Solve Systems of Algebraic Equations in Two Variables
Hello I need some help on setting up 2 equations of this problem. The answers are cheeseburger costs $1.55 and the milkshake $0.85

Four cheeseburgers and two chocolate milkshakes cost a total of $ 7.90. Two
Shakes cost 15 cents more than a hamburger with
cheese so What is the price of a cheeseburger?
And the price of a shake?

[tex]answer \\ = 2 , 4 , 5 \\ additional \: information \\ let \: r \: be \: a \: relation \: a \: to \: b. \: then \: the \: set \\ of \: first \: components \: or \: the \: set \: of \: \\ elements \: of \: a \: are \: called \: domain \\ and \: the \: set \: of \: second \: components \\ or \: the \: set \: of \: elements \: of \: b \: are \: called \: the \: range. \\ hope \: it \: helps[/tex]

Answer:

c

Step-by-step explanation:

when the absolute value of slope gets smaller, the graph of line gets less steeper.

Answer:

a) We can not estimate the probability.

b) Zero probability.

c) There is a probability between 95% and 99% that they have between 475 and 525 customers on a given day.

Step-by-step explanation:

a) We can not said nothing because we only know the average of customers per day. We need to know the probability distribution of the amount of customers per day to answer this question.

b) Now that we know that the variance is 100, although we do not know the exact distribution of the values, we can use the empirical rules to estimate the probability of having at least 700 customers on a given day.

If the variance is 100, the standard deviation is √100=10.

Applying the empirical rule (68-95-99.7 rule), we know that there is probability 0.15% of having at least 500+3*10=530 customers per day (more than 3 deviations from the mean).

Then, we can conclude that the probability of having at least 700 customers per day is zero.

c) To estimate this probability, we have to calculate how many deviations from the mean this values represent:

[tex]\Delta_1=475-500=-25=2.5\sigma\\\\\Delta_2=525-500=25=2.5\sigma[/tex]

We have an interval that have a width of ±2.5 deviations from the mean.

For 2 deviations from the mean, it is expected to have 95% of the data.

For 3 deviations from the mean, it is expected to have 99.7% of the data.

Then, for the interval 475 to 525, we can estimate a probability between 95% and 99%.

Answer:

work is shown and pictured

Answer: x<3

Step-by-step explanation:

Answer:

0.96 radians

Step-by-step explanation:

Formula

1° = [tex]\frac{\pi }{180}[/tex] radians

Multiplying both sides by 55, It becomes

55° = [tex](\frac{\pi }{180} )*55[/tex]

55° = [tex]\frac{55\pi }{180}[/tex]

= 172.8/180

= 0.96 radians

Answer:

–2(5 – 4x) < 6x – 4

<=>

-10 + 8x < 6x - 4

<=>

2x < 6

<=>

x < 3

Hope this helps!

:)

Answer:

Step 1: –10 + 8x < 6x – 4

Step 2: –10 < –2x – 4

Step 3: –6 < –2x

Step 4: ________

What is the final step in solving the inequality –2(5 – 4x) < 6x – 4?

A. x < –3  

B. x > –3

C. x < 3

D. x > 3

Step-by-step explanation:

The correct answer here is C. x < 3

Answer:

x ≤ -4

Step-by-step explanation:

2(3 - x) ≥ 14

Divide by 2

2/2(3 - x) ≥ 14/2

(3 - x) ≥ 7

Subtract 3 from each side

3-x-3  ≥ 7-3

- x ≥ 4

Divide each side by -1, remembering to flip the inequality

x ≤ -4

Answer:

-4

Step-by-step explanation:

6-2x≥14 (/expand )

-2x≥14-6=-2x≥8

x≤8/-2=-4

Answer:

m > 82.28

Step-by-step explanation:

Price to Pay (P)

distance (m)

Company A

Pa = 0.80m

Company B

Pb = 65 + 0.01m

Company A charge more than B is written like this

0.8m > 65 + 0.01m

then we can solve this inequality

(0.8 - 0.01)m > 65

0.79m > 65

m > 65/0.79

m > 82.28 miles

so if Maya will go more than 82.28 miles, I suggest Company B is cheaper

Answer:

The average would be 42 / 28 = $1.50 / day.

