The perimeter of the scalene triangle is 54. 6 cm. A scalene triangle where all sides are different lengths. The base of the triangle, labeled 3 a, is three times that of the shortest side, a. The other side is labeled b. Which equation can be used to find the value of b if side a measures 8. 7 cm? 8. 7 plus b equals 54. 6 17. 4 plus b equals 54. 6 26. 1 plus b equals 54. 6 34. 8 plus b equals 54. 6.

Answer:

E = 8

Step-by-step explanation:

y - x = 4

y - (3y) = 4

y - 3y = 4

2y = 4

y = 4/2

y = 2

x = 3y

x = 3×2

x = 6

x + y = 2+6

x+y = 8

The average effect size of each gene on the trait would be 17.6 / 100 = 0.176 grams, and the minimum number of genes affecting this trait would be estimated as 2.47.

To estimate the minimum number of genes affecting this trait, we can use Falconer's formula:

Vg = (n/2) * (1/n) * (π * a)^2,

where:

Vg is the genotypic variance

n is the number of genes affecting the trait

a is the average effect size of a single gene on the trait

We can rearrange this formula to solve for n:

n = 2 * Vg / (π * a)^2

Given that Vg = 0.88, and the difference in mean phenotype between the two strains is 17.6 grams, we can estimate a as follows:

a = 17.6 / (number of genes affecting the trait)

Substituting a in the formula for n, we get:

n = 2 * Vg / (π * (17.6/n))^2

Simplifying this expression, we get:

n = 2 * 0.88 / (π * (17.6/n))^2

n = 0.5 / (π^2 * (17.6/n)^2)

We can now use trial and error or iterative methods to solve for n. For example, we can plug in different values of n until we find a value that satisfies the equation.

Let's try n = 100:

n = 0.5 / (π^2 * (17.6/100)^2)

n = 0.5 / (3.1416^2 * 0.176^2)

n = 2.47

This means that if 100 genes were involved, the average effect size of each gene on the trait would be 17.6 / 100 = 0.176 grams, and the minimum number of genes affecting this trait would be estimated as 2.47. However, this is just an estimate and the actual number of genes affecting the trait may be different.

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Answer:9 cm long

Step-by-step explanation:

7 + 2 = 9

so that will be the total

Answer:

14b+2c-8

Step-by-step explanation:

Step-by-step explanation:

4b + 2(5b + c) - 8

= 4b + 10b + 2c - 8

= 14b + 2c - 8

= 2(7b + c - 4).

Answer:

y = 2x+2

Step-by-step explanation:

Answer:

Step-by-step explanation:

Find the y-intercept first, then, from that point, go tide over run to find your slope. This line has a positive slope, so count up two and over one (2/1). After that, input what data you've collected into your equation (y = mx + b) and you'll have your answer.

Answer: |t - 15| ≤ 30 ; -30 ≤ t - 15 ≤ 30

Step-by-step explanation:

To set up the equation, we have to find the center, and the tolerance, so that we can use formula "|x - c| ≤ t"

First, we can find the tolerance by adding both number, then dividing by 2 --> -15 + 45 = 30 --> 30/2 = 15, so we now know that the center is 15

Next, we can find the tolerance by finding the distance between the center and one of the number --> 15 - (-15) = 30, so we now know that the tolerance is 30

Now we can set up our equation,

center (c) = 15

tolerance (t) = 30

|t - 15| ≤ 30

Now that we have our equation, we can set up the inequality

|x - c| ≤ t = -t ≤ x - c ≤ t

so,

-30 ≤ t - 15 ≤ 30

Hope this helps!

(sorry it was so long)

According to Baddeley and Hitch's research, the most important factor in determining whether rugby players will remember a particular game is the amount of time that has elapsed since the game was played.

Specifically, players were more likely to remember games that occurred early in the season and those that were particularly important or emotionally charged, while they were less likely to remember games that occurred later in the season or those that were less meaningful or emotionally significant.

This phenomenon is known as the "serial position effect" and has been observed in other contexts as well.

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Let's begin by identifying key information given to us:

Length of beachfront before storm = 5,

Answer:

y=2x-2

Step-by-step explanation:

m=(y2-y1)/(x2-x1)

m=(6-(-6))/(4-(-2))

m=(6+6)/(4+2)

m=12/6

m=2

y-y1=m(x-x1)

y-(-6)=2(x-(-2))

y+6=2(x+2)

y=2x+4-6

y=2x-2

Note that the slope-intercept form is y=mx+b where m=slope and b=y-intercept.

The probability that a 5-card straight will be drawn from a standard deck of 52 cards if the first three cards drawn are the 2 of spades, the 4 of diamonds, and the 6 of diamonds is 0.005.

A standard deck has 52 cards.

In this case, three cards are already drawn from the deck, which are the 2 of spades, the 4 of diamonds, and the 6 of diamonds. Thus, remaining number of cards=  49.

