canThe first First step we need to do is to make the decomposition of the vectors W and P.

Both will have a component perpendicular and parallel to the plane. The perpendicular will be used to calculate the maximum static friction force, and the horizontal will be used to find the P required to prevent the block from sliding.

From the sketch, we are able to define both, parallel and perpendicular components of P, as it follows:

[tex]\begin{gathered} P_{\text{//}}=P\cos (30\degree)=\frac{P\sqrt[]{3}}{2} \\ P_{perp}=P\sin (30\degree)=\frac{P}{2} \end{gathered}[/tex]Now, we can do the same for W.

And for W we also can provide the two components as follows:

[tex]\begin{gathered} W_{//}=W\sin (30\degree)=\frac{W}{2} \\ W_{\text{perp}}=W\cos (30\degree)=\frac{W\sqrt[]{3}}{2} \end{gathered}[/tex]Now, we can elaborate on both equations: one for the perpendicular direction and the other for parallel. In the perpendicular direction, we have a component of W, one component of P, and the normal force N. Because the block is going to move, or change its movement along this direction, the sum of the forces pointing upwards must be equal to the sum of the forces pointing downwards. From this, we can write the following:

[tex]\begin{gathered} N=P_{\text{perp}}+W_{\text{perp}} \\ N=\frac{P}{2}+\frac{W\sqrt[]{3}}{2}=\frac{P+W\sqrt[]{3}}{2} \end{gathered}[/tex]Now, for the horizontal, we have the P component to the right and the W component to the left. If we imagine the block is almost sliding. We can write the following equation, from the premise the forces will cancel each other just like the perpendicular case:

[tex]\begin{gathered} P_{//}+F_{\mu}=W_{//} \\ \frac{P\sqrt[]{3}}{2}+N\times\mu_{static}=\frac{W}{2} \end{gathered}[/tex]Here it is used the fact that the friction force is equal to the multiplication of the coefficient of static friction by the normal force. Here we assumed also that the friction is maximum because the block is on the verge of motion downwards, and for this reason, the Friction is upwards, with the P component.

Now, substituting N and the coefficient, we find:

[tex]\begin{gathered} \frac{P\sqrt[]{3}}{2}+\frac{P+100\sqrt[]{3}}{2}0.65=\frac{100}{2}=50 \\ \frac{P(\sqrt[]{3}+0.65)+65\sqrt[]{3}}{2}=50 \\ P(\sqrt[]{3}+0.65)+65\sqrt[]{3}=100 \\ P(\sqrt[]{3}+0.65)=100-65\sqrt[]{3} \\ P=\frac{100-65\sqrt[]{3}}{\sqrt[]{3}+0.65}\cong\frac{100-65\times1.732}{1.732+0.65}=\frac{100-112.58}{2.382} \\ P=-\frac{12.58}{2.382}\cong-5.275\text{lbf} \end{gathered}[/tex]From this, we can see that the force P made to the left with an intensity equal to -5.275 lbf will bring the block on the verge of motion downwards. If we consider that P is strong enough to make it almost move upwards, it is, the Normal Force will be downwards, we can remake the calculation as it follows:

[tex]\begin{gathered} P_{//}=W_{//}+F_{\mu} \\ \frac{P\sqrt[]{3}}{2}=\frac{W}{2}+N\times\mu_{static} \end{gathered}[/tex]And substituting values, we have:

[tex]\begin{gathered} \frac{P\sqrt[]{3}}{2}=50+\frac{P+100\sqrt[]{3}}{2}0.65 \\ \frac{P(\sqrt[]{3}-0.65)}{2}=50+50\sqrt[]{3}\times0.65 \\ P=\frac{2}{\sqrt[]{3}-0.65}\times50(1+\sqrt[]{3}\times0.65)\cong196.46 \end{gathered}[/tex]From this, we know that the max value for P, where the block will not slide is going to be 196.46 lbf to the right.

n(n+1)(n+5) is multiple of?

n(n+1)(n+5) can be a **multiple** of 3.

Utilizing the **mathematical induction formula** for any n > N, we are going to demonstrate it.

