Write the ratio as a fraction in lowest terms.
Compare in inches.
4 feet to 49 inches

Answer:

-4

Step-by-step explanation:

The equation for slope is:

[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]

m: Slope

(6, 2) = [tex](x_1, y_1)[/tex]

(4, 10) = [tex](x_2, y_2)[/tex]

Substitute these values into the equation:

[tex]m=\frac{10-2}{4-6}=\frac{8}{-2}=-4[/tex]

Therefore the slope is -4.

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[tex]\Large\maltese\underline{\textsf{A. What is Asked}}[/tex]

What is the slope of the line that passes through the points? 2 points given

[tex]\Large\maltese\underline{\textsf{B. This problem has been solved!}}[/tex]

The formula used here, is [tex]\bf{\dfrac{y2-y1}{x2-x1}}[/tex].

[tex]\rule{300}{1.7}[/tex]

[tex]\bf{\dfrac{10-2}{4-6}}[/tex] | subtract

[tex]\bf{\dfrac{8}{-2}}[/tex] | evaluate

[tex]\bf{-4}[/tex]

[tex]\rule{300}{1.7}[/tex]

[tex]\bf{Result:}[/tex]

           [tex]\bf{=Slope\;-4}[/tex]

[tex]\boxed{\bf{aesthetic\not101}}[/tex]

Answer:

10

Step-by-step explanation:

There are ten zeros therefore in standard form it is 1 x 10 to the power of 10 or [tex]10_{12}[/tex]

Answer:

pi [π] is the ratio of a circle's circumference to its diameter, and it is constant [meaning it is always the case] for all circles.

{this is a long number, 3.141592653589793238... is not even the full length, but 3.14 [or 3.14159] is typically used for estimation}

The significance of pi is typically centered in math--it can be used to find values that we don't know of circles. There are other areas of math that have been related back to the value of pi--which is incredible, and genuinely relevant.

We can find pi in the shape of rivers, physics--including waves--DNA

[+ anywhere there is a circle]

hope this helps!! :)

Answer:

ratio of circle's circumference to diameter

it is constant

∠A ≅ ∠D , BC≅ EF , AC ≅   DF  , option B , C , F are the correct answer.

CPCTC stands for corresponding parts of congruent triangles are congruent .

This means when two triangles are congruent then the corresponding sides are also congruent.

In the given triangles , Δ ABC ≅ ΔDEF

∠A ≅ ∠D

BC≅ EF

AC ≅   DF

Therefore option B , C , F are the correct options

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The probability for part (a) is 0.131, for part (b) is 0.795, for part (c) is 0.0733.

It is defined as the ratio of the number of favorable outcomes to the total number of outcomes, in other words, the probability is the number that shows the happening of the event.

We have:

41% of adults say cashews are their favorite kind of nut.

P = 41% = 0.41

Q = 1 - P = 1 - 0.41 = 0.59

n = 2

From the binomial distribution:

[tex]\rm P(X = r) = C(n, r) P^r(1-P)^{n-r}[/tex]

a) Exactly​ three

[tex]P(X=3) = C(12, 3) (0.41)^3(0.59)^9[/tex]

P(X = 3) = 0.131

b) At least​ four:

P(X≥4) = P(X=4)+ P(X=5)+ P(X=6)+..............+ P(X=13)

[tex]\rm P(X\geq 4)=C(12, 4) (0.41)^4(0.59)^9+C(12, 5) (0.41)^5(0.59)^8+...............+C(12, 3)(0.41)^3(0.59)^9[/tex]

P(X ≥ 4) = 0.795

c) At most two:

P(X≤2) =P(X=0)+ P(X=1)+ P(X=2)

[tex]\rm =C(12, 0) (0.41)^0(0.59)^12+C(12, 1) (0.41)^1(0.59)^1^1+C(12, 2)(0.41)^2(0.59)^1^0[/tex]

P(X ≤ 2) = 0.0733

Thus, the probability for part (a) is 0.131, for part (b) is 0.795, for part (c) is 0.0733.

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Answer:

2.6 hours

Step-by-step explanation:

Let t be the time that the trains meet.

[tex]90t = 416 - 70t[/tex]

[tex]160t = 416[/tex]

[tex]t = 2.6[/tex]

Using proportions, it is found that it would take 55 hours for him to make $720.50.

A proportion is a fraction of a total amount, and the measures are related using a rule of three.

He is paid $524 for a 40 hour work week, hence per hour he earns?

r = 524/40 = $13.1.

The amount of hours he would need to make $720.50 is given by:

h = 720.50/13.1 = 55.

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Answer:

40 meters

Step-by-step explanation:

The maximum distance between the runners at any given time 40 meters. Therefore, option C is the correct answer.

Given that, Addison and Kelsey are running on a path modeled by x² + y² - 14x - 16y - 287 = 0.