Probability of getting first card: 1/4

Probability of getting the second card from same suit= 1/13+ 1/13+ 1/12+ 1/11= 563/1716

Probability of getting the third card from same suit= 1/12+1/12+ 1/11+ 1/10= 472/ 1320

Probability of getting the fourth card from same suit= 1/11+ 1/11+ 1/10+ 1/9= 389/ 990

Probability of getting the fifth card from same suit= 1/10+ 1/10+ 1/9+ 1/8= 314/ 720

Therefore, total probability of the event that a 5-card straight will be drawn,

= (1/4)* (563/1716)* (472/ 1320)* (389/990)* (314/720)

= 0.005

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Step-by-step explanation:

4-(-4x-3) > 36

4 + 4x +3 > 36

4x + 7 > 36

4x > 36-7

4x > 29

x > 29/4

m=-4. Or atleast that’s what I’ve heard.

Answer:

4 / 9.5

Step-by-step explanation:

16 / 4 = 4

38 / 4 = 9.5

The required equation is, y = 4 + x.

Hence, The correct answer would be an option (A).

The equation is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are equal.

Now, Jayne stopped for gas before embarking on a road trip.

There were already 4 gallons of gas in the tank.

Hence, As per the question, the required equation would be as:

⇒ y = 4 + x

Thus, This equation relates the total amount of gasoline in the tank, y, to the number of gallons that she put in the tank, x. The total amount of gasoline in the tank, y, is equal to the number of gallons that she put in the tank, x, plus the 4 gallons that were already in the tank.

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Answer:

The function g(x) that outputs a y value to satisfy the equation -4·x - 6 = -5·y + 2 is g(x) = y = 4/5·x + 8/5

Step-by-step explanation:

The y value of the equation that the required function g(x) outputs = -4·x - 6 = -5·y + 2

Therefore, we have;

-4·x - 6 = -5·y + 2

-5·y + 2 = -4·x - 6

-5·y = -4·x - 6 - 2 = -4·x - 8

Therefore, y = (-4·x - 8)/(-5) = 4/5·x + 8/5

y = 4/5·x + 8/5

Which gives;

g(x) = y = 4/5·x + 8/5

Therefore;

The function g(x) that outputs a y value to satisfy the equation -4·x - 6 = -5·y + 2 is g(x) = y = 4/5·x + 8/5

Answer:

76

Step-by-step explanation:

Calculation of the discriminant of the polynomial : 2−10⋅x+3⋅x2

The discriminant of the polynomial 2−10⋅x+3⋅x2 is equal to 76

Answer:

76

Step-by-step explanation:

Given a quadratic equation in standard form (ax² + bx + c = 0 , a ≠ 0 ), then

the discriminant is

Δ = b² - 4ac

Given

3x² - 10x = - 2 ( add 2 to both sides )

3x² - 10x + 2 = 0 ← in standard form

with a = 3, b = - 10, c = 2 , then

b² - 4ac = (- 10)² - (4 × 3 × 2) = 100 - 24 = 76

Answer:

-25/9

Step-by-step explanation:

1 + (-2/3) - m

Plug in:

1 + (-2/3) - 9/2

1 + 2/3 - 9/2

1/3 - 9/2

-25/9

Hope this helped.

Answer:

4 5/6

Step-by-step explanation:

1+-2/3--m

Subtracting a negative is like adding

1-2/3 +m

1/3+m

m = 9/2

1/3 +9/2

Get a common denominator of 6

1/3 *2/2 +9/2*3/3

2/6 + 27/6

29/6

Changing to a mixed number

4 5/6

Answer:

Step-by-step explanation:

To find the perimeter of an equilateral triangle is equalled to 3s.

35 x 3

105

The odds for and against the event of rolling a fair die and getting a 6 or 5 can be found by calculating the probability of the event and its complement. Probability of getting a 6 or 5 on a die = 2/6 = 1/3Probability of not getting a 6 or 5 on a die = 4/6 = 2/3Odds in favor of getting a 6 or 5 on a die can be calculated as the ratio of the probability of getting a 6 or 5 to the probability of not getting a 6 or 5.

Hence, odds in favor of getting a 6 or 5 are (1/3)/(2/3) = 1:2.Odds against getting a 6 or 5 on a die can be calculated as the ratio of the probability of not getting a 6 or 5 to the probability of getting a 6 or 5. Hence, odds against getting a 6 or 5 are (2/3)/(1/3) = 2:1. Thus, the odds in favor of rolling a fair die and getting a 6 or 5 are 1:2, and the odds against it are 2:1.

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To accumulate $2,176,097.00 in his retirement account by age 65, Derek needs to make annual deposits of $5,000.00 starting on his 27th birthday and ending on his 65th birthday, assuming an 8.00% interest rate.