Answer:

$1.50 per day

Step-by-step explanation:

Take the dollar amount and divide by the number of days

42 dollars / 28 days

1.50 dollars per day

$1.50 per day

Answer:

Yes, it would be unusual.

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal probability distribution

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

If [tex]Z \leq -2[/tex] or [tex]Z \geq 2[/tex], the outcome X is considered unusual.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

In this question, we have that:

[tex]\mu = 22, \sigma = 5, n = 25, s = \frac{5}{\sqrt{25}} = 1[/tex]

Would it be unusual for this sample mean to be less than 19 days?

We have to find Z when X = 19. So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

By the Central Limit Theorem

[tex]Z = \frac{19 - 22}{1}[/tex]

[tex]Z = -3[/tex]

[tex]Z = -3 \leq -2[/tex], so yes, the sample mean being less than 19 days would be considered an unusual outcome.

Answer:

the dimension of the poster = 90 cm length and 60 cm  width i.e 90 cm by 60 cm.

Step-by-step explanation:

From the given question.

Let p be the length of the of the printed material

Let q be the width of the of the printed material

Therefore pq = 2400 cm ²

q = [tex]\dfrac{2400 \ cm^2}{p}[/tex]

To find the dimensions of the poster; we have:

the length of the poster to be p+30 and the width to be [tex]\dfrac{2400 \ cm^2}{p} + 20[/tex]

The area of the printed material can now be:  [tex]A = (p+30)(\dfrac{2400 }{p} + 20)[/tex]

=[tex]2400 +20 p +\dfrac{72000}{p}+600[/tex]

Let differentiate with respect to p; we have

[tex]\dfrac{dA}{dp}= 20 - \dfrac{72000}{p^3}[/tex]

Also;

[tex]\dfrac{d^2A}{dp^2}= \dfrac{144000}{p^3}[/tex]

For the smallest area [tex]\dfrac{dA}{dp }=0[/tex]

[tex]20 - \dfrac{72000}{p^2}=0[/tex]

[tex]p^2 = \dfrac{72000}{20}[/tex]

p² = 3600

p =√3600

p = 60

Since p = 60 ; replace p = 60 in the expression  q = [tex]\dfrac{2400 \ cm^2}{p}[/tex]   to solve for q;

q = [tex]\dfrac{2400 \ cm^2}{p}[/tex]

q = [tex]\dfrac{2400 \ cm^2}{60}[/tex]

q = 40

Thus; the printed material has the length of 60 cm and the width of 40cm

the length of the poster = p+30 = 60 +30 = 90 cm

the width of the poster = [tex]\dfrac{2400 \ cm^2}{p} + 20[/tex] = [tex]\dfrac{2400 \ cm^2}{60} + 20[/tex]  = 40 + 20 = 60

Hence; the dimension of the poster = 90 cm length and 60 cm  width i.e 90 cm by 60 cm.

Answer:

the answer is square root 5 over 2 square root 2

Step-by-step explanation:

Answer:

what is this boiii?

Answer:

3a) 30% more than original price

b) 70% of the original price

c) 17times the original price

d) 70% less than original price

e) t + 0.85t

f) t - 0.15t

g) t - 0.85t

h) t + 0.15t

4. The expression that can be used to find the amount of money in his bank = m + 0.25m

Question:

3. Match each statement with an expression that could be used to find the price.

'The expressions for a to d were not stated in the question'.

a) p+ 0.3p

b) 0.7p

c) 17p

d) p-07p

'From e to h, we were not told what to determine'.

Write the expression in terms of time

e. 85% more than the original time

f. 15% less time than the original

g. 85% time decrease

h. 15% time increase

4. Ronnie increased the amount of money in his piggy bank by 25%. Which expression can be used to find the amount of money in his bank? Let "m" represent the original​.

