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?

Step-by-step explanation:

area of parallelogram= height * length of base

Answer:

1096750 impressions

Step-by-step explanation:

Given that :

Mean = 850,000

Standard deviation = 150,000

If we assume that X should be the numbers of impressions created;

Then ;

[tex]X \approx N (\mu , \sigma^2)[/tex]

Now ; representing x as the value for the number of impression needed ; Then ;

[tex]P(X>x) = 0.95[/tex]

[tex]P(\dfrac{X- \mu}{\sigma} > \dfrac{x -850000}{150000}) = 0.95[/tex]

[tex]P(Z> \dfrac{ x -850000}{150000}) = 0.95[/tex]

From normal tables:

[tex]P(Z >1.645) = 0.95[/tex]

[tex]\dfrac{x - 850000}{150000} =1.645[/tex]

(x- 850000) = 1.645(150000)

x - 850000 = 246750

x = 246750 + 850000

x = 1096750 impressions

Answer:

$71.59

Step-by-step explanation:

43.25+26.25

=69.5

69.5×103/100

=71.585

Answer:

A =50.24 in ^2

Step-by-step explanation:

The diameter is 8 inches

The radius is 1/2 diameter

r = d/2 = 8/2 = 4

The area of the circle is given by

A = pi r^2

A = 3.14 (4)^2

A =50.24 in ^2

Answer:

C. 50.24 in²

Step-by-step explanation:

d= 8 in

r= 8/2= 4 in

Area= πr²= 3.14×4²= 50.24 in²

Answer:

[tex]z^{0.5}[/tex]

Step-by-step explanation:

So first simplify inside:

[tex]z^4z^{-1.5}=z^{2.5}[/tex]

Now divide that by 5:

[tex]z^{0.5}[/tex]

Answer:

LIKE TERMS: 6 and 9, 0.5kt and -10kt, and -7y2 and y2. UNLIKE TERMS: 3ad and 2bd, 5x and 5, and the last one is -4p and p2

Step-by-step explanation:

Answer: like terms: 6&9 , 0.5kt&-10kt , -7y^2&y^2

unlike terms 3ad&2bd, 5x&5, -4p&p^2

Step-by-step explanation:

passed

Answer:

A=450

Step-by-step explanation:

A=a+b

2h=12+33

2·20=450

Answer:

Area=450

Step-by-step explanation:

[tex]a+b/2h[/tex]

Answer:

Step-by-step explanation:

Hello!

The objective is to test ESP, for this, a psychic was presented with cards face down and asked to determine if each of the cards was one of four symbols: a star, cross, circle, square.

Be X: number of times the psychic identifies the symbols on the cards correctly is a size n sample.

p the probability that the psychic identified the symbol on the cards correctly

You have to calculate the sample size n to estimate the proportion with a confidence level of 95% and a margin of error of d=0.01

The CI for the population proportion is constructed "sample proportion" ± "margin of error" Symbolically:

p' ± [tex]Z_{1-\alpha /2} * (\sqrt{\frac{p'(1-p')}{n} } )[/tex]

Where  [tex]d= Z_{1-\alpha /2} * (\sqrt{\frac{p'(1-p')}{n} } )[/tex] is the margin of error. As you can see, the formula contains the sample proportion (it is normally symbolized p-hat, in this explanation I'll continue to symbolize it p'), you have to do the following consideration:

Every time the psychic has to identify a card he can make two choices:

"Success" he identifies the card correctly

"Failure" he does not identify the card correctly

If we assume that each symbol has the same probability of being chosen at random P(star)=P(cross)=P(circle)=P(square)= 1/4= 0.25

Let's say, for example, that the card has the star symbol.

The probability of identifying it correctly will be P(success)= P(star)= 1/4= 0.25

And the probability of not identifying it correctly will be P(failure)= P(cross) + P(circle) + P(square)= 1/4 + 1/4 + 1/4= 3/4= 0.75

So for this experiment, we'll assume the "worst case scenario" and use p'= 1/4 as the estimated probability of the psychic identifying the symbol on the card correctly.

