Two consecutive even numbers are such that five times the smaller number , subtracted from eight times the bigger gives 58. Find the two Numbers? show working​

He used 620 gallons of gas

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Answer:

  7 1/75 football fields

Step-by-step explanation:

Multiply it out. The units of feet and yards cancel, leaving football fields.

  = (2104·1·1)/(3·100) football fields ≈ 7.0133... football fields

  = 7 1/75 football fields

Answer: the required sample size =1658944

Step-by-step explanation:

When the prior population proportion for the study is unknown , then the formula for sample size is [tex]Sample \ size = 0.25(\dfrac{z^*}{Margin\ of \ error})^2[/tex]

z-value for 99% confidence = 2.576

[tex]Sample \ size = 0.25(\dfrac{2.576}{0.001})^2\\\\=0.25(2576)^2\\\\=1658944[/tex]

Hence, the required sample size =1658944

Step-by-step explanation:

Question 264138: How many liters of a 40% alcohol solution must be mixed with a 65% solution to obtain 20 liters of a 50% solution? x=8 gallons of 65% solution is used. 20-8=12 gallons of 40% solution is used.

please mark as brainliest

Answer:

x = 1/4

y = -1/2

z = 9/4

Step-by-step explanation:

Here we have a system of 3 equations with 3 variables:

4*x + 2*y + 1 = 1

2*x - y = 1

x + 3*y + z = 1

The first step to solve this, is to isolate one of the variables in one of the equations, let's isolate "y" in the second equation:

2*x - y = 1

2*x - 1 = y

Now that we have an expression equivalent to "y", we can replace this in the other two equations:

4*x + 2*(2*x - 1) + 1 = 1

x + 3*(2*x - 1) + z = 1

Now let's simplify these two equations:

8*x - 1 = 1

7*x - 3 + z = 1

Now, in the first equation we have only the variable x, so we can solve that equation to find the value of x:

8*x - 1 = 1

8*x = 1 + 1 = 2

x = 2/8 = 1/4

Now that we know the value of x, we can replace this in the other equation to find the value of z.

7*(1/4) -3 + z = 1

7/4 - 3 + z = 1

z = 1 + 3 - 7/4

z = 4 - 7/4

z = 16/4 - 7/4 = 9/4

z = 9/4

Now we can use the equation y = 2*x - 1 and the value of x to find the value of y:

y = 2*(1/4) - 1

y = 2/4 - 1

y = 1/2 - 1

y = -1/2

Then the solution is:

x = 1/4

y = -1/2

z = 9/4

Answer:

C. [tex]\frac{}{AB}[/tex]

Step-by-step explanation:

You can solve this in two ways, firstly by eliminating all the wrong answers, and secondly by just knowing that the horizontal line in [tex]_[/tex][tex]\frac{}{AB}[/tex] means that we are talking about a line.

This is how we solve this question by using the eliminating process.

(A. ∠C) is not the right answer because the ∠ sign lets us know that this answer represents an angle, not a line

(B. B) is not the right answer because it represent a point, not a line (in math we use a singular capital letter to represent points)

(D. ΔABC) is not the right answer because the Δ sign lets us know that the answer represents a triangle, not a line.

Therefore, the only option left is C. [tex]\frac{}{AB}[/tex]

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Answer:

  B

Step-by-step explanation:

If the probability of event "A" is 'p', then the probability of the event "not A" is

  P(not A) = 1 - P(A) = 1 - p

For p=0.5, this is ...

  P(not A) = 1 -0.5 = 0.5 . . . . . matches choice B

Answer:

○B. 0.5 is the proof the outcome (not A).

Answer:

1042.5

Step-by-step explanation:

Given :-

Using Unitary Method :-

→ Cost of 1 m is P 69.95

→ Cost of 15m is P ( 69.5 * 15 ) = P 1042.5

Answer:

[tex]b = 74^o[/tex] --- acute base

Step-by-step explanation:

Given

See attachment for the figure

Required

The acute base angle of the trapezoid

From the question, the isosceles triangle and the trapezoid share the same base.