Step-by-step explanation:

let original price = p

a) p+ 0.3p = p + 30% of p

30% more than original price

b) 0.7p = 70% of p

= 70% of the original price

c) 17p = 17 × p

= 17times of the original price

d) p-0.7p = p - 70% of p

= 70% less than original price

Let original time = t

e) 85% more than the original time = t + 85%of t

= t + 0.85t

f) 15% less time than the original time = t - 15% of t

= t - 0.15t

g) 85% time decrease = t - 85% of t

= t - 0.85t

h) 15% time increase = t + 15% of t

= t + 0.15t

4. Since "m" represent the original amount in Hus piggy bank

An increase of 25% = original amount + 25% of original amount

= m + 25% of m

'Of' means multiplication

= m + 0.25 ×m

= m + 0.25m

= 1.25m

The expression that can be used to find the amount of money in his bank = m + 0.25m

Answer:

a) P(X < 30) = 0.0392.

b) P(28 < X < 32) = 0.2760

c) P(X > 35) = 0.1190

d) P(X > 31) = 0.8810

e) At least 35.7965 mpg

Step-by-step explanation:

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this question, we have that:

[tex]\mu = 33, \sigma = 1.7[/tex]

a. P(X<30)

This is the pvalue of Z when X = 30. So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{30 - 33}{1.7}[/tex]

[tex]Z = -1.76[/tex]

[tex]Z = -1.76[/tex] has a pvalue of 0.0392.

Then

P(X < 30) = 0.0392.

b) P(28 < X < 32)

This is the pvalue of Z when X = 32 subtracted by the pvalue of Z when X = 28. So

X = 32

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{32 - 33}{1.7}[/tex]

[tex]Z = -0.59[/tex]

[tex]Z = -0.59[/tex] has a pvalue of 0.2776.

X = 28

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{28 - 33}{1.7}[/tex]

[tex]Z = -2.94[/tex]

[tex]Z = -2.94[/tex] has a pvalue of 0.0016.

0.2776 - 0.0016 = 0.2760.

So

P(28 < X < 32) = 0.2760

c) P(X>35)

This is 1 subtracted by the pvalue of Z when X = 35. So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{35 - 33}{1.7}[/tex]

[tex]Z = 1.18[/tex]

[tex]Z = 1.18[/tex] has a pvalue of 0.8810.

1 - 0.8810 = 0.1190

So

P(X > 35) = 0.1190

d. P(X>31)

This is 1 subtracted by the pvalue of Z when X = 31. So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{31 - 33}{1.7}[/tex]

[tex]Z = -1.18[/tex]

[tex]Z = -1.18[/tex] has a pvalue of 0.1190.

1 - 0.1190 = 0.8810

So

P(X > 31) = 0.8810

e. the mileage rating that the upper 5% of cars achieve.

At least the 95th percentile.

The 95th percentile is X when Z has a pvalue of 0.95. So it is X when Z = 1.645. Then

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]1.645 = \frac{X - 33}{1.7}[/tex]

[tex]X - 33 = 1.645*1.7[/tex]

[tex]X = 35.7965[/tex]

At least 35.7965 mpg

The upper 5% of cars have a mileage rating of 35.805 mpg

Z score is used to determine by how many standard deviations the raw score is above or below the mean. It is given by:

z = (raw score - mean) / standard deviation

Given;  mean of 33 mpg and a standard deviation of 1.7

a) For < 30:

z = (30 - 33)/1.7 = -1.76

P(x < 30) = P(z < -1.76) = 1 - 0.8413 = 0.0392

b) For < 28:

z = (28 - 33)/1.7 = -2.94

P(x < 28) = P(z < -2.94) = 0.0016

c) For > 35:

z = (35 - 33)/1.7 = 1.18

P(x > 35) = P(z > 1.18) = 1 - P(z < 1.18) = 1 - 0.8810 = 0.119

d) For > 31:

z = (31 - 33)/1.7 = -1.18

P(x > 31) = P(z > -1.18) = 1 - P(z < -1.18) = 0.8810

e) The  upper 5% of cars achieve have a z score of 1.65, hence:

1.65 = (x - 33)/1.7

x = 35.805 mpg

The upper 5% of cars have a mileage rating of 35.805 mpg

Find out more on z score at: https://brainly.com/question/25638875

Answer:

The correct answer would be D) 4.8x + 1.2 = 3.6; x = 0.5 mile

Step-by-step explanation:

This is because laps would be the dependent variable, so we know the number of them (4.8) would be multiplied by the variable (x). We also know that 1.2 is the constant. Now we can solve to make sure this is the right equation.

4.8x + 1.2 = 3.6

4.8x = 2.4

x = 0.5

Answer:

D) 4.8x + 1.2 = 3.6; x = 0.5 miles

Answer:

To solve a polynomial inequality, we factor the polynomial into irreducible factors and find all the real _zeros_ polynomial. Then we find the intervals determined by the real _zeros and use test points in each interval to find the_ sign of the polynomial on that interval.