The value of Z will be [tex]Z_{1-\alpha /2}= Z_{0.975}= 1.96[/tex]

Now using the formula you have to clear the sample size:

[tex]d= Z_{1-\alpha /2} * (\sqrt{\frac{p'(1-p')}{n} } )[/tex]

[tex]\frac{d}{Z_{1-\alpha /2}} = \sqrt{\frac{p'(1-p')}{n} }[/tex]

[tex](\frac{d}{Z_{1-\alpha /2}})^2 =\frac{p'(1-p')}{n}[/tex]

[tex]n*(\frac{d}{Z_{1-\alpha /2}})^2 = p'(1-p')[/tex]

[tex]n = p'(1-p')*(\frac{Z_{1-\alpha /2}}{d})^2[/tex]

[tex]n = (0.25*0.75)*(\frac{1.96}{0.01})^2= 7203[/tex]

To estimate p with a margin of error of 0.01 and a 95% confidence level you have to take a sample of 7203 cards.

I hope this helps!

Answer:

The sample size should be 6157

Step-by-step explanation:

Given that the margin of error (e) = ± 0.01 and the confidence (C) = 95% = 0.95.

Let us assume that the guess p = 0.25 as the value of p.

α = 1 - C = 1 - 0.95 = 0.05

[tex]\frac{\alpha }{2} =\frac{0.05}{2}=0.025[/tex]

The Z score of α/2 is the same as the z score of 0.475 (0.5 - 0.025) which is 1.96. Therefore [tex]Z_\frac{\alpha }{2}=Z_{0.025}=1.96[/tex]

To determine the sample size n, we use the formula:

[tex]Z_{0.025}*\sqrt{\frac{p(1-p)}{n} }\leq e\\Substituting:\\1.96*\sqrt{\frac{0.2(1-0.2)}{n} } \leq 0.01\\\sqrt{\frac{0.2(0.8)}{n} }\leq \frac{1}{196}\\\sqrt{0.16} *196 \leq \sqrt{n}\\78.4\leq \sqrt{n}\\ 6146.56\leq n\\n=6157[/tex]

Answer:

y = 4/5x + 1

Step-by-step explanation:

y = mx + b

m = slope

b = y-intercept

y = 4/5x + 1

Answer:4y-5x=5

Step-by-step explanation:

Answer:

(a) [tex]\mathbf{P_2 = \left[\begin{array}{c}140 \\ 160 \\ 200 \end{array}\right]}[/tex]

(b)   After an infinite period of time; we will get back to a result similar to after the two time period which will be [tex]= \left[\begin{array}{c}140 \\ 160 \\ 200 \end{array}\right]}[/tex]

Step-by-step explanation:

The Markov Matrix can be interpret as :

[tex]M = \left[\begin{array}{ccc} \dfrac{1}{5} & \dfrac{2}{5} &\dfrac{1}{5} \\ \\ \dfrac{2}{5}&\dfrac{2}{5}&\dfrac{1}{5}\\ \\ \dfrac{2}{5}& \dfrac{2}{5}& \dfrac{2}{5} \end{array}\right][/tex]

From (a) ; we see that the initial population are as follows: 130 individuals in location 1, 300 in location 2, and 70 in location 3.

Le P represent the Population; So ;  [tex]P = \left[\begin{array}{c}130 \\ 300 \\ 70 \end{array}\right][/tex]

The objective is to find How many are in each location after two time periods;

So, after two time period ; we have the population [tex]P_2 = [M]^2 [P][/tex]

where;

[tex][M]^ 2 = \left[\begin{array}{ccc} \dfrac{1}{5} & \dfrac{2}{5} &\dfrac{1}{5} \\ \\ \dfrac{2}{5}&\dfrac{2}{5}&\dfrac{1}{5}\\ \\ \dfrac{2}{5}& \dfrac{2}{5}& \dfrac{2}{5} \end{array}\right] \left[\begin{array}{ccc} \dfrac{1}{5} & \dfrac{2}{5} &\dfrac{1}{5} \\ \\ \dfrac{2}{5}&\dfrac{2}{5}&\dfrac{1}{5}\\ \\ \dfrac{2}{5}& \dfrac{2}{5}& \dfrac{2}{5} \end{array}\right][/tex]

[tex][M]^ 2 = \dfrac{1}{25} \left[\begin{array}{ccc} 1+2+4 & 1+2+4 &1+2+4 \\ \\ 2+2+4&2+2+4&2+2+4\\ \\ 2+4+4&2+4+4& 2+4+4 \end{array}\right][/tex]

[tex][M]^ 2 = \dfrac{1}{25} \left[\begin{array}{ccc}7&7&7 \\ \\ 8 &8&8\\ \\10&10& 10 \end{array}\right][/tex]

Now; Over to after two time period ; when the population [tex]P_2 = [M]^2 [P][/tex]

[tex]P_2 = \dfrac{1}{25} \left[\begin{array}{ccc}7&7&7 \\ \\ 8 &8&8\\ \\10&10& 10 \end{array}\right] \left[\begin{array}{c}130 \\ 300 \\ 70 \end{array}\right][/tex]

[tex]\mathbf{P_2 = \left[\begin{array}{c}140 \\ 160 \\ 200 \end{array}\right]}[/tex]

(b) The total number of individuals in the migration process is 500. After a long time, how many are in each location?