Represent the base angle with b.

So:

[tex]b + b + 32^o = 180^o[/tex] --- angles in a triangle

[tex]2b = 180^o-32^o[/tex]

[tex]2b = 148^o[/tex]

Divide by 2

[tex]b = 74^o[/tex]

Step-by-step explanation:

A. 2(x+4)=2x+8

=G

B. 3(2x-1)=6x-3

=I

C. 4(x+2)=4x+8

=J

D. 2(x+3)=2x+6

=K

E. 3(4x+1)=12x+3

=H

A - G

B - I

C - J

D - K

E - H

HOPE IT HELP

Answer:

prime factorization of 225 = 32•52.

Step-by-step explanation:

The number 225 is a composite number so, it is possible to factorize it. 225 can be divided by 1, by itself and at least by 3 and 5.

A composite number is a positive integer that has at least one positive divisor other than one or the number itself. In other words, a composite number is any integer greater than one that is not a prime number.

Answer: [tex]y=6x-7[/tex]

Step-by-step explanation:

We use the formula y=mx+b to put it into slope-intercept form

m=6 (slope)

b=-7 (y-intercept)

Therefore, the answer is y=6x-7

Answer:

0.2143 = 21.43% probability that a contestant wins the game if he/she gets to select 4 of the buckets.

Step-by-step explanation:

The buckets are chosen without replacement, which means that the hypergeometric distribution is used to solve this question.

Hypergeometric distribution:

The probability of x sucesses is given by the following formula:

[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}[/tex]

In which:

x is the number of sucesses.

N is the size of the population.

n is the size of the sample.

k is the total number of desired outcomes.

Combinations formula:

[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

In this question:

8 covered buckets, so N = 8.

4 buckets are selected, so n = 4.

2 contain a ball, which means that k = 2.

Find the probability that a contestant wins the game if he/she gets to select 4 of the buckets.

This is P(X = 2). So

[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}[/tex]

[tex]P(X = 2) = h(2,8,4,2) = \frac{C_{2,2}*C_{6,2}}{C_{8,2}} = 0.2143[/tex]

0.2143 = 21.43% probability that a contestant wins the game if he/she gets to select 4 of the buckets.

Answer:

Period: [tex]\pi[/tex]

Phase shift: n

Step-by-step explanation:

Tangent function:

Has the following format:

[tex]f(x) = \tan{ax - n}[/tex]

In which the period is [tex]\frac{\pi}{x}[/tex] and the phase shift is n.

In this question:

[tex]f(x) = -4\tan{(x-n)}[/tex]

[tex]a = 1[/tex], and thus, the period is [tex]\pi[/tex], with a phase shift of n.

Answer:

[tex]P(x < 4) = \frac{9}{50}[/tex]

Step-by-step explanation:

Given

[tex]n(S) = 50[/tex]

See attachment for distribution

Required

[tex]P(x < 4)[/tex]

This is calculated as:

[tex]P(x < 4) = \frac{n(1) + n(2) + n(3)}{n(S)}[/tex]

Using the data on the frequency distribution table, we have:

[tex]P(x < 4) = \frac{4 + 2 + 3}{50}[/tex]

[tex]P(x < 4) = \frac{9}{50}[/tex]

Answer:

60m^2 is the answer im pretty sure

Step-by-step explanation:

yeah man thats it

Answer:

Evans would have $852.8

Step-by-step explanation:

Given

[tex]PV = \$800[/tex]

[tex]r = 3.25\%[/tex]

[tex]t = 2[/tex]

[tex]n = 1[/tex] --- annually'

Required

The future value

This is calculated using:

[tex]FV = PV*(1 + \frac{r}{n})^{nt[/tex]

So, we have:

[tex]FV = 800 * (1 + 3.25\%/1)^{2*1}[/tex]

[tex]FV = 800 * (1 + 3.25\%)^{2}[/tex]

[tex]FV = 800 * (1 + 0.0325)^{2}[/tex]

[tex]FV = 800 * (1 .0325)^2[/tex]

[tex]FV = 852.845[/tex]

[tex]FV = 852.8[/tex]

FV =

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Answer:

  B.  (-5, -2)

Step-by-step explanation:

That point is ...

