Tension needs to eat at least an extra 1,000 calories a day to prepare for running a marathon. He has only $25 to spend on the extra food he needs and will spend it on $0.75 donuts that have 360 calories each and $2 energy drinks that have 110 calories. This results in the following system of equations:
0.75d+2e≤25
360d+110e≥1,000

where d is donuts and e is energy drinks. Can Tension buy 8 donuts and 4 energy drinks?

Select the correct answer below:
Yes or No

Answer:

  (-2.497, -6.860)

Step-by-step explanation:

For any magnitude r and direction θ, the translation to rectangular coordinates is ...

  (r, θ) ⇒ (x, y)

  (r, θ) ⇒ (r·cos(θ), r·sin(θ))

Your coordinates translate to ...

  (7.3, 250°) ⇒ (7.3·cos(250°), 7.3·sin(250°)) ≈ (-2.497, -6.860)

Answer:

20

Step-by-step explanation:

do 9/12 = 15/?

you do 12 times 15 divided by 9

hope this helps

Answer:

negative

Step-by-step explanation:

The slope of the line is negative because it goes from the upper corner down to the lower corner.

I remember it as negative because a rock would roll down it, if I would have to push it, it is positive.

Your answer would be 76.2% to the nearest tenth.

We can find this by first dividing 16 by 21 to get 0.7619. which is the proportion as a decimal. To convert this into a percentage, we need to multiply it by 100 to get 76.19% = 76.2% to the nearest tenth.

I hope this helps! Let me know if you have any questions :)

Answer:

  [tex]\textbf{J. }\dfrac{1}{x^2-x}[/tex]

Step-by-step explanation:

Factor the denominator and cancel the common factor.

  [tex]\dfrac{x+1}{x^3-x}=\dfrac{x+1}{x(x^2-1)}=\dfrac{x+1}{x(x-1)(x+1)}=\dfrac{1}{x(x-1)}\\\\=\boxed{\dfrac{1}{x^2-x}}[/tex]

Answer:

a. The 99% confidence interval for the population proportion is (0.7872, 0.8610).

D. Yes, we can conclude that the population proportion exceeds 75% because 75% is below the lowest believable value of the confidence interval.

b. The 99% confidence interval would be wider than a 95% confidence interval.

As the confidence level increases, the width interval increases, as we are requiring more confidence with the same information (there is no new sample). This means that, to be more confident, the only way is to include more values in the interval.

Step-by-step explanation:

We have to calculate a 99% confidence interval for the proportion.

The sample proportion is p=0.8241.

[tex]p=X/n=581/705=0.8241[/tex]

The standard error of the proportion is:

[tex]\sigma_p=\sqrt{\dfrac{p(1-p)}{n}}=\sqrt{\dfrac{0.8241*0.1759}{705}}\\\\\\ \sigma_p=\sqrt{0.000206}=0.0143[/tex]

The critical z-value for a 99% confidence interval is z=2.5758.

The margin of error (MOE) can be calculated as:

[tex]MOE=z\cdot \sigma_p=2.5758 \cdot 0.0143=0.0369[/tex]

Then, the lower and upper bounds of the confidence interval are:

[tex]LL=p-z \cdot \sigma_p = 0.8241-0.0369=0.7872\\\\UL=p+z \cdot \sigma_p = 0.8241+0.0369=0.8610[/tex]

The 99% confidence interval for the population proportion is (0.7872, 0.8610).

We can conclude that there is, at least, 99% chances that the true proportion is higher than 0.7872. So there is at least 99% chances that the population proportion is higher than 0.75.

Answer:

  490 J

Step-by-step explanation:

The formula is ...

  PE = mgh

where g is the acceleration due to gravity: 9.8 m/s². Filling in your numbers, you find the energy to be ...

  PE = (5 kg)(9.8 m/s²)(10 m) = 490 kg·m²/s² = 490 J

Answer:

A corda deve ter um comprimento mínimo de 80 cm.

The string should have a minimum length of 80 cm.

Step-by-step explanation:

Espera-se que a corda seja colada em todo o contorno da moldura quadrada.