After a long time; that is referring to an infinite time (n)

So; [tex]P_n = [M]^n [P][/tex]

where ;

[tex][M]^n \ can \ be \ [M]^2 , [M]^3 , [M]^4 .... \infty[/tex]

; if we determine the respective values of [tex][M]^2 , [M]^3 , [M]^4 .... \infty[/tex] we will always result to the value for [tex][M]^n[/tex]; Now if  [tex][M]^n[/tex] is said to be a positive integer; then :

After an infinite period of time; we will get back to a result similar to after the two time period which will be [tex]= \left[\begin{array}{c}140 \\ 160 \\ 200 \end{array}\right]}[/tex]

Answer:  b) 1/3

Step-by-step explanation:

The numbers LESS THAN 3:  1, 2

[tex]\dfrac{\text{Quantity of numbers less than 3}}{Total\ number}\quad =\dfrac{2}{6}\quad \rightarrow \large\boxed{\dfrac{1}{3}}[/tex]

Answer:

x = 5/v

Step-by-step explanation:

Solve for x:

2 v x - 5 = 5

Add 5 to both sides:

2 v x = 10

Divide both sides by 2 v:

Answer: x = 5/v

Answer:

I'd say start with "Add 5 to both sides"

Step-by-step explanation:

VX +VX-5 = 5

Add 5 to both sides

2VX=10

Divide both sides by 2

VX=5

Divide both sides by V

X=[tex]\frac{5}{V}[/tex]

Answer: (b) 15.07 to 19.93 miles

Step-by-step explanation:

Confidence interval is written in the form,

(Sample mean - margin of error, sample mean + margin of error)

The sample mean, x is the point estimate for the population mean.

Margin of error = z × s/√n

Where

s = sample standard deviation = 3.8

n = number of samples = 20

From the information given, the population standard deviation is unknown and the sample size is small, hence, we would use the t distribution to find the z score

In order to use the t distribution, we would determine the degree of freedom, df for the sample.

df = n - 1 = 20 - 1 = 19

Since confidence level = 99% = 0.99, α = 1 - CL = 1 – 0.99 = 0.01

α/2 = 0.02/2 = 0.005

the area to the right of z0.005 is 0.025 and the area to the left of z0.025 is 1 - 0.005 = 0.995

Looking at the t distribution table,

z = 2.861

Margin of error = 2.861 × 3.8/√20

= 2.43

the lower limit of this confidence interval is

17.5 - 2.43 = 15.07 miles

the upper limit of this confidence interval is

17.5 + 2.43 = 19.93 miles

Answer:

40*d

Step-by-step explanation:

The word product means multiplication, and here it is multiplying 40 and the distance(d).

Answer:

40x5

Step-by-step explanation:

Answer:

(B) 0.7%

Step-by-step explanation:

X = Land Elevation (in ,000 feet)

Y = Unidentified Artifacts (in %)

The hypothetical theory says that:

The higher the elevation, the higher the percentage of unidentified artifacts in the location.

To find the percentage of variation in Y that can be explained by variations in X, we find the slope of the graph of X on Y.

Transforming X to thousand feets, we have 5220, 5690, 6250, 6750, 7250. This is in the attachment, plotted against 17, 12, 33, 37 and 62 respectively.

Further calculations, along with the graph, are in the attachment below. The answer therein is (B) 0.7%

Answer:

C. With a p-value less than 0.0001, there is sufficient evidence to reject the null hypothesis and accept the alternative as true.

Step-by-step explanation:

She performed an hypothesis test with the sample of size n=15 that she takes. The t-statistic has a value of 6.661.

The degrees of freedom for this sample size are:

[tex]df=n-1=15-1=14[/tex]

The P-value for a statistic t=6.661 and 14 degrees of freedom is:

[tex]\text{P-value}=P(t>6.661)=0.00001[/tex]

With these P-value we know that the effect is significant and the null hypothesis is rejected. There is enough evidence to support the claim that the mean height of Mountain Ash trees is greater than the coastal Douglas Firs.

