(4) + 4(2) + 5(8) = 56

8 + 8 + 40 = 56

56 =56

| 4(4) - 2 | = 14

|16-2| = 14

14 = 14

Answer:2

Step-by-step explanation:

(2x+5)/3 = 3/2

Multiply both sides by 3:

2x + 5 = 9/2

Subtract 5 from both sides:

2x = 9/2 - 5 = 9/2 - 10/2 = 3/2

Divide both sides by :

x = 3/4

Answer:

-1/3

Step-by-step explanation:

A number x is multiplied by 2, then has 3 added to it, then is divided by x+5, and the answer is 3 halves.

Or, as an equation:

[tex] \frac{2x + 3}{x + 5} = \frac{3}{2} [/tex]

Let's cross multiply:

[tex]4(2x + 3) = 2(x + 5)[/tex]

Expand:

[tex]8x + 12 = 2x + 10[/tex]

Now solve:

[tex]6x + 12 = 10[/tex]

[tex]6x = -2[/tex]

[tex]x = \frac{-1}{3} [/tex]

So the answer is -1/3

Answer:

I think so, but maybe if the schools are different they change.

The inequality which represents the number of jeans and sweater which he must purchase is; $17x + $9y >= $75.

It follows from the task content that, to receive free shipping, $75 or more must be spent on the pieces of clothing to receive free shipping.

On this note, it follows that the required inequality is; $17x + $9y >= $75.

This follows from the fact that jeans are $17 each and sweaters are $9 each.

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The work done in pushing the box is 64000 lb-ft²/s²

Since person pushing a 40 pound box up an incline that is 30 degrees above the horizontal and 100 feet long, the work done, W is

W = mgh where

So, W = mgh

W = mgLsinФ

So, substituting the values of the variables into the equation, we have

W = mgLsinФ

W = 40 lb × 32 ft/s² × 100 ftsin30°

W = 1280 lb-ft/s² × 100 ft × 0.5

W = 1280 lb-ft/s² × 50 ft

W = 64000 lb-ft²/s²

So, the work done in pushing the box is 64000 lb-ft²/s²

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Answer:

801.5625

Step-by-step explanation:

25.65×100/1.6×2=801.5625

The principal on a savings account with 1.6% interest rate that has earned $25.65 over 2 years will be 801.56 dollars.

Simple interest is a method of calculating the interest charge.

Simple interest can be calculated as the product of principal amount, rate and time peroid.

Simple Interest = (Principal × Rate × Time) / 100

The principal on a savings account with 1.6% interest rate that has earned $25.65 over 2 years.

Simple Interest = (Principal × Rate × Time) / 100

25.65 × 100/(1.6 × 2 )

= 801.5625

Therefore, the  principal on a savings account with 1.6% interest rate that has earned $25.65 over 2 years will be 801.56 dollars.

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(3x-5)/2 = 8

3x - 5 = 2 × 8

3x - 5 = 16

3x = 16 + 5

3x = 21

x = 21/3

x = 7

Answer:

Step-by-step explanation:

Equation

(3x - 5)/2 =  8                         Multiply both sides by 2

2*(3x - 5)/2 = 8 * 2                Combine

3x - 5 = 16                             The 2s on the left cancel. Add 5 to each side

3x - 5 + 5 = 16+5                    Combine

3x = 21                                    Divide both sides by 3

3x/3 = 21/3

x = 7

Answer: x = 7

The percentage of a given number in another implies the fraction of the given number to that other number with respect to 100%. Thus the required expression is: [tex]\frac{m}{100}[/tex] x n

When a given number is written in percentage, it implies that the fraction of the number to the total number in relation to 100%. For example, to determine the percentage of a number r in s, -we have:

[tex]\frac{r}{s}[/tex] x 100%

Therefore in the given question, the required expression is;

m% = [tex]\frac{m}{100}[/tex]

So that;

m% of n can be expressed as;

[tex]\frac{m}{100}[/tex] x n

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Using proportions, her gross pay is given as follows:

d. $779.10.

A proportion is a fraction of a total amount, and the measures are related using a rule of three.

Her gross pay is divided as follows:

Hence the total pay is:

33 x 14.70 + 2 x 10 x 14.70 = $779.10.