P(n) = n(n+1) n(n+5) = 3d, where d N

P(1)=1(2)(6)=12, that is cleavable by three, for n=1.

Suppose P(k) is **true**.

Where m N k three +6k a pair of +5k=3m k, P(k)=k(k+1)(k+5)=3m.

3\s =−6k \s2\s −5k+3m

We will currently demonstrate that **P(k+1) is true**.

P(k+1)=K+1, K+2, K+6, K 3 +9 K 2, K twenty K + twelve

When we plug the worth of k three into the equation on top of, we tend to get 3m6k a pair of 5k)+9k a pair of +20k+12 =3.

m+3k \s2\s +15k+12\s=3

(m+k \s2\s +5k+4)

in which r=m+k a pair of + 5k + four

P(k+1) is often true since P(k) is often **true**.

Therefore, in step with the **induction principle**, P(n) is cleavable by three for all n N.

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A college basketball team offers season passes for $85, but you pay $4.45 for a program

at each game. Non-season-pass holders pay $9.45 for admission to each game, but the

game program is free. For what number of games is the cost of these plans the same?

For 9 of games is the cost of these plans the same.

What are basic linear equations?Moving the **variables** to one side of the equation and the **numeric portion** to the other allows us to solve a linear equation with one **variable**. As an illustration, the equation x - 1 = 5 - 2x can be resolved by transferring the **numerical components** to the right side of the equation while leaving the** variables **on the left. Therefore, we receive x + 2x = 5 + 1. Thus, 3x Equals 6. As a result, x = 2. The formula for a two-variable linear equation is Ax + By + C = 0, where A and B are the **coefficients**, C is a **constant term**, and x and y are the two **independent variables**, each with a **degree of 1**. A linear equation involving two variables, for illustration, is 7x + 9y + 4 = 0.

Consequently, you would multiply $9.45 and $4.45 by the same number (I selected 9 because there are only one or two possible answers), then add $85 to the result for the $4.45 amount.

9.45 x 9

= 85.05

4.45 x 9

= 40.05 +85

= 125.05

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Xiao Mei covers a table with 8 rows of square unit tiles. There are 7 tiles in each row. What is the area that Xiao Mei covers in square units?

The **area** that Xiao Mei covers in **square** **tiles** is 56 sq. units.

Given,

In the question:

Xiao Mei covers a table with 8 rows of square unit tiles.

and, There are 7 tiles in each row.

To find the **area** that Xiao Mei covers in square tiles.

Now, According to the question:

**Tables** covers = 8 rows of sq. unit

In each row = 7 tiles

All you would have to do is multiply 8 times 7

it means, 8 x 7 = 56

Hence, The **area** that Xiao Mei covers in **square** **tiles** is 56 sq. units.

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Allen wanted to find the height of a tree in his yard. He knew that the fence surrounding his yard was 4 feet

high. At 3 pm the shadow of the fence was 2.5 feet long. The shadow of the tree was 11.3 feet long. What

was the height of the tree?

The height of the tree should be 18.08 feet.

Hope this helps

Hope this helps

A car travels about 32 miles on 1 gallon of gas. While a truck drives about 260 miles on 9.75 gallons of gas. Which gets better gas mileage?

In order to determine which vehicle gets better gas mileage, we need to determine which of the two vehicles consumes less gas for each mile travelled. The car consumes 1 gallon of gas for every 32 miles. We shall now determine how many miles the truck covers to consume 1 gallon of gas.

[tex]\begin{gathered} \text{Truck} \\ 9.75gl=260\text{miles} \\ 1gl=\frac{260}{9.75}\text{miles} \\ 1gl=26.67miles \end{gathered}[/tex][tex]\begin{gathered} \text{Car} \\ 1gl=32\text{miles} \end{gathered}[/tex]Therefore, the results shows that the truck gets better gas mileage

Below, the two-way table is given for a classof students.FreshmenSophomore Juniors Seniors TotalMale4622Female 3463TotalIf a male student is selected at random, what is theprobability the student is a freshman.

