Simultaneous equations 5x-4y=19
x+2y=8

Answer:

What function?

Step-by-step explanation:

Answer:

Yes it is very good for establishing identities.

Step-by-step explanation:

Since its a very preferable start it is a very good way to establish identity.

Answer:

1984

Step-by-step explanation:

Answer:

6/7

Step-by-step explanation:

7 days make a week. 7 would go into the denominator and 6 would go in the numerator. 6 is the amount of days through the week that it is dry.

Answer:

6/7

Step-by-step explanation:

[tex]\frac{number \ of \ dry \ days}{total \ number \ of \ days \ in \ a \ week} =\frac{6}{7}[/tex]

Hi there!

[tex]\large\boxed{f(9) = 12}[/tex]

Evaluating f(x) at x = 9 means we must use the piecewise function where x = 9 is included.

f(x) = 12 includes 9 because a "≤" is inclusive of the interval. Thus:

f(9) = 12

Answer:

Step-by-step explanation:

Let take a look at the given function y = 4x - 1 whose point is located between (1,3) and (4,15) on the graph.

Here, the function of y is non-negative. Now, expressing y in terms of x in y = 4x- 1

4x = y + 1

[tex]x = \dfrac{y+1}{4}[/tex]

[tex]x = \dfrac{1}{4}y + \dfrac{1}{4}[/tex]

By integration, the required surface area in the revolve is:

[tex]S = \int^{15}_{ 3} 2 \pi g (y) \sqrt{1+g'(y^2) \ dy }[/tex]

where;

g(y) = [tex]x = \dfrac{1}{4}y + \dfrac{1}{4}[/tex]

∴

[tex]S = \int^{15}_{ 3} 2 \pi \Big( \dfrac{1}{4}y + \dfrac{1}{4}\Big) \sqrt{1+\Bigg(\Big( \dfrac{1}{4}y + \dfrac{1}{4}\Big)'\Bigg)^2 \ dy }[/tex]

[tex]S = \dfrac{1}{2} \pi \int^{15}_{ 3} (y+1) \sqrt{1+\Bigg(\Big( \dfrac{1}{4}\Big ) \Bigg)^2 \ dy } \\ \\ \\ S = \dfrac{1}{2} \pi \int^{15}_{ 3} (y+1) \dfrac{\sqrt{17}}{4} \ dy[/tex]

[tex]S = \dfrac{\sqrt{17}}{8} \pi \int^{15}_{ 3} (y+1) \ dy[/tex]

[tex]S = \dfrac{\sqrt{17} \pi}{8} (\dfrac{1}{2}(y+1)^2)\Big|^{15}_{3} \\ \\ S = \dfrac{\sqrt{17} \pi}{8} (\dfrac{1}{2}(15+1)^2-\dfrac{1}{2}(3+1)^2 ) \\ \\ S = \dfrac{\sqrt{17} \pi}{8} *120 \\ \\\mathbf{ S = 15 \sqrt{17}x}[/tex]

Hello!

[tex]\large\boxed{(x + 2)(x + 3)}[/tex]

x² + 5x + 6

Find two numbers that add up to 5 and multiply to 6. We get:

2, 3

Therefore:

(x + 2)(x + 3)

Answer:

C. -4

Step-by-step explanation:

Answer:

(c) - 4

is your right answer

9514 1404 393

Answer:

  ∠4

Step-by-step explanation:

"Alternate" means the angle is on the other side of the transversal t. "Exterior" means it is on the outside of line e crossing the transversal. The alternate exterior angle to angle 8 is angle 4.

Answer: 0.2

Step-by-step explanation: 20/100=1/5

and 1/5 equals 1 divided by five so it is 0.2

9514 1404 393

Answer:

  88 ounces

Step-by-step explanation:

Let x represent the number of ounces of the less expensive alloy in the mix. Then the cost of the mix will be ...

  6.75x +10(55) = 8(55+x)

  110 = 1.25x . . . . . . subtract 440+6.75x

  88 = x . . . . . . . . divide by 1.25

88 ounces of $6.75/oz silver must be used.

9514 1404 393

Answer:

Step-by-step explanation:

Of the items sold, sodas were 2/(2+1) = 2/3 of the total.