Isso significa que a cadeia precisa cobrir pelo menos todo o perímetro da moldura quadrada pelo menos uma vez.

Perímetro de um quadrado = 4L

L = comprimento lateral do quadrado.

O comprimento lateral da moldura quadrada = 20 cm

Comprimento mínimo da corda necessária = Perímetro da moldura quadrada = 4 × 20 = 80 cm.

Espero que isto ajude!!!!

English Translation

Sofia is going to glue a piece of string to the outline of a square frame 20 cm from the side. How long should this string be?

Solution

The string is expected to be glued all around the outlne of square frame.

This means the string needs to at least cover the whole perimeter of the square frame a minimum of one time.

Perimeter of a square = 4L

L = side length of the square.

The side length of the square frame = 20 cm

Minimum length of the string required = Perimeter of the square frame = 4 × 20 = 80 cm.

Hope this Helps!!!!

Answer:

[tex]P(\bar X>3.4) = 0.385[/tex]

Step-by-step explanation:

Relevant Data provided according to the question is as follows

[tex]\mu[/tex] = 3.2

[tex]\sigma[/tex] = 0.8

n = 4

According to the given scenario the calculation of probability that the sample means will be more than 3.4 pounds is shown below:-

[tex]z = \frac{\bar X - \mu}{\frac{a}{\sqrt{n} } }[/tex]

[tex]P(\bar X>3.4) = 1 - P(\bar X\leq 3.4)[/tex]

[tex]= 1 - P \frac{\bar X - \sigma}{\frac{a}{\sqrt{n} } } \leq \frac{3.4 - \sigma}{\frac{a}\sqrt{n} }[/tex]

Now, we will solve the formula to reach the probability that is

[tex]= 1 - P \frac{\bar X - 3.2}{\frac{0.8}{\sqrt{4} } } \leq \frac{3.4 - 3.2}{\frac{0.8}\sqrt{4} }[/tex]

[tex]= 1 - P (Z \leq \frac{0.2}{0.4})[/tex]

[tex]= 1 - P (Z \leq 0.5})[/tex]

[tex]= 1 - \phi (0.5)[/tex]

= 1 - 0.6915

= 0.385

Therefore the correct answer is

[tex]P(\bar X>3.4) = 0.385[/tex]

So, for computing the probability we simply applied the above formula.

Answer:

its  21

Step-by-step explanation:

its not 21 i really dont know

Answer:

$2.06

Step-by-step explanation:

$2.99 x 6 = $17.94

$20.00 - $17.94 = $2.06

Hope this helps

Answer: $0.26

Step-by-step explanation:

Cost of 6 pens

= 2.99 x 6

= 17.94

Add sales tax at 10%,

= 17.94 x 1.1

= 19.74

Change due to me

= 20 - 19.74

= 0.26

Answer:

x = 4 or x = -13/4 = -4.33

Step-by-step explanation:

log (3x - 2) + log (x + 1) = 2 - log 2

Note 2 is also equals to log 100

log (3x - 2) + log (x + 1) = log 100 - log 2

log (3x - 2)(x + 1) = log (100/2)

log 3x² + 3x - 2x - 2 = log 50

log 3x² + x - 2 = log 50

3x² + x - 2 = 50

3x² + x - 2 - 50 = 0

3x² + x - 52 = 0

find the number to multiply that will give you -52 × 3 = -156 and add to give you 1. The numbers are -12 and 13.

3x² - 12x + 13x - 52 = 0

3x(x - 4) + 13( x - 4) = 0

(3x + 13)(x - 4) = 0

x = 4 or x = -13/4 = -4.33

If you insert 4 in the logarithm equation you will see that the left side is equal to the right

log (3x - 2) + log (x + 1) = log 100 - log 2

log 10 + log 5 = log 50

log 50 = log 50

Answer:

216 cm³

Step-by-step explanation:

The volume of a cube is denoted by V = s³, where s is the side length.

Here, the side length is 6 centimetres, so plug this into the formula to find V:

V = s³

V = 6³ = 6 * 6 * 6 = 216

The answer is thus 216 cm³.