Answer:

29%

Explanations:Probability is the** likelihood or chance** that ab event will occur. Mathematically;

Probability = Expected/Total

From the given table, the** total number of male student** is the total outcome as shown:

Total outcome = 4 +6+ 2 + 2

Total outcome = 14

If a **male freshmen is selected **at random, the expected **outcome will be 4.**

Determine the probability

[tex]\begin{gathered} Pr(Freshman\text{ \mid Male})=\frac{Male\text{ freshmen}}{Total\text{ male studnt}} \\ Pr(Freshman\text{ \mid Male})=\frac{4}{14} \\ Pr(Freshman\text{ \mid Male})=0.2857\times100 \\ Pr(Freshman\text{ \mid Male})\approx29\% \\ \end{gathered}[/tex]Hence the** probability** that the male student is freshman is** approximately 29%**

PLEASE HELP ITS DUE SOON! I DONT GET ANY OF THIS! HELP WOULD BE MUCH APPRECIATED! NEED THIS DONE BEEN STUCK ON THIS FOR WAY TO LONG!

YOU WILL GET 100 POINTS IF YOU HELP! QUESTION DOWN BELOW!!!!!

**Answer:**

1. given

2. isoceles triangle

3. PN = QN

4. Angle 3 = 4

5. MP = OQ

6. common

7. MP + PQ = OQ + PQ

8. not sure about this one sorry!

9. Angle Side Angle

**Step-by-step explanation:**

a. Draw the figure and its reflection in the x-axis.

A(2,0), B(1,5), C(4,3)

**Answer:**

A: 2,0 B: 1,-5 C: 4,-3

**Step-by-step explanation:**

w

Malcolm's Bakery Shop sells gourment cupcakes. The shop's cost for making 3 cupcakes is $6.75, and the cost of making 5 cupcakes is $9.75 . What is the shop's cost per minute?

A. $1.50

B. $1.95

C. $2.25

D. $3.00

D? Because £9.75-£6.75 is £3.00 ??

There were 20 baby devils 4 born in 2013 on Maria Island. In 2014, the number born was 200% of the 2013 devils. How many were born in 2014?

There are 20 baby devils in 2013 on Maria Island

in 2014 200 % where born

the number of baby devils born in 2014 can be gotten by

20 -------- 100

x -----------200

by proper analysis x = (200 x 20)/100 = 4000/100 = 40

**40 baby devils were born in 2014**

Question 1] Find the mean for each set of data6,9,2,4,3,6,5

**Given:**

The given set of data is

[tex]6,9,2,4,3,6,5[/tex]**To find: **The mean for the given set of data?

**Explanation:**

We can calculate the mean of a given set of data by using the formula

[tex]Mean=\frac{Sum\text{ of the terms}}{Number\text{ of terms}}[/tex]Here,

We can calculate the sum of terms as

The sum of terms = 6+9+2+4+3+6+5

The sum of terms =35.

and

The number of terms = 7.

Now, by substituting the value in the above formula

Therefore,

[tex]\begin{gathered} Mean=\frac{35}{7} \\ \\ Mean=5 \end{gathered}[/tex]Hence, the mean = 5.

**Answer: The mean for a given set of data is 5**.

Simplify 6x(9-2)-6 divided by 2

i don't have any idea but ok JQJAJDJDJKSBA

Can someone help me with this? Please and thank you

Given the line shown in the figure passes through the points (-3, -4) and (1, 2)

We will write the equation of the line.

First, we will find the slope of the line using the following formula:

[tex]slope=m=\frac{rise}{run}=\frac{y_2-y_1}{x_2-x_1}[/tex]Substitute with the given points:

[tex]m=\frac{2-(-4)}{1-(-3)}=\frac{2+4}{1+3}=\frac{6}{4}=\frac{3}{2}=1.5[/tex]The equation of the line in point-slope form will be as follows:

[tex]\begin{gathered} y+4=1.5(x+3) \\ or \\ y-2=1.5(x-1) \end{gathered}[/tex]Convert tot he slope-intercept form, so, the equation will be:

[tex]\begin{gathered} y=1.5(x+3)-4 \\ y=1.5x+4.5-4 \\ \\ y=1.5x+0.5 \end{gathered}[/tex]Now, we will check the options to see the correct equations.