  (2/3)(228) = 152 . . . sodas were sold

  152/2 = 76 . . . . hot dogs were sold

Answer:

The expected number of winning balls that Heather draws is 0.3.

Step-by-step explanation:

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

Hypergeometric distribution:

The probability of x successes 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 successes.

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]

Expected value of the hypergeometric distribution:

The expected value is given by:

[tex]E(X) = \frac{nk}{N}[/tex]

Expected number of blue and green balls:

40 balls, which means that [tex]N = 40[/tex]

2 are chosen, which means that [tex]n = 2[/tex]

25 are blue, which means that [tex]k = 25[/tex]

So

[tex]E(X) = \frac{nk}{N} = \frac{25(2)}{40} = 1.25[/tex]

1.25 balls are expected to be blue and 2 - 1.25 = 0.75 green.

Of the blue balls, 12% are winning.

Of the green balls, 20% are winning.

Calculate the expected number of winning balls that Heather draws.

[tex]E_w = 1.25*0.12 + 0.75*0.2 = 0.3[/tex]

The expected number of winning balls that Heather draws is 0.3.

Answer:

0.7

Step-by-step explanation:

67/10 is the same as 6.7 when you subtract the 0.7 you will remain with 6

Answer:

The answer is

x equal -243

Answer:

-243 is yr correct answer.

Step-by-step explanation:

hope it helps

Step-by-step explanation:

2tan 30° / 1 + tan² 30° =

2(⅓√3) /1 + (⅓√3)² =

⅔√3 / 1+ ⅓ =

⅔√3 / 4/3 =

2/4 √3 =

½√3 = sin 60° (proven)

Answer:

0.015 and 3/200.

Step-by-step explanation:

1.5% is equal to 0.015. Percents are always equal to their decimal counterparts; basically, the number over 100. Dividing 1.5 by 100 will yield us 0.015.

0.015 is going to be equal to 15/1000, or 3/200. Since we did 1.5/100, we need to multiply both sides of the fraction by 10 so there are no decimal points. Therefore, this is 15/1000. If we divide both sides of this fraction by 5, then we get 3/200, which is the most simplified form.

Answer:

[tex]Pr= 0.00725[/tex]

Step-by-step explanation:

Given

[tex]p = 0.05[/tex] ---- probability that each component fails

[tex]n = 3[/tex]

Required

[tex]P(System\ Overheats)[/tex]

We understand that the system will overheat if at least 2 component fails; Assume the components are: x, y and z

The events that the system will overheat are: xyz', xy'z, x'yz and xyz

Where ' means that the component did not fail, and the probability is 1 - p (i.e. complement rule)

So, we have:

[tex]xyz' \to 0.05 * 0.05 * (1 - 0.05) = 0.002375[/tex]

[tex]xy'z \to 0.05 * (1 - 0.05)* 0.05 = 0.002375[/tex]

[tex]x'yz \to (1 - 0.05)* 0.05 * 0.05 = 0.002375[/tex]

[tex]xyz \to 0.05 * 0.05 * 0.05 =0.000125[/tex]

So, the required probability is:

[tex]Pr= 0.002375 +0.002375 +0.002375 + 0.000125[/tex]

[tex]Pr= 0.00725[/tex]

9514 1404 393

Answer:

  2√13

Step-by-step explanation:

The distance between the center of the circle and a point on the circle is the radius. That distance is given by the distance formula:

  d = √((x2 -x1)² +(y2 -y1)²)

  d = √((-5 -1)² +(6 -2)²) = √(36 +16) = √52

  d = 2√13

The radius of the circle is 2√13.

Answer:

0.0207 = 2.07% approximate probability of finding at least 157 defects

Step-by-step explanation:

Poisson distribution:

In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following formula:

[tex]P(X = x) = \frac{e^{-\lambda}*\lambda^{x}}{(x)!}[/tex]

In which

x is the number of sucesses

e = 2.71828 is the Euler number

[tex]\lambda[/tex] is the mean in the given interval.

Normal Probability Distribution

Problems of normal distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score 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 p-value, we get the probability that the value of the measure is greater than X.

n instances of a Poisson distribution can be approximated to a normal distribution, with [tex]\mu = n\lambda, \sigma = \sqrt{\lambda}\sqrt{n}[/tex]

The average defect rate on a 2010 Volkswagen vehicle was reported to be 1.33 defects per vehicle.