To determine the annual deposits Derek needs to make, we can use the future value of an ordinary annuity formula. First, we calculate the number of years between Derek's 25th and 65th birthdays, which is 65 - 25 = 40 years. Next, we calculate the future value of the retirement account using the given interest rate of 8.00%. Using the formula:

Future Value = Present Value * (1 + interest rate)^number of periods

In this case, the future value is $2,176,097.00, the interest rate is 8.00%, and the number of periods is 40. We can rearrange the formula to solve for the present value:Present Value = Future Value / (1 + interest rate)^number of periods

Substituting the values:Present Value = $2,176,097.00 / (1 + 0.08)^40 = $123,529.31 (rounded to 2 decimal places)

Now, we need to find the annual deposit amount. Since Derek starts making deposits on his 27th birthday and ends on his 65th birthday, he makes deposits for 65 - 27 = 38 years.Annual Deposit = Present Value / ((1 + interest rate)^number of periods - 1)Substituting the values:

Annual Deposit = $123,529.31 / ((1 + 0.08)^38 - 1) = $5,000.00 (rounded to 2 decimal places)Therefore, Derek must make annual deposits of $5,000.00 into his retirement account starting on his 27th birthday and ending on his 65th birthday to accumulate $2,176,097.00 by the time he turns 65.

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Answer:

t(x) = 5 + 2x

Step-by-step explanation:

t(x) = 5 + 2x

Since the 5 is a constant, u just put the 5 there first. Then for every mile, 2 dollars therefore 2x

Answer:2x+5 x would be the number of miles driven

Step-by-step explanation:$305. Plug in 150 for x, and the equation is 2*150+5=x, x being your answer that you are looking for. Do the Order of Operations, which is PEMDAS (Parenthesis, Exponents, Multiplication and Division from left to right, Addition and Subtraction from left to right.) So in other words, do 2*150 first, and you get 300. Now your equation is 300+5=x. Add 300+5, and you get 305=x. So your answer is $305.

Answer: $5.14

Step-by-step explanation:

divide $539.70 by 105 to get the answer

so 539.70 divide by 105 is 5.14

step1 get rid of the decimal but you will ad it later so

53970

/   105

=514

step2 move the decimal 2 places to the left.

Answer:

There should be an order of 5 boxes of pizza.

Step-by-step explanation:

Since there are 10 slices of pizza in each box, then there should be 2 people per box.

10 divided by 2 = 5 Boxes of pizza

According to the information, it can be inferred that there is a correlation between the data because they vary, however the variation is not constant.

Based on the information in the table, we can see the average minutes spent by different people (of different ages) watching television and reading. In the case of reading, there is evidence of a constant increase in the time spent reading as age increases. In the case of television, the variable tends to rise, however it is not a constant increase.

Due to the above, we can establish that the relationship of the data is a correlation because in a certain way age can influence the number of minutes that a person spends reading or watching television. However, it is not the only factor that influences. Other factors that could influence are free time, time at work, time at school or university, time in other hobbies, among others.

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Answer:

\(\frac{2x^{2} }{{25} } + \frac{2y^{2}}{{25} } = 1\)

Step-by-step explanation:

Since the required hyperbola has its vertex at (5,0), its transverse axis is on the x-axis and center at (0,0).

So, we use the equation in standard form

\(\frac{x^{2} }{a^{2} } + \frac{y^{2} }{b^{2} } = 1\)

Also, since the path of the space probe gets closer to y = -x, this is the asymptote to the hyperbola.

Our standard asymptote equation is y = ±bx/a taking the negative sign and comparing with y = -x,

-bx/a = -x ⇒ b/a = 1 ⇒ a = b

Also, the coordinate of the vertex (c, 0) = (5, 0) and c² = a² + b²

substituting c = 5 and a = b into the equation, we have

c² = a² + b²

5² = a² + a²

25 = 2a²

a² = 25/2

a = √(25/2)

a = ±5/√2

rationalizing, we have

a = ±5/√2 × √2/√2

a = ±5√2/2

Since a = b, b = ±5√2/2

Inserting a and b into the equation for the hyperbola, we have

\(\frac{x^{2} }{a^{2} } + \frac{y^{2} }{b^{2} } = 1\\\frac{x^{2} }{(\frac{5\sqrt{2} }{2} )^{2} } + \frac{y^{2} }{\frac{5\sqrt{2} }{2} ^{2} } = 1\\\frac{x^{2} }{\frac{25 X 2 }{4} } + \frac{y^{2} }{\frac{25X2 }{4} } = 1\\\frac{x^{2} }{\frac{25}{2} } + \frac{y^{2} }{\frac{25}{2} } = 1\\\frac{2x^{2} }{{25} } + \frac{2y^{2}}{{25} } = 1\)

So, the required equation is

\(\frac{2x^{2} }{{25} } + \frac{2y^{2}}{{25} } = 1\)