So, the answer will be, we will select the options:

**A. y+4 = 1.5 (x+3)**

**B. y = 1.5x + 0.5**

**C. y - 2 = 1.5 (x - 1)**

A group of friends wants to go to the amusement park tey have no more than $115 to spend on parking and admission parking is $15 and the tickets cst $25 per person including tax wrote and solve an inequality which can be used to determine x the number of people who can go to the amuement park

An **inequality **which can be used to determine x the **number of people **who can go to the amusement park is: 15 + 25x ≤ 115

Also, approximately **4 people can go to the amusement park**.

In the given question,

**cost **for admission parking = $15

Tickets = $25 per person

Let x be the **number of people **those** **who go to the amusement park.

On parking and admission spent not more than $115

So we get an **inequality**,

15 + 25x ≤ 115

We solve above **inequality**.

25x ≤ 115 - 15

25x ≤ 100

25x / 25 ≤ 100/25

x ≤ 4

This means that approximately 4people can go to the amusement park.

Therefore, an **inequality **which can be used to determine x the **number of people **who can go to the amusement park is: 15 + 25x ≤ 115

Also, approximately **4 people can go to the amusement park**.

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What is the solution set for: 4x - 3>29 *X> 4OX >8OX8OX > 3

Let us first solve the inequality

[tex]\begin{gathered} 4x-3>29\rightarrow \\ 4x>29+3=32 \\ 4x>32 \\ x>\frac{32}{4}=8 \\ x>8 \end{gathered}[/tex]So the answer is x>8

Two numbers are called relatively prime if their greatest common divisor is $1$.

Grogg's favorite number is $10!$, the product of the integers from $1$ to $10$. (He pronounces it TEN!)

What is the smallest integer greater than $800$ that is relatively prime to Grogg's favorite number?

**Answer:**

Two numbers are called relatively prime if their greatest common divisor is $1$. Grogg's favorite number is the product of the integers from $1$ to $10$

**Answer: The answer is 803. :) lol**

**Step-by-step explanation:**

You gotta keep trying numbers. But the numbers cant be even because if it's even, it can be divided by 2! Try the odd numbers starting at 800. If the number is not divisible by any of the numbers from 1-10 then it's the correct number. Got it on my second try. LOL! I'm from AOPS like you. :) !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

please help- I’m failing math. an explanation would help too

**Answer:**

11

**Step-by-step explanation:**

The answer would be 11, because when you add 5 and 6 together, you get 11. Pretend you had 5 cookies, and you got 6 more.

5 Cookies- O,O,O,O,O

6 More Cookies- O,O,O,O,O,O

If you add the cookies up, you get 11.

Let f(x) = 2x - 1 and g(x) = x² + 1. Find and simplify: (g ° ƒ) (1/2)

To find the composition we need, let's first find the general expression:

[tex]\begin{gathered} (g\circ f)(x)=g(f(x)) \\ =g(2x-1) \\ =(2x-1)^2+1 \\ =4x^2-4x+1+1 \\ =4x^2-4x+2 \end{gathered}[/tex]Hence:

[tex](g\circ f)(x)=4x^2-4x+2[/tex]Now we can evaluate when x=1/2:

[tex]\begin{gathered} (g\circ f)(\frac{1}{2})=4(\frac{1}{2})^2-4(\frac{1}{2})+2 \\ =4(\frac{1}{4})-2+2 \\ =1-2+2 \\ =1 \end{gathered}[/tex]**Therefore:**

Determine whether the graph represents a linear, quadratic, or exponential function.o Exponentialo Linearo Quadratic

When we graph a linear equation we draw a line. When we want to graph a quadratic equation we draw a parabola, a parabola is a U-shaped curve. The graph of an exponential function grows or decays and has asymptotic values.

In this case, the **first graph **is a line, so it represents a **linear equation**.