If P(x) = x(x+2)(x-1)

And P(x) ≥ 0

We see that P(x) ≥ 0 on the intervals (-2, 0) and (1, ∞).

Step-by-step explanation:

The complete question is attached to this solution

To solve inequality of a polynomial, we first obtain the solutions of the polynomial. The solutions of the polynomial are called the zeros of the polynomial.

If P(x) = x(x+2)(x-1)

The solutions of this polynomial, that is the zeros of this polynomial are 0, -2 and 1.

To now solve the inequality that arises when

P(x) ≥ 0

We redraw the table and examine the intervals

The intervals to be examined as obtained from the zeros include (-∞, -2), (-2, 0), (0, 1) and (1, ∞)

Sign of | x<-2 | -2<x<0 | 0<x<1 | x>1

x               | -ve | -ve | +ve | +ve

(x + 2)       | -ve | +ve | +ve | +ve

(x - 1)         | -ve | -ve | -ve | +ve

x(x+2)(x-1) | -ve | +ve | -ve | +ve

The intervals that satisfy the polynomial inequality P(x) = x(x+2)(x-1) ≥ 0 include

(-2, 0) and (1, ∞)

Hope this Helps!!!

Step-by-step explanation:

-8x + 4 > 5 - 3x

-8x + 3x > 5 - 4

-5x > 1

x > 1 / - 5

Answer:

  C

Step-by-step explanation:

The function of table A can be written as ...

  y = 100x -92

__

The function of table B can be written as ...

  y = 10x +446

__

The function of table C can be written as ...

  y = (5/3)·3^x

__

The function of table D can be written as ...

  y = 2x +413

__

The exponential function of Table C will have the largest y-values for any value of x greater than 6.

_____

Comment on the functions

When trying to determine the nature of the function, it is often useful to look at the differences of the y-values for consecutive x-values. Here, the first-differences are constant for all tables except C. That means functions A, B, D are linear functions.

If the first differences are not constant, one can look at second differences and at ratios. For table C, we notice that each y-value is 3 times the previous one. That constant ratio means the function is exponential, hence will grow faster than any linear function.

Answer:

yes, what the other user  is correct i just took the quiz

Step-by-step explanation:

Answer:

[tex] P(X\leq x) =\frac{x-a}{b-a}, a \leq x \leq b[/tex]

And using this formula we have this:

[tex] P(X<11) = \frac{11-0}{12-0}= 0.917[/tex]

Then we can conclude that the probability that that a person waits fewer than 11 minutes is approximately 0.917

Step-by-step explanation:

Let X the random variable of interest that a woman must wait for a cab"the amount of time in minutes " and we know that the distribution for this random variable is given by:

[tex] X \sim Unif (a=0, b =12)[/tex]

And we want to find the following probability:

[tex] P(X<11)[/tex]

And for this case we can use the cumulative distribution function given by:

[tex] P(X\leq x) =\frac{x-a}{b-a}, a \leq x \leq b[/tex]

And using this formula we have this:

[tex] P(X<11) = \frac{11-0}{12-0}= 0.917[/tex]

Then we can conclude that the probability that that a person waits fewer than 11 minutes is approximately 0.917

Answer:

( 5 ^ -2)^4

= 5 ^ -8

= 1 /5^8

= 1 / 390,625

Answer:

10 players

Step-by-step explanation:

If you count the x’s, there are 10.

Why ask this question? You could have just counted

Answer:

22 players

Step-by-step explanation:

It specifically says 'at least 3 runs' so you would have to count all the x's in the columns 3, 4, and 5.

There are 10 x's in the 3 column

There are 3 x's in the 4 column

There are 9 x's in the 5 column

Hope this helps!

Answer:

A= 1/2bh

Step-by-step explanation:

(how its supposed to be said: Area= one half base times height)

:)

Answer:

(1) As a simple definition, a triangle is a two-dimensional figure that has 3 sides (and 3 angles as well).

(2) A triangle as shown in attached picture has the area that is typical calculated by the multiplication of half of base and height.

A = (1/2) x Base x Height

Base can be a particular side of triangle

Height is the perpendicular line segment between the opposite vertex of selected base and that base.