  A + 1/5(B - A)

  = (-7, -4) + 1/5(3 -(-7), 6 -(-4)) = (-7, -4) +1/5(10, 10)

  = (-7, -4) +(2, 2) = (-5, -2)

The point (-5, -2) is 1/5 of the way from A to B.

Answer:alternate exterior angles

Step-by-step explanation:

Since they’re on the outside of the parallel lines that makes them exterior

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Answer:

  30 grams

Step-by-step explanation:

The time 120 seconds is 4 times the half-life of 30 seconds. That means (1/2)^4 = 1/16 of the original amount will remain. That is (480 g)(1/16) = 30 g.

  30 g of the radioactive rhodium will be left

Completing the square gives

[tex]x^2-2x-2=(x-1)^2-3[/tex]

and comparing to [tex]y=x^2[/tex], the graph of [tex]y=x^2-2x-2[/tex] would be a horizontal shift to the right by 1 unit, and a vertical shift down by 3 units.

Hope this help!!!

Have a nice day!!!

Answer:

A) 0.7696

B) 0.0474

C) Yes it's unusual

D) 0.05746

E) No, it is not unusual

F) No, it is not unusual

Step-by-step explanation:

This is a binomial probability distribution question.

We are told that 92.4% of those admitted graduated.

Thus; p = 92.4% = 0.924

From binomial probability distribution, q = 1 - p

Thus;

q = 1 - 0.924

q = 0.076

Formula for binomial probability distribution is;

P(x) = nCx × p^(x) × q^(n - x)

A) At least 11 graduated out of 12.

P(x ≥ 11) = P(11) + P(12)

P(11) = 12C11 × 0.924^(11) × 0.076^(12 - 11)

P(11) = 0.3823

P(12) = 12C12 × 0.924^(12) × 0.076^(12 - 12)

P(12) = 0.3873

P(x ≥ 11) = 0.3823 + 0.3873

P(x ≥ 11) = 0.7696

B) that exactly 9 of them graduated out of 12. This is;

P(9) = 12C9 × 0.924^(9) × 0.076^(12 - 9)

P(9) = 0.0474

C) We are not given significance level here but generally when not given we adopt a significance level of α = 0.05.

Now, exactly 9 out of 12 that graduated which is P(9) = 0.0474.

We see that 0.0474 is less than the significance level of 0.05. Thus, we can say that it is unusual to randomly select 12 students from the special programs and get exactly 9 that graduate

D) that at most 9 of them out of 12 graduated.

P(x ≤ 9) = P(0) + P(1) + P(2) + P(3) + P(4) + P(5) + P(6) + P(7) + P(8) + P(9)

This is going to be very long so I will make use of an online probability calculator to get the values of P(0) to P(8) since I already have P(9) as 0.0474.

Thus, we have;

P(0) = 0

P(1) = 0

P(2) = 0

P(3) = 0.00000001468

P(4) = 0.00000040161

P(5) = 0.00000781232

P(6) = 0.00011081163

P(7) = 0.00115477385

P(8) = 0.00877476184

Thus;

P(x ≤ 9) = 0 + 0 + 0 + 0.00000001468 + 0.00000040161 + 0.00000781232 + 0.00011081163 + 0.00115477385 + 0.00877476184 + 0.04741450256

P(x ≤ 9) = 0.05746

E) P(x ≤ 9) = 0.05746 is more than the significance level of 0.05, thus we will say it is not unusual.