This means that [tex]\lambda = 1.33[/tex]

Suppose that we inspect 100 Volkswagen vehicles at random.

This means that [tex]n = 100[/tex]

Mean and standard deviation:

[tex]\mu = n\lambda = 100*1.33 = 133[/tex]

[tex]\sigma = \sqrt{\lambda}\sqrt{n} = \sqrt{1.33}\sqrt{100} = 11.53[/tex]

What is the approximate probability of finding at least 157 defects?

Using continuity correction(Poisson is a discrete distribution, normal continuous), this is [tex]P(X \geq 157 - 0.5) = P(X \geq 156.5)[/tex], which is 1 subtracted by the p-value of Z when X = 156.5. So

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

[tex]Z = \frac{156.5 - 133}{11.53}[/tex]

[tex]Z = 2.04[/tex]

[tex]Z = 2.04[/tex] has a p-value of 0.9793.

1 - 0.9793 = 0.0207

0.0207 = 2.07% approximate probability of finding at least 157 defects

Answer:

See Explanation

Step-by-step explanation:

According to the Question,

Given that, A retired couple has up to $50,000 to invest. As their financial adviser, you recommend that they place at least $35,000 in Treasury bills yielding 1% and at most $10,000 in corporate bonds yielding 3%.

Therefore,

Let, x be the amount of money invested in Treasury bills

y be the amount invested in corporate bonds

Thus, the system of equations of linear inequalities is

x + y ≤ 50000

x ≥ 35000

0 ≤ y ≤ 10000

For, the graph of the system of equations of linear inequalities describes the possible amounts of each investment.

(Please find in the attachment)

Answer:

It is A and B

Step-by-step explanation:

Answer:

the second option : ST and WX

Step-by-step explanation:

congruent means they would completely cover each other when oriented in the same direction and positioned at the same location.

after dying the two mirroring actions we get

VS correlates to ZW

ST correlates to WX

TU correlates to XY

UV correlates to ZY

Answer:

Place the event

But he sobered down when he saw that Jimmy was wounded.

Jimmy comes

up with the plan of curing the Emperor by telling him to eat watermelon.

The Emperor fa

lls sick with dysentery, which has plagued the kingdom.

The Emperor is cured after eating a few slices of fresh watermelon.

The next day, the page asks the Emperor t

o consume a slice of watermelon as a cure.

↓

↓

Reset Submit

Step-by-step explanation:

Answer:

-18

Step-by-step explanation:

B=-6 C=2 P.E.M.D.A.S.

b - 6(c)

-6 - 6(2)

-6 - 12 . The negatives cancel out, adding each other

-6 + -12

= -18 :)

Answer:

b - 6c

= -6 - 6x2

= -6 x( 1+2)

= -6x3

= -18

Answer:

y = 5/4 x - 23/4

Step-by-step explanation:

4x + 5y = 31

5y = - 4x +31

y = -4/5 x + 31/5

⊥ slope = 5/4

-7 = 5/4 (-1) + B

-28 = -5 + 4b

-23 = 4B

b = -23/4

You'll need 2 more lines to complete this two column proof.

---------------------

Line 4

For the "statement" portion, you'll say something like [tex]\angle 2 \cong \angle 3[/tex]

The reason for this statement is "transitive property"

We're basically combining lines 1 and 3 to form this new line.

The transitive property is the idea that if A = B and B = C, then A = C. We connect the statements like a chain.

---------------------

Line 5

The statement is what you want to prove since this is the last line.

So the statement is [tex]p || q[/tex]

The reason is "converse of corresponding angles theorem"

As you can probably guess, this theorem says "If two corresponding angles are congruent, then the lines are parallel".

Step-by-step explanation:

ΔABC, where AB = 8 cm, BC = 6 cm, B = 70° Construction: (i) Draw the ∆ABC with the given measurements. (ii) Construct the perpendicular bisector at any two sides (AB and BC) and let them meet at S which is the circumcircle. (iii) S as centre and SA = SB = SC as radius, draw the circumcircle to pass through A, B, and C. Circum radius = 4.3cm .draw-triangle-abc-where-cm-bc-and-70-and-locate-its-circumcentre-and-draw-the-circumcircle