Which means that option d is correct.

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It is false that the midpoint is in quadrant IV

The endpoints are given as:

S (1,4) and T (5,2

The midpoint is

(x, y) = 0.5 *(x1 + x2, y1 + y2)

So, we have:

(x, y) = 0.5 *(1 + 5, 4 + 2)

Evaluate the expression

(x, y) = (3, 3)

The point (3, 3) is located in the first quadrant

Hence, it is false that the midpoint is in quadrant IV

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Answer:

m = 300w OR w = m/300

Step-by-step explanation:

They start with 10k, but that's immediately sold, so they're back at a flat 0. Every week they gain 1000 but lose 700 for a net profit of positive 300.

Therefore, the maximum capacity would be 300 multiplied by the number of weeks. If we know the maximum, then the answer would be m (maximum) divided by 300.

Considering the volume of a rectangular prism, the capacity of the second sandbox would be of 80 cubic feet.

The volume of a rectangular prism with length l, width w and height h is given by the multiplication of the measures, that is:

V = lwh.

In this problem, the capacity is of 10 cubic feet, that is:

V = lwh = 10.

When each measure is doubled, the volume will be given as follows:

V=  2l x 2w x 2h = (2 x 2 x 2)lwh = 8lwh = 8V = 80 cubic feet.

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Using Pythagoras theorem, the top of the ladder will slide down the wall 1.64 ft

The ladder leaning against the wall forms a right-angled triangle of sides 8 ft and 6 ft.

The length of the ladder is y.

Using Pythagoras theorem:

[tex]y = \sqrt{8^{2} + 6^{2}} = 10 \:ft[/tex]

When the ladder is  pulled 1 foot away from the wall, the new height, h the ladder rises up the wall is given below:

[tex]h = \sqrt{10^{2} - 9^{2}} = 4.36 \:ft[/tex]

The top of the ladder will slide 6 - 4.36 ft = 1.64 ft

In conclusion, the length the ladder will slide down is obtained using Pythagoras theorem.

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The total amount of money which the Stewart family would have to pay into the annuity each quarter is $242.12.

Mathematically, annuity can be calculated by using this formula:

[tex]A = P[\frac{(1+\frac{r}{n} )^{nt} - 1)}{\frac{r}{n} }][/tex]

Given the following data:

Substituting the given parameters into the formula, we have;

[tex]13000 = P[\frac{(1+\frac{0.036}{4} )^{4 \times 11} - 1)}{\frac{0.036}{4} }]\\\\13000 = P[\frac{(1+0.009 )^{44} - 1)}{0.009 }]\\\\13000 = P[\frac{(1.009 )^{44} - 1)}{0.009 }]\\\\13000 = P[\frac{1.48323960867 - 1}{0.009 }]\\\\13000 = P[\frac{0.48323960867 }{0.009 }]\\\\13000 = 53.6932898522P[/tex]

P = 13000/53.6932898522

P = $242.12.

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Complete Question:

The Stewart family wants to save money to travel the world. They plan to invest in an ordinary annuity that earns 3.6% interest, compounded quarterly. Payments will be made at the end of each quarter. How much money do they need to pay into the annuity each quarter for the annuity to have a total value of $13,000 after 11 years?

Answer:

A turning point is the highest or lowest point on a quadratic graph.

Step-by-step explanation:

A quadratic graph looks something like the graph below.

The equation of a quadratic graph would normally look like

+/- ax^2 + bx + c

An example might be -16x^2 + 5x + 4

Note the negative symbol in front of the 16. The negative means that the graph will be facing downwards, or that the turning point is the highest point. A positive graph will mean that the graph is facing upwards, or that the turning point is the lowest point.

Essentially, it is the location where a graph has its lowest or highest point and where the y-values (can include x-values in horizontal quadratics) "turn" to the direction they originated.

I do not agree that passing the state math and reading tests will be a predictor of a student's success in college.

The factors that determine a student's success in college include the following:

Do you agree with the board? Mention the factors that determine a student's success in college.

Thus, it is not necessarily true that passing the state math and reading tests will be a predictor of a student's success in college.

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