The equation of circle provides an algebraic way to describe a circle, given the center and the length of the radius of a circle. The equation of a circle is different from the formulas that are used to calculate the area or the circumference of a circle.

The standard equation of a circle with center at (x1,y1) and radius r is (x-x1)²+(y-y1)²=r²

Here, the circular path is modeled by x² + y² - 14x - 16y - 287 = 0

We complete the squares to place it in the standard format, thus:

x² - 14x + 49 + y² - 16y +64 = 287+49+64

⇒ (x-7)² + (y-8)² = 400

⇒ (x-7)² + (y-8)² = 20²

So, r² = 20²

⇒ r = 20 meters

Maximum distance = d = 2r

= 40 meters

The maximum distance between the runners at any given time 40 meters. Therefore, option C is the correct answer.

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Answer:

The square root of -1 is i

Step-by-step explanation:
"i" is the imaginary unit and represents the value of sqrt -1

Then the money borrowed insurance company is $1,000.

Money borrowed from insurance company = $1000

Let the money borrowed by her friend at 8% interest = x

Then the money borrowed by the bank at 9% interest = 2x

Total money borrowed = $10,000

So, the money borrowed from the insurance company = 10,000-(2x+x)

= 10,000-3x

Total interest for the first year = $830

We have the equation,

8%(x) + 9%(2x) +5% (10,000-3x) = 830

8x+18x+50,000-15x = 83,000

11x = 83000-50000

11x = 33,000

x = $3000

Then the money borrowed insurance company = 10,000-3x

Then the money borrowed insurance company is $1,000.

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Answer:

A,C,E

(if you find a better answer choose that.)

Step-by-step explanation:

This one has two acute angles and one obtuse.

This one is a scalene.

So, tick A,C,E

Answer: [tex](-\infty, -3)[/tex]

Step-by-step explanation:

[tex]2w-2 < -8\\\\2w < -6\\\\w < -3[/tex]

[tex]4w+3 < 11\\\\4w < 8\\\\w < 2[/tex]

So, the solution is [tex](-\infty, -3)[/tex]

Total: 48

DIning Hall: 48(3/8)=18

so theres 30 left for the classes

30/5(#of classes)=6 per class

The terminal points when the value of r is 1 will be 0.5 and 0.86 and the value of tan 60 will be 1.732.

An angle measure is the measurement of the angle created by two rays or arms at a shared vertex in geometry. A protractor is used to measure angles in degrees (°).

Given;

Ø = 60°

Let's assume the value of r = 1 units

The terminal points are;

x= rcosΘ

x=1 × cos 60°

x=0.5

y=rsinΘ

y=rsin60°

y = 0.86

The terminal points when the value of r is 1 will be 0.5 and 0.86.

The value of the tan for the given value of the angle;

Tan 60° = 1.732

Hence, the terminal points when the value of r is 1 will be 0.5 and 0.86 and the value of tan 60 will be 1.732.

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The answer is A. Complex number

Answer:

X = 14

Let the unknown no. be X

mean= sum of all no. / no. of terms

17 = 15 + 17 + 20 + 22 + X+ X / 6

17 * 6 = 74 + 2X

102 - 74 = 2X

28 = 2X

28/2 = X

14= X

The values of x for which the expression [tex](x^{2} +4x+32)/(x^{2} -x-10)(2x^{2} +4x^{3} )+4x^{3} /x^{2} +3x/x^{2} +3x+2/x[/tex]is undefined are 0,[tex]\sqrt{41} /2[/tex] and imaginary numbers.

Given Expression :x^2+4x+32/x^2−x−10∗2x^2+4x^3/x^2+3x÷x^2+3x+2/x

We have to find out those values of x for which the expression does not exists.

[tex](x^{2} +4x+32)/(x^{2} -x-10)(2x^{2} +4x^{3} )+4x^{3} /x^{2} +3x/x^{2} +3x+2/x[/tex]

We have to take LCM of the expression which is equal to [tex]x^{3}(x^{2}-x-10)(2x^{2} +4x^{3})[/tex]

LCM is the smallest positive integer that is divisible by both the numbers whose LCM is found.

and it is present in the denominator.

Expression if exists cannot take denominator equal to 0.

So, by putting  LCM equal to zero we find

x=0,x=imaginary numbers and x=[tex]\sqrt{41} /2[/tex].

Hence the given expression have not take values of x=0,[tex]\sqrt{41} /2[/tex], imaginary number.

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Answer:

b. y = x - 3

Step-by-step explanation:

The general form of the equation of the line is y = mx + c.

1) Find for m (gradient) using the following formula:

m = y2 - y1 / x2 - x1

Substitute the values into it and solve for m.

m = 2 - 1 / 5 - 4

m = 1 / 1

m = 1

2) Substitute into m of the y = mx + c.

y = 1x + c

3) Choose one the coordinates that the line goes through ((4, 1) or (5, 2)) to find c (y-intercept). I will choose (4, 1). Then, substitute your chosen coordinates into your newfound equation (y = 1x + c)

1 = 1(4) + c

1 = 4 + c

1 - 4 = c

-3 = c

Substitute -3 in place of c.

y = 1x - 3, which can be simplified to y = x - 3. Therefore, the correct choice is b.