~ an aesthetics lover

Answer:

216

Step-by-step explanation:

6³ = 216

Answer:

Ok, we have that f(x) is defined for all real values of x, except for x = x0.

[tex]\lim_{x \to \ x0} f(x)[/tex]

Does it exist? why?

Remember that when we are taking the limit we are not evaluating the function in x0, instead, we are evaluating the function in values really close to x0 (values defined as x0⁺ and x0⁻, where the sign defines if we approach from above or bellow).

And because f(x) is defined in the values of x near x0, we can conclude that  the limit does exist if:

[tex]\lim_{x \to \x0+} f(x) = \lim_{x \to \x0-} f(x)[/tex]

if that does not happen, like in f(x) = 1/x where x0 = 0

where the lower limit is negative and the upper limit is positive, we have that the limit does not converge.

Answer:

The critical value of  [tex]f(\theta) = 6\cdot \cos \theta + 3\cdot \sin 2\theta[/tex] are given by [tex]\theta \approx 0.091\pi \pm 2\pi\cdot n[/tex] or [tex]\theta \approx 0.909\pi \pm 2\pi \cdot n[/tex], [tex]\forall \,n \in \mathbb{N}[/tex]

Step-by-step explanation:

The function to be evaluated is [tex]f(\theta) = 6\cdot \cos \theta + 3\cdot \sin 2\theta[/tex], the first derivative of the function must be taken in order to determine the set of critical numbers. Each derivative are found by using the differentiation rule for a sum of functions and rule of chain and subsequently simplified by trigonometric and algebraic means:

First derivative

[tex]f'(\theta) = - 6 \cdot \sin \theta +6\cdot \cos 2\theta[/tex]

[tex]f'(\theta) = -6\cdot \sin \theta + 2\cdot (\cos^{2}\theta-\sin^{2}\theta)[/tex]

[tex]f'(\theta) = -6\cdot \sin \theta + 2\cdot [(1-\sin^{2}\theta-\sin^{2}\theta)][/tex]

[tex]f'(\theta) = -6\cdot \sin \theta + 2\cdot (1-2\cdot \sin^{2}\theta)[/tex]

[tex]f'(\theta) = -6\cdot \sin \theta + 2 - 4\cdot \sin^{2}\theta[/tex]

[tex]f'(\theta) = -4\cdot \sin^{2}\theta - 6\cdot \sin \theta +2[/tex]

The procedure to determine the critical number of the given function are described briefly:

1) First derivative is equalised to zero.

2) The resultant equation is solved.

Then,

[tex]-4\cdot \sin^{2}\theta - 6\cdot \sin \theta +2 = 0[/tex]

Whose roots are:

[tex]\sin \theta_{1} \approx 0.281[/tex] and [tex]\sin \theta_{2} \approx -1.781[/tex]

The sine function is a continuous function with a range between 1 and -1, so, only the first root offers a realistic solution. In addition, such function is positive at first and second quadrants and has a periodicity of [tex]2\pi[/tex] radians, the family of critical values are determined by the unse of inverse trigonometric functions:

[tex]\theta \approx \sin^{-1} 0.281[/tex]

There are two subsets of solutions:

[tex]\theta \approx 0.091\pi \pm 2\pi\cdot n[/tex] or [tex]\theta \approx 0.909\pi \pm 2\pi \cdot n[/tex], [tex]\forall \,n \in \mathbb{N}[/tex]

Answer:

Hey there!

3/2= 1.5, which is good.

2/3=0.666666666666... no

3/4=0.75, which is good.

5/7= 0.71428... no

Answer:

these sequences are limited

you can try it in a calculator

Answer:

The angle of depression formed by Darius's sight line to the ranger station is 53.13°.

Step-by-step explanation:

Denote Darius's camp site as C, the ranger station as R and the tree as T.

Consider the triangle CTR.

TX is the altitude of the right angled triangle TXR.

The altitude of a right angled triangle forms two triangle that similar to each other.

So, ΔTXC [tex]\sim[/tex] ΔTXR.