The **second graph** is a U-shaped curve, then it represents a **quadratic equation**.

The **third graph** decays, then it** represents an exponential equation.**

Find the value of b that makes quadrilateral RSTU a parallelogram.

We are asked to find the value of **b** that makes quadrilateral **RSTU** a **parallelogram**.

We know from the properties of a parallelogram that the **opposite angles are always equal**.

Let us equate the angles and solve the equation for **b**.

Similarly,

[tex]undefined[/tex]1ptWhat value of c would make x2 – 14.c +ca perfect square?C=What is the factored form of this expression for this value of c?(.)?

The value of c would be 49 and the factored form will be;

[tex](x-7)^2[/tex]Here, we want to get the value of c that will make the expression a perfect square

We proceed as follows;

Divide the coefficient of x by 2 ;

That would be; -14/2 = -7

Now, square this value; that would be (-7)^2 = 49

The value 49 would make the expression a perfect square

Thus, we have the factored form as follows;

[tex](x^2-14x+49)\text{ = (x-7)(x-7)}[/tex]Solve for x usingcross multiplication.3x + 6 = 4x - 364=35x = [?]Enter

Solving for **x**,

You buy five equally priced gifts for a total of $75 what was the price of each candle

**Answer:**

**$15**

**Explanation:**

To find the price of each candle, we need to divide $75 by 5, so the price of each candle is:

$75 ÷ 5 = $15

So, the answer is $15

17. Identify all the angles that are congruent to

**Answer:**

ad, bc, eh, bf, ae, jk, mp, pn, ln, lm

A 2070 kg space station orbits Earth at an altitude of 457 km. Find the magnitude of the force with which the space station attracts Earth. The mass and mean radius of Earth are 5.98×1024 kg and 6370 km, respectively.

The **magnitude **of the **force **with which the space station attracts Earth.

17714.8532 N

This is further explained below.

The magnitude of theAn influence that has the potential to alter the **motion **of an item is referred to as a **force**.

An object having mass may experience a change in its velocity, often known as acceleration, when subjected to a **force**.

Generally, the **equation **for the magnitude of the **force **is

F = G.M.m/r2

Where

G=**gravitational constant**

M and m mass

r=radius

F=**force of attraction**

Therefore

6.67*10^{-11} * 5.98*10^{24} * 2070/((6370+457)2*10^6)

= 17714.8532 N

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The midpoint of overline PQ is M = (- 2, 1) . One endpoint is P = (- 5, - 1) Find the coordinates of the other endpoint , Q.

**Answer;**

The coordiantes of the point Q is;

[tex](1,3)[/tex]**Explanation;**

Here, we want to get the coordinates of the other endpoint

Mathematically, we can find the midpoint of two endpoints using the formula below;

[tex](x,y)\text{ = (}\frac{(x_1+x_2)}{2},\frac{(y_1+y_2)}{2})[/tex]The notation 1 and 2 represents the coordinates of the two end points

Now, by replacing the values given in the question, we have it that;

(x,y) is the coordinate of the point m which is (-2,1)

Now the first end point has the coordinates (-5,-1)

The second endpoint Q has the endpoint (x2,y2) which we want to calculate

We proceed to make the substitutions as follows;

[tex](-2,1)\text{ =}\frac{(-5+x_2)}{2},\frac{(-1+y_2)}{2}[/tex]We proceed to susbtitute the individual branches as follows;

[tex]\begin{gathered} -2\text{ = }\frac{-5+x_2}{2} \\ 2(-2)=-5+x_2 \\ -4=-5+x_2 \\ x_2=-4+5 \\ x_2\text{ = 1} \end{gathered}[/tex]Finally, we have;

[tex]\begin{gathered} 1=\frac{-1+y_2}{2} \\ 2(1)=-1+y_2 \\ 2+1=y_2 \\ y_2\text{ = }3 \end{gathered}[/tex]Three clocks exist in a room:

The round clock is 10 minutes behind the actual time

The rectangular clock is 5 minutes after the actual time

The squared clock is 5 minutes slower than the round clock

The time now on the squared clock is 08:05, what is the time now on the rectangular clock?

