A cart weighing 60 lb is placed on a ramp inclined at 15° to the horizontal. The cart is held in place by a rope inclined at 60° to the horizontal, as shown in the figure. Find the force that the rope must exert on the cart to keep it from rolling down the ramp. (Round your answer to one decimal place in lbs.)

Answer:

Inequality: 4x+5<45, $10 or less

Step-by-step explanation:

Sallad costs $5. Therefore, the total cost of the pizzas is $40 ( $45-$5). Then since they are 4 pizzas, you find the quotient of ($40÷4)

Answer:

1.  9+(-8) = 1

2. -5+-4 = -9

Step-by-step explanation:

Answer:

9

Step-by-step explanation:

The answer is 9. You can figure it out by counting up from 8!

Answer:

It's a positive slope it's not going down it's going up every time you go up to you go over to making it a positive slope

Step-by-step explanation:

Answer:

(7;1)

Step-by-step explanation:

The abscissa of B' is going to be the same as abscissa of B , becuse the points are simmetrical over axis x.

However the ordinate of the point B'  will have the opposite sign as ardinate  B. However the module of ordinate B'  is going to be the same as module of orrdinate B.

Answer:si

Step-by-step explanation:

Answer:

The base is decreasing at 2 cm/min.

Step-by-step explanation:

The area (A) of a triangle is given by:

[tex] A = \frac{1}{2}bh [/tex]   (1)

Where:

b: is the base

h: is the altitude = 10 cm

If we take the derivative of equation (1) as a function of time we have:

[tex] \frac{dA}{dt} = \frac{1}{2}(\frac{db}{dt}h + \frac{dh}{dt}b) [/tex]

We can find the base by solving equation (1) for b:

[tex] b = \frac{2A}{h} = \frac{2*120 cm^{2}}{10 cm} = 24 cm [/tex]

Now, having that dh/dt = 1 cm/min, dA/dt = 2 cm²/min we can find db/dt:

[tex] 2 cm^{2}/min = \frac{1}{2}(\frac{db}{dt}*10 cm + 1 cm/min*24 cm) [/tex]

[tex]\frac{db}{dt} = \frac{2*2 cm^{2}/min - 1 cm/min*24 cm}{10 cm} = -2 cm/min[/tex]    

Therefore, the base is decreasing at 2 cm/min.

I hope it helps you!  

Answer:

The probability that sample mean is less than 2  is 0.1423.

Step-by-step explanation:

Let X denote the number of accidents per week at a hazardous intersection.

It is provided that the mean and standard deviation of X are, μ = 2.2 and σ = 1.4.

(a)

According to the Central Limit Theorem if an unknown population is selected with mean μ and standard deviation σ and appropriately huge random samples (n > 30) are selected from this population with replacement, then the distribution of the sample means will be approximately normally.  

Then, the mean of the sample means is given by,

[tex]\mu_{\bar x}=\mu[/tex]

And the standard deviation of the sample means is given by,

[tex]\sigma_{\bar x}=\frac{\sigma}{\sqrt{n}}[/tex]

As the sample size is not large enough, i.e. n = 9 < 30, the Central Limit Theorem cannot be applied to approximate the sampling distribution of the mean number of accidents per week at the intersection.

And since the distribution of X is not specified, the probability cannot be computed.

(b)

In this case, the sample size is large enough, i.e. n = 52 > 30, the Central Limit Theorem can be applied to approximate the sampling distribution of the mean number of accidents per week at the intersection.

Compute the probability that sample mean is less than 2 as follows:

[tex]P(\bar X<2)=P(\frac{\bar X-\mu_{\bar x}}{\sigma_{\bar x}}<\frac{2-2.2}{1.4/\sqrt{56}})\\\\=P(Z<-1.07)\\\\=0.14231\\\\\approx 0.1423[/tex]

Thus, the probability that sample mean is less than 2  is 0.1423.

Answer:

12

Step-by-step explanation:

(3+x)+x=27

2x+3=27

2x=24

x=12

Answer:

This comes out to around 25 percent. Simply multiply 40 by 1/4 to get 10 dollars.

Step-by-step explanation:

Answer:

Step-by-step explanation:

40x0.085=3.4

40+3.4= 43.4

43.4x0.18=7.8

43.4+7.8=51.212$

Answer:

1/4

Step-by-step explanation:

-4 - 1 = -5

-4 - 16 = -20

-5/-20 = 1/4

Answer:

Move r to left or right then divide the numbers

Answer:

9

Step-by-step explanation:

2(5y°) = 90° ⇒ y = 9

Answer:

what measure one

Step-by-step explanation:

What are u talking bout

There is no picture or anything

Answer:

I wish I could help.

Step-by-step explanation:

There is no picture or a complex explanation.

Answer:12. V is not needed, and just substitute the letters with the numbers the correspond to.

Step-by-step explanation:

Answer:

[tex]P(F/E) = 0.6[/tex]

Step-by-step explanation:

If we are given two dependent events [tex]A[/tex] and [tex]B[/tex] such that their chances of occurrence or the probabilities of the events are: [tex]P(A)[/tex] and [tex]P(B)[/tex].