Compute the measure of TX as follows:

[tex]\frac{CX}{TX}=\frac{TX}{RX}\\\\TX^{2}=CX\times RX\\\\TX=\sqrt{CX\times RX}[/tex]

      [tex]=\sqrt{18\times 32}\\\\=24\ \text{yd}[/tex]

The angle d represents the angle of depression formed by Darius's sight line to the ranger station.

Compute the value of d as follows:

[tex]tan\ d^{o}=\frac{RX}{TX}\\\\d^{o}=tan^{-1} [\frac{RX}{TX}][/tex]

    [tex]=tan^{-1} [\frac{32}{24}]\\\\=53.13[/tex]

Thus, the angle of depression formed by Darius's sight line to the ranger station is 53.13°.

Answer:

4

Step-by-step explanation:

We are told that figure B is a scaled copy of B, which means figure A was enlarged by a certain scale factor to get a similar figure as A, now referred to as figure B.

The scale factor = ratio of any two corresponding sides of both similar figures.

Thus,

Scale factor of the similar figures given = 40/10 = 4.

This means that, figure A was scaled up by 4 times its original size to get figure B. Each side of figure B is 4 × the corresponding side in figure A.

Scale factor = 4

Answer:

When you multiply a difference of squares, two terms cancel each other out and result in a binomial instead of a trinomial. To understand this, you can use an example.

When you multiply (x-3) and (x+3), you can use FOIL to expand them. By doing this, you get x^2-3x+3x-9. As you can see, -3x and 3x cancel each other out, so this results in a binomial instead of a trinomial.

Answer:

when you multiply them the two terms cancel each other out which will result in a binominal

Step-by-step explanation:

Answer:

6 mg

Step-by-step explanation:

12 mg

0.018 g * 1000 mg/g = 18 mg

18 mg - 12 mg = 6 mg

Answer:

a. With 90% confidence the proportion of all Americans who favor the new Green initiative is between 0.6290 and 0.6948.

b. If the sample size is changed, the confidence interval changes as the standard error depends on sample size.

About 90% percent of these confidence intervals will contain the true population proportion of Americans who favor the Green initiative and about 10% percent will not contain the true population proportion.

Step-by-step explanation:

We have to calculate a 90% confidence interval for the proportion.

The sample proportion is p=0.6619.

[tex]p=X/n=370/559=0.6619[/tex]

The standard error of the proportion is:

[tex]\sigma_p=\sqrt{\dfrac{p(1-p)}{n}}=\sqrt{\dfrac{0.6619*0.3381}{559}}\\\\\\ \sigma_p=\sqrt{0.0004}=0.02[/tex]

The critical z-value for a 90% confidence interval is z=1.6449.

The margin of error (MOE) can be calculated as:

[tex]MOE=z\cdot \sigma_p=1.6449 \cdot 0.02=0.0329[/tex]

Then, the lower and upper bounds of the confidence interval are:

[tex]LL=p-z \cdot \sigma_p = 0.6619-0.0329=0.6290\\\\UL=p+z \cdot \sigma_p = 0.6619+0.0329=0.6948[/tex]

The 90% confidence interval for the population proportion is (0.6290, 0.6948).

This is not the complete question, the complete question is:

P18-1 (LO2,3) (Allocate Transaction Price, Upfront Fees)

Tablet Tailors sells tablet PCs combined with Internet service, which permits the tablet to connect to the Internet anywhere and set up a Wi-Fi hot spot. It offers two bundles with the following terms.

1. Tablet Bundle A sells a tablet with 3 years of Internet service. The price for the tablet and a 3-year Internet connection service contract is $500. The standalone selling price of the tablet is $250 (the cost to Tablet Tailors is $175). Tablet Tailors sells the Internet access service independently for an upfront payment of $300. On January 2, 2017, Tablet Tailors signed 100 contracts, receiving a total of $50,000 in cash.