-4-2×-2×64

-4+4×64

-4+256

=252

Answer:  (36)

hope this helps you have a wonderful day

Step-by-step explanation:

Answer:

20-39 => 2

40-59 => 1

60-79 => 1

80-99 => 6

100-119 => 5

Answer: 2, 1, 1, 6, 5

Step-by-step explanation:

20-39

2 | 3

3 | 9

40-59

5 | 0

60-79

7 | 5

80-99

8 | 1 2 4

9 | 3 9 9

100-119

10 | 1 1 5 6

11 | 1

Answer:

66%

Step-by-step explanation:

15% of homes have both features.

The percentage of homes that have a pool and no garage is:

Pool only = 19% - 15% = 4%

The percentage of homes that have a garage and no pool is:

Garage only = 62% - 15% = 47%

Therefore, the percentage of homes that have a pool, a garage or both is:

[tex]P = 4\%+47\%+15\%\\P=66\%[/tex]

Answer:

B, E

Step-by-step explanation:

A line has a negative slope when it decreases going left to right.

As the absolute value of the slope gets larger (-2 to -3 would be 2 to 3), the graph gets steeper (-3 is steeper than -2).

Answer:

B & E

Step-by-step explanation:

Answer:

x = 2 is the solution of the given equation

Step-by-step explanation:

Step(i):-

Given equation

  [tex]\sqrt{x+6-4} = x[/tex]

squaring on both sides , we get

[tex](\sqrt{x+2})^{2} = x^{2}[/tex]

⇒ x + 2 = x²

⇒x² - x -2 =0

Step(ii):-

  Given x² - x -2 =0

⇒ x² - 2x + x - 2 =0

⇒ x ( x-2) + 1(x - 2) =0

⇒ (x + 1) ( x-2) =0

⇒ x = -1 and x =2

x = 2 is the solution of the given equation

Verification:-

[tex]\sqrt{x+6-4} = x[/tex]

Put x= 2

[tex]\sqrt{2+6-4} = 2[/tex]

[tex]\sqrt{4} = 2[/tex]

 2 = 2

Answer: $5.96

Step-by-step explanation:

4.99 + 0.46 + 0.89 is what she paid, not with tax. That equals 6.34.

Applying 6% means we calculate 6% of 6.34 and then subtract it from 6.34. (Or, we can also calculate 100-6%=94% of 6.34). Either way, the answer is 5.9596, or rounded, 5.96.

Hope that helped,

-sirswagger21

Answer:

Below.

Step-by-step explanation:

18. Since A is congruent to B, you can conclude that B is congruent to A by the Reflexive Property of Congruence.

Answer: find the solution in the explanation

Step-by-step explanation:

Let's use resolution of forces by resolving into x - component and y- component.

X - component.

Sum of forces = F1 - F3 - F4cos 15

Sum of forces = 0

5 - 5 - 0.97F4 = 0

- 0.97 F4 = 0

F4 = 0

Y - component

Sum of forces = F2 + F4 sin 15

Sum of forces = 0

5 + 0.26F4 = 0

0.26 F4 = -5

F4 = -5/0.26

F4 = -19.23 N

Simulating F4 back into the equation

Sum of forces = F1 - F3 - F4cos 15

- F4cos Ø = 0

- (-19.23) cos Ø = 0

Cos Ø = 0

Ø = 1

Does the angle formed approximate 15 degrees ? NO

Answer:

Dear user,

Answer to your query is provided below

Scientific notation = 1.8x10^0

Step-by-step explanation:

This is usually expressed simply as 1.8 (Recall that 10^0 = 1.)

1.8×10^0

Answer:

3 3/5 hours.

Step-by-step explanation:

There are 3 students who logged 1 1/5 so:

[tex]1\frac{1}{5} +1\frac{1}{5} +1\frac{1}{5} =3\frac{3}{5}[/tex]

3 3/5 hours have been logged total by those who logged 1 1/5 hours.

Answer:

Do you mean "Riley has a farm on a rectangular piece of land that is  200   meters wide. This area is divided into two parts: A square area where she grows avocados (whose side is the same as the length of the farm), and the remaining area where she lives.  

Every week, Riley spends  $3  per square meter on the area where she lives, and earns  $7  per square meter from the area where she grows avocados. That way, she manages to save some money every week." ?

The answer is 7L^2>3l(200-l)

Answer:

4/25

Step-by-step explanation:

The probability the first spin lands on gray is 8/10 = 4/5.

The probability the second spin lands on blue is 2/10 = 1/5.

The probability of both events is 4/5 × 1/5 = 4/25.