F) from online binomial probability calculator, probability of getting only 9 out of 12 is more than the significance value of 0.05. Thus, we will say it is not unusual

Answer:

Sorry if this is wrong, but seeing the question I think the best answer following the question would be answer B, because for A it shows that 1 hour is 35 miles when it says 70 miles in 1 hour, not C because as the time rises so does the distance, and I checked D and it's wrong.

Step-by-step explanation:

Answer:

x=-10

Step-by-step explanation:

2(x+3)=x-4

2*x+2*3=x-4

2x+6=x-4

2x-x=-4-6

x=-10

Answer:

[tex]x = - 10[/tex]

Step-by-step explanation:

Let's solve:

[tex]2(x+3)=x−4[/tex]

Step 1: Simplify both sides of the equation.

[tex]2(x+3)=x−4 \\ (2)(x)+(2)(3)=x+−4(Distribute) \\ 2x+6=x+−4 \\ 2x+6=x−4[/tex]

Step 2: Subtract x from both sides.

[tex]2x+6−x=x−4−x \\ x+6=−4[/tex]

Step 3: Subtract 6 from both sides.

[tex]x+6−6=−4−6 \\ x=−10[/tex]

Answer:

See Explanation

Step-by-step explanation:

Given

[tex]Reason \to Frequency[/tex]

[tex]Congestive\ heart\ failure \to 990[/tex]

[tex]Coronary\ atherosclerosis\to 1400[/tex]

[tex]Heart\ attack \to 744[/tex]

[tex]Infant\ birth\to 3800[/tex]

Solving (a): Frequency bar graph

To do this, we simply plot the reasons (on the x-axis) against the frequency (on the y-axis).

See attachment

Solving (b): Relative frequency distribution

The relative frequency is calculated as:

[tex]RF = \frac{F}{Total}[/tex]

Where

[tex]Total = 990+1400+744+3800[/tex]

[tex]Total = 6934[/tex]

So, we have:

[tex]Congestive\ heart\ failure \to \frac{990}{6934} = 0.1427[/tex]

[tex]Coronary\ atherosclerosis\to \frac{1400}{6934} = 0.2019[/tex]

[tex]Heart\ attack \to \frac{744}{6934} = 0.1073[/tex]

[tex]Infant\ birth\to \frac{3800}{6934} = 0.5481[/tex]

So, the relative distribution is:

[tex]Reason \to Frequency \to Relative\ Frequency[/tex]

[tex]Congestive\ heart\ failure \to 990 \to 0.1427[/tex]

[tex]Coronary\ atherosclerosis\to 1400 \to 0.2019[/tex]

[tex]Heart\ attack \to 744 \to 0.1073[/tex]

[tex]Infant\ birth\to 3800 \to 0.5481[/tex]

Solving (c): Relative frequency bar graph

To do this, we simply plot the reasons (on the x-axis) against the relative frequency (on the y-axis).

See attachment

Solving (d): Relative frequency Pareto chart

First, calculate the cumulative relative frequency

This is done by adding up the previous relative frequency,

So, we have:

[tex]Reason \to Relative\ Frequency \to Cumulative[/tex]

[tex]Congestive\ heart\ failure \to 0.1427 \to 0.1427[/tex]

[tex]Coronary\ atherosclerosis \to 0.2019 \to 0.2019+0.1427=0.3446[/tex]

[tex]Heart\ attack \to 0.1073\to 0.3446+0.1073 = 0.4519[/tex]

[tex]Infant\ birth \to 0.5481 \to 0.5481+4519 =1[/tex]

So, we have:

[tex]Reason \to Relative\ Frequency \to Cumulative[/tex]

[tex]Congestive\ heart\ failure \to 0.1427 \to 0.1427[/tex]

[tex]Coronary\ atherosclerosis \to 0.2019 \to 0.3446[/tex]

[tex]Heart\ attack \to 0.1073\to 0.4519[/tex]

[tex]Infant\ birth \to 0.5481 \to 1[/tex]

Next, we simply plot the reasons (on the x-axis) against the cumulative relative frequency (on the right) and the left of the Pareto chart.

See attachment