08:25

08:20

08:15

08:30

**Answer:**

First choice: 08:25

**Step-by-step explanation:**

Squared Clock is 5 minutes slower than the round clock

since the round clock is 10 minutes behind actual time, square clod is 15 minutes behind actual time

Time on square clock = 8:05

So actual time = 8:05 + 15 = 8:20

Rectangular clock is 5 minutes ahead of actual time

So time on rectangular clock is 8:20 + 05 = 8:25

Answer: First choice: 08:25

Which number line represents the solution set for the inequality 2x - 6 2 6(x - 2) + 8?-1.5-1-0.500.51.5-1.5-1-0.500.51.55-0.500.51.5-1-0.500.51.5

Solve the inequality:

2x - 6 ≥ 6(x - 2) + 8

Operating the parentheses:

2x - 6 ≥ 6x - 12 + 8

Subtracting 6x:

2x - 6x - 6 ≥ - 12 + 8

Adding 6:

2x - 6x ≥ - 12 + 8 + 6

Simplifying:

- 4x ≥ 2

Dividing by -4 and changing the symbol:

x ≤ 2/(-4)

x ≤ -0.5

The solution in the number line starts at -0.5 and goes to the left with an arrow:

What is 14.481 rounded to the nearest tenth?A) 14B) 14.4C) 14.5D) 15

To round to the nearest tenth, we must round it to the nearest hundredth first, we have

[tex]14.481[/tex]See that we have 1 at the last decimal, then we will keep the hundredth value, it means that we will round to

[tex]14.481\rightarrow14.48[/tex]Now the last decimal is 8, it's above 5, then we must add one at the tenth and remove the hundredth

[tex]14.48\rightarrow14.5[/tex]Therefore the nearest tenth is the **letter C, 14.5**

**Answer:c**

**Step-by-step explanation:THIS SOOO CORRECT!**

Scenario: I am interested in selling cookies in my online bakery store. But before that, I need to find out how much I should price it to maximize revenue. I surveyed 1500 people and found out that if I price it at $2.00 a cookie then 800 people would buy it. If I price it at a dollar more at $3.00. a cookie, then 600 people would buy it. On the other hand, if I price it at a dollar less at $1.00 a cookie, then 1000 people would buy it. Based on this information, I noticed that for every one dollar increase in price, 200 fewer people would buy it. 1. Solve the scenario problem above for the optimal item price that maximizesrevenue. Be sure to show all your work and reflect on your findings.

the Let number of people = y

Let price = x

Gradient = -200

[tex]\begin{gathered} -200\text{ = }\frac{y\text{ - 800}}{x\text{ - 2}} \\ y\text{ - 800 = -200(x - 2)} \\ y\text{ - 800 = -200x + 400} \\ y\text{ = -200x + 400 + 800} \\ y\text{ = -200x + 1200} \end{gathered}[/tex]Revenue = price X number of people

[tex]\begin{gathered} R(x)\text{ = x }\times\text{ y} \\ R(x)\text{ = x(-200x + 1200)} \\ R(x)=-200x^2\text{ + 1200x} \\ R^{\prime}(x)\text{ = -400x + 1200} \\ To\text{ maximize , R(x) = 0} \\ -400x\text{ + 1200 = 0} \\ 400x\text{ = 1200} \\ x\text{ = }\frac{1200}{400} \\ \text{x = 3} \end{gathered}[/tex]Optimal item price = $3

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Ken exercise at a park first he run 3 miles in 30 minutes.Then he rests for 15 minutes.Then he runs 2 miles in 15 minutes.Finally he walks 1 mile in 15 minutes.Assume each running and walking segment was done at a constant rate.skecth a graph to represent ken's exercing at the park.the fisrt segment should begin at (0,0).
Professor browning assigns students a twenty-minute speech as part of their class requirements, in discovering the general purpose, which is not a type of speech to consider?.
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Given the replacement set: {9, 10, 11, 12}.Which value of x correctly solves this equation?3.2x5=40.2Enter your answer in the box.
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