Then the conditional probability that the event [tex]B[/tex] will occur given that [tex]A[/tex] has already occurred is given by the following formula:

[tex]P(B/A) = \dfrac{P(A \cap B)}{P(A)}[/tex]

Here the two events given are [tex]E[/tex] and [tex]F[/tex].

[tex]P(E\ and\ F)\ or\ P(E\cup F) = 0.3[/tex]

and [tex]P(E) = 0.5[/tex]

As per the above formula that we have already discussed, the formula can be written as:

[tex]P(F/E) = \dfrac{P(E \cap F)}{P(E)}\\\Rightarrow P(F/E) = \dfrac{0.3}{0.5}\\\Rightarrow P(F/E) = \dfrac{3}{5}\\\Rightarrow \bold{P(F/E) = 0.6}[/tex]

Answer:

61.2

Step-by-step explanation:

To solve this, we would have to use the arithmetic progression formula

S(n) = a + (n - 1) d, where

S(n) = is the value of the nth term

a = value of the first term

n = the nth term we're interested in

d = difference between successive terms

We're given that the first term, a1 = 1.we also know that the 6th term, a6 = 44

If so, we can use this to get our "d", saying

44 = 1 + (6 - 1) d

where

44 is the value of the 6th term, and n is 6. Also, the first term a = 1. Simplifying further we have

44 = 1 + 5d

5d = 44 - 1

5d = 43

d = 43/5

d = 8.6

This means that the difference between successive term is 8.6, we then use this "d" to find our 8th term

S(n) = 1 + (8 - 1) 8.6

S(n) = 1 + 7 * 8.6

S(n) = 1 + 60.2

S(n) = 61.2

Therefore, the 8th term is 61.2

Answer:

10

Step-by-step explanation:

For an odd number of values, the median is the middle value when you write the values in ascending order.

5, 7, 9, 10, 16, 17, 20

The median is 10.

Answer:

Step-by-step explanation:

should be A.

Answer:

answer is 1/1

Step-by-step explanation:

Answer:

Sixteen and forty-three hundredths

Step-by-step explanation:

Answer:

y=5/2x-23/2 or y=2.5x-11.5

Step-by-step explanation:

First, add 2y to move it to the other side of the equation. This should give you 2y+23=5x. Now, subtract 23, giving you 2y=5x-23. Divide the whole equation by 2 so that y will be by itself. Written in fraction form, it would be: y=5/2x-23/2. Written in decimal form: y=2.5x-11.5.

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[tex]2 {x}^{3} + 2 {x}^{2} - 40x = [/tex]

[tex]2x( {x}^{2} + x - 20) = [/tex]

[tex]2x(x - 4)(x + 5)[/tex]

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The correct answer is (( a )) .

♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️

The first option is the correct one.

[tex]2 {x}^{3} + 2 {x}^{2} - 40x[/tex]

[tex]2x( {x}^{2} + x - 20)[/tex]

[tex]2x(x - 4)(x + 5)[/tex]

Answer:

y = -x - 6

Step-by-step explanation:

From point A, to get to point C, you would need to go down 2 and right 2 which is -2/2 and -2/2 is the same thing as -x.

The y-intercept is -6 because the line goes thorough -6 in the y axis.

Hope this helps and pls do mark me brainliest if you can:)

Answer:

Three. 2x, -3y, and 8.

Step-by-step explanation:

For every constant or variable, there is a term.

In this expression, there are two variables (x and y) and there is a constant (8).

Hence, there are three terms.

Hope this helped!

Answer:  96 workers

Step-by-step explanation:

First you multiply 8 and 6 then by 2.

8 x 6= 48

48 x 2= 96

96 workers to help the business

Answer:

Explained below.

Step-by-step explanation:

According to the Central Limit Theorem if an unknown population is selected with mean μ and standard deviation σ and appropriately huge random samples (n > 30) are selected from this population with replacement, then the distribution of the sample means will be approximately normally.  

Then, the mean of the sample means is given by,

[tex]\mu_{\bar x}=\mu[/tex]

And the standard deviation of the sample means is given by,

[tex]\sigma_{\bar x}=\frac{\sigma}{\sqrt{n}}[/tex]

a

The expected value of the sample mean of their weights is same as the population mean, μ = 1515 lbs.

b

The standard deviation of the sampling distribution of the sample mean weight is:

[tex]\sigma_{\bar x}=\frac{\sigma}{\sqrt{n}}=\frac{25}{\sqrt{16}}=6.25[/tex]

c.

The average weights for a sample of 16 people will result in the total weight exceeding the weight limit of 2500 lbs. is:

[tex]\text{Average Weight}=\frac{2500}{16}=156.25[/tex]

d

Compute the probability that a random sample of 16 persons on the elevator will exceed the weight limit as follows:

[tex]P(\bar X > 156.25)=P(\frac{\bar X-\mu_{\bar x}}{\sigma_{\bar x}}>\frac{156.25-151}{6.25})\\\\=P(Z>0.84)\\\\=1-P(Z<0.84)\\\\=1-0.79955\\\\=0.20045\\\\\approx 0.20[/tex]