2. After 2 years of the 3-year contract, Tablet Tailors offers a modified contract and extension incentive. The extended contract services are similar to those provided in the first 2 years of the contract. Signing the extension and paying $90 (which equals the standalone selling of the revised Internet service package) extends access for 2 more years of Internet connection. Forty Tablet Bundle A customers sign up for this offer.

INSTRUCTION

a) Prepare the journal entries when the contract is signed on January 2, 2019, for the 40 extended contracts. Assume the modification does not result in a separate performance obligation.

b) Prepare the journal entries on December 31, 2019, for the 40 extended contracts (the first year of the revised 3-year contract).

Answer:

Step-by-step explanation:

(A)

Date        Particulars                               Debit                     Credit

2-Jan-19        Cash                                        3600  

                      Unearned Service Revenue                               3600

40 * 90 = 3600

services in the extended period are the same as the services that were provided in the original contract period. As they are not distinct hence the modifications will be considered as part of the original contract.

(B)

Date           Particulars                                    Debit           Credit

31-Dec-19 Unearned Service Revenue            2413  

                       Service revenue                                             2413

internet = 300, price = 550, connection service = 500

(300/550) * 500 = 273

so

Original internet service contract = 40 * 273 = 10,920

Revenue recognized in 1st two years = 10,920 * 2/3 = 7280

Remaining service at original rates = 10920 - 7280 = 3640

Extended service = 3600

3640 + 3600 = $7240  

7240 / 3 = $2413

Answer: El número es 902 en el sistema decimal.

Step-by-step explanation:

Supongo que tenemos el número:

32012 en base 4, y lo queremos representar en base decimal.

Entonces, usando la regla general, podemos escribir este número como:

unidades*base^0 + decenas*base^1 + centenas*base^2......  

Es decir, acá tenemos:

2*4^0 + 1*4^1 + 0*4^2 + 2*4^3 + 3*4^4 = 902

El número es 902 en el sistema decimal.

Answer:

This question is very simple,

Ok first you will need to find the x and y intercepts by letting y=0 and x=0

First let x=0

so, 0-y=1

y=-1

let y=0

x-0=1

x=1

now we know

x-intercept=(1,0)

y-intercept=(0-1)

Hence, find the graph that has the two corresponding points and that would be the graph you are looking for.

Step-by-step explanation:

Answer:

2{3[9+4(7-5)-4]}

2{3[9+4(2)-4]}

2{3[13(2)-4]}

2{3[26-4]}

2{3[22]}

2{66}

132

Step-by-step explanation:

Answer:

1/90 = 1.11%

Step-by-step explanation:

We have that the number of ways of total selections and assignments possible is a permutation.

We know that permutations are defined like this:

nPr = n! / (n-r)!

In our case n = 10 and r = 2, replacing:

10P2 = 10! / (10 - 2)! = 10! / 8!

10P2 = 90

In addition to this, there will only be one way to randomly select the two members currently holding the positions of President and Vice President and reassign them to their current positions. Thus,

Probability would come being the following:

P = 1/90 = 1.11%

Answers:

a) 0.0625

b) 0.9375

==================================================

Work Shown:

The probability of landing on heads is 1/2 = 0.5 since both sides are equally likely to land on. Getting 4 heads in a row is (1/2)^4 = (0.5)^4 = 0.0625

The event of getting at least one tail is the complement of getting all four heads. This is because you either get all four heads or you get at least one tail. One or the other must happen. We subtract the result we got from 1 to get 1-0.0625 = 0.9375

You can think of it like this

P(getting all four heads) + P(getting at least one tail) = 1

The phrasing "at least one tail" means "one tail or more".

Answer:

17) 53.2

18) 17

Step-by-step explanation:

In similar triangles theorem, the ratio of the corresponding sides of two triangles are equal.

17) To determine x, ratio of the sides of 1st triangle/Ratio of the sides of 2nd triangle.

Ratio of base to the missing side:

7.6/x = 13.6/95.2

7.6/x = 13.6/95.2

7.6/x = 0.1428

7.6= 0.1429x

x = 53.2

18) ratio of shortest side/ longest side

3.4/7.9 = x/39.5

x = 3.4/7.9 × 39.5

x = 17