Using a system of equations, it is found that the number of golfers in the cafeteria is of 5.

A system of equations is when two or more variables are related, and equations are built to find the values of each variable.

In this problem, the variables are:

The number of baseball players is one less than twice the number of golfers, hence:

x = 2y - 1.

Since x = 9:

9 = 2y - 1

2y = 10

y = 5.

There are 5 golfers in the cafeteria.

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Answer:

(-4,-3)

Step-by-step explanation:

The point where those 2 equations intersect is (-4,-3)

Answer:

3.5 km

Step-by-step explanation:

Answer:

option N is the correct option, apply Formula of area of rectangle and triangle by splitting figure into 2 parts

Step-by-step explanation:

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About 492 pounds of milk and egg were consumed each year

Given the following parameters from the chart

Total consumption = 1640 pounds per person

The percentage of milk and egg = 100 -(38 + 10 + 10 +8 + 4)

The percentage of milk and egg = 30%

Determine the amount consumed each year

Amount of milk and egg consumed = 30% of 1640

Amount of milk and egg consumed = 492 pounds

Hence about 492 pounds of milk and egg were consumed each year

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Answer:

Last one/D 9^9/5/5^9/10

Step-by-step explanation:

In a study of birth orders and intelligence, IQ tests were given to 18 and 19 years old men to estimate the size of the difference, we have that  [tex]|t|=0.618\leq t_c =2.101[/tex] and for this reason, we cannot reject the null hypothesis.

Null and Alternative Hypotheses

[tex]H_o: \mu_{1} = \mu_{2}\\\\Ha: \mu_1 \neq \mu_2 .[/tex]

Since the population standard deviations are unknown, we will apply a t-test on the means of the two populations, using two independent samples.

The degrees of freedom are df = 18, and the significance threshold is set at alpha = 0.05, based on the data presented. If we assume that the population variances are the same, we can calculate the degrees of freedom in this way:

The rejection region for this two-tailed test is R = \{t : |f| > 2.101}

Therefore the Test Statistics is

[tex]t= \frac{X 1 -X 2 }{\frac{\sqrt{ (n_1 -1)s_1 ^ 2 +(n_2 -1)s_2 ^2}} {n_1 +n_2 -2} (( 1/n_1 + 1 n_2 )}}[/tex]

[tex]t= \frac{X 1 -X 2 }{\frac{\sqrt{ (n_1 -1)s_1 ^ 2 +(n_2 -1)s_2 ^2}} {n_1 +n_2 -2} (( 1/n_1 + 1 n_2 )}}[/tex]

t=0.618

In conclusion. we have that  [tex]|t|=0.618\leq t_c =2.101[/tex]

For this reason, we cannot reject the null hypothesis.

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Answer: The player expects to lose 184.21 dollars.

=========================================================

Explanation:

X = net winnings in dollars

Ignore the "28" because it's really not that relevant here. All we care about is the probability 1/38 which is the probability of winning money. The probability of losing money is 1 - (1/38) = 37/38. Put another way: there's 1 way to win, and 37 ways to lose.

If the player wins, then they walk away with 7+245 = 252 dollars

If the player loses, then their "winnings" is -7

So either X = 252 or X = -7 are the only two options.

Let's form a table showing those options with their corresponding probabilities.

[tex]\begin{array}{|c|c|} \cline{1-2}X & P(X)\\\cline{1-2}252 & 1/38\\\cline{1-2}-7 & 37/38\\\cline{1-2}\end{array}[/tex]

Now multiply each X value and P(X) value across the rows.

252*(1/38) = 6.631579

-7*(37/38) = -6.815789

These values are approximate.

[tex]\begin{array}{|c|c|c|} \cline{1-3}X & P(X) & X*P(X)\\\cline{1-3}252 & 1/38 & 6.631579\\\cline{1-3}-7 & 37/38 & -6.815789\\\cline{1-3}\end{array}[/tex]

Add up the results of the third column

6.631579 + (-6.815789) = -0.18421

This represents the net winnings for any average spin of the wheel. The player unfortunately expects to lose, on average, about $0.18421 or 18.421 cents per spin.

Do this 1000 times and the player should expect to lose about

1000*(0.18421) = 184.21 dollars

Keep in mind that due to the random nature of roulette wheel, the player may get lucky or their luck may be worse than what is described. The idea is that over the long run, the average should be somewhat close to losing 184.21 dollars.

Another way to think of it could be to have 1000 players doing the same game (rather than have 1 person play the same game 1000 times). Some players may get lucky, while others may not get so lucky. But their collective average should be losing that $184.21