Hope this helps!

:)

Answer:

8400

Step-by-step explanation:

Its too long and I answered it before

Answer:

[tex]\frac{9}{8}[/tex]

Step-by-step explanation:

27 ÷ 9 = 3

3 * 3 = 9

9 ÷ 8 = [tex]\frac{9}{8}[/tex]

Answer:

D

Step-by-step explanation:

Length × Width = Area

So we'll substitute the Area of the circle having formula, πr²

Measure of the angle which is made by rotating a side as terminal side by one-sixth of a revolution counterclockwise is 60 degree and π/3 radian.

The terminal side of an angle is the rotated side of the initial side around a point to form an angle. This rotation can be clockwise or counter clock wise.

The terminal side of an angle in standard position rotated one-sixth of a revolution counterclockwise from the positive x-axis.

The total degree in a complete rotation of a side is 360 degrees. The side is rotated 1/6. Thus the angle is rotated is,

[tex]\theta=\dfrac{1}{6}\times360\\\theta=60^o[/tex]

Multiply it with π/180 to find the measure of the angle in radian.

[tex]\theta=60\dfrac{\pi}{180}\\\theta=\dfrac{\pi}{3}\\[/tex]

Hence, the measure of the angle which is made by rotating a side as terminal side by one-sixth of a revolution counterclockwise is 60 degree and π/3 radian.

Learn more about the terminal side of an angle here

https://brainly.com/question/7040335

Answer:

12

Step-by-step explanation:

f(-4) = -8-5(-4) = -8+20 = 12

Answer:

f(-4) = 12

Step-by-step explanation:

f(-4) = -8 - 5(-4)

= -8 + 20

= 12

Answer:

Step-by-step explanation:

We have to find the reported happiness of person of family income of $25,000, $35,000 and $45,000

Given that the formula for finding relation between a people happiness and his income is

y = 0.065x - 0.613

a) find the happiness of person of family income os $25,000

we put x = 25 as in the equation above

[tex]y=0.065(25)-0.613\\\\=1.625-0.613\\\\=1.02 \approx 1[/tex]

Hence, person happiness with with family income of $25,000 on a scale of 3 is y = 1

That means they come under catergory "not to happy"

b) Find the happiness of person of family income os $35,000

we put x = 35 as in the equation above

[tex]y=0.065(35)-0.613\\\\=1.667-0.613\\\\=1.667 \approx 1.7[/tex]

Hence, person happiness with with family income of $35,000 on a scale of 3 is y = 1.7

That means they come under catergory "not to happy" and "fairly happy"

c) Find the happiness of person of family income os $45,000

we put x = 45 as in the equation above

[tex]y=0.065(45)-0.613\\\\=2.925-0.613\\\\=2.312 \approx 2.3[/tex]

Hence, person happiness with with family income of $45,000 on a scale of 3 is y = 2.3

That means they come under catergory  "fairly happy"

The scale would show the data as follows:

Happiness Scale at Income 25, 35, 45 &amp; 55 thousand :

1.012 (Not too happy), 1.662 (Fairly Happy), 2.315 (Fairly Happy) , 2.965 (Very Happy)

Important Information :

Relationship between happiness scale 'y' and income in 1000s 'x' :y = 0.065x − 0.613, for people in income group between [tex]25000 & 55000[/tex]

Happiness scale : At level of income, between 25 and 55 thousands.

Putting value of income 'x' to find scale of happiness i.e. 'y'

For income 'x' = 25 thousand : [tex]y = 0.065 (25) - 0.613 = 1.625 - 0.613 = 1.012[/tex] For income 'x' = 35 thousand : [tex]y = 0.065 (35) - 0.613 = 2.275 - 0.613 = 1.662[/tex]For income 'x' = 45 thousand : [tex]y = 0.065 (45) - 0.613 = 2.925 - 0.61 = 2.315[/tex] For income 'x' = 55 thousand :[tex]y = 0.065 (55) - 0.613 = 3.575 - 0.61 = 2.965[/tex]

Learn more about "Happiness Scale" here:

brainly.com/question/25609130

Answer:

We know that:

The original price was $515

and

It was $125 off

so we need to find the price of the sofa after the discount.

$515 - $125 = $390

The sale price of the sofa after the discount was $390

hope This helps and pls mark me brainliest if it did :)