Factor out the coefficient of the variable.

The expression 13b−13 factored is

Part (i)

We can use the slope formula on the points A(0,4) and C(8,0)

\(m = \frac{y_2-y_1}{x_2-x_1}\\\\ m = \frac{0-4}{8-0}\\\\ m = \frac{-4}{8}\\\\ m = -\frac{1}{2}\)

The slope of line AC is -1/2.

Line BM is perpendicular to AC. This indicates we'll apply the negative reciprocal to -1/2 to end up with 2.

The slope of line BM is 2.

Note that the perpendicular slopes multiply to -1. This is true of any perpendicular pair of slopes as long as neither line is vertical nor horizontal.

Answers:

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Part (ii)

The slope of \(\text{line }\text{B}\text{M} \) was m = 2 from the previous part above.

We'll use the coordinates of point B(9,7) along with this slope value to find the equation of \(\text{line }\text{B}\text{M}\).

\(y - y_1 = m(x - x_1)\\\\ y - 7 = 2(x - 9)\\\\ y - 7 = 2x - 18\\\\ y = 2x - 18+7\\\\ y = 2x - 11\\\\\)

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

Part (iii)

The equations for lines \(\text{A}\text{L}\) and \(\text{B}\text{M}\) are \(7y+x = 28\) and \(y = 2x-11\) in that order. Solving this system of equations will produce the location of point P, where the lines intersect.

Let's apply substitution to solve for x.

\(7y+x = 28\\\\ 7( y ) + x = 28\\\\ 7( 2x-11 ) + x = 28 \ \text{ ... y replaced with 2x-11}\\\\ 14x-77+x = 28\\\\ 15x = 28+77\\\\ 15x = 105 \\\\ x = 105/15\\\\ x = 7\\\\\)

Then use this to find the y coordinate.

\(y = 2x-11\\\\ y = 2(7)-11\\\\ y = 14-11\\\\ y = 3\)

The location of point P is (7,3). This is the orthocenter of the triangle where the altitudes intersect.

Answer:

\(\frac{5a^4b^5}{9}\)

Step-by-step explanation:

\(\frac{15a^1^6b^1^1}{(3a^4b^2)^3}\)

\(=\frac{15a^1^6b^1^1}{27a^1^2b^6}\)

\(=\frac{15a^4b^5}{27}\)

\(=\frac{5a^4b^5}{9}\)

Answer = \(=\frac{5a^4b^5}{9}\)  

The number of ways to award the prizes is 5,527,2000

Permutations:  

Permutations are the number of different ways of arranging objects in a definite order. The symbol ⁿPₓ is used to denote the number of permutations of n objects, taken x objects at a time.

Here we have,

Fifty tickets numbered 1, 2, 3,  ... 50 are sold to 50 different people for drawing  

Five prizes are awarded including the grand prize (a trip to the FIFA world soccer championship with two seats )  

No person can get more than one prize

As we know Number of permutations of n things taking m at

a time is given by ⁿPₓ = n!/(n-x)!  

The number of ways of choosing 4 prizes from 50 different people

=>  ⁵⁰P₄ = 50!/(50-4)!  

= 50 × 49× 48× 47× 46! /46!

= 50 × 49× 48× 47 = 5,527,2000      

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Answer:

8.35,7.94

Step-by-step explanation:

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Answer:

to find the number between you just add the numbers and divide by two , hopefully the image above helps !

let me know if you any more explaining :)

To answer this question, we need to know the median and upper quartile of the data set. Once we have these values, we can determine what percentage of the data falls to the right of the median and to the left of the upper quartile.
Let's say the median of the data set is 50 and the upper quartile is 75. To find the percentage of measurements to the right of the median, we need to look at the data values that are greater than 50 and divide that number by the total number of measurements. Let's say there are 40 data values greater than 50 and a total of 100 measurements.

Then, the percentage of measurements to the right of the median would be:

(40/100) x 100% = 40%

To find the percentage of measurements to the left of the upper quartile, we need to look at the data values that are less than or equal to 75 and divide that number by the total number of measurements. Let's say there are 60 data values less than or equal to 75 and a total of 100 measurements. Then, the percentage of measurements to the left of the upper quartile would be:

(60/100) x 100% = 60%


Your answer:
1. 40% of the measurements lie to the right of the median.
2. 60% of the measurements lie to the left of the upper quartile (Q3).

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Answer:

It costed $1200

Step-by-step explanation:

First Month Saved 1/3 of total cost

Second Month (1/3 of total cost) - 125

Third Month 525

525-125= 1/3 of total (If she saved the same amount the second month as the first month, then she's already saved 2/3 of the money)

400 = 1/3 of total cost

3X400=1200

Answer:

Step-by-step explanation:

458210 in binary

=10001111001102

The claim is false that the population means 9.2. and the required value of the t statistic is -1.02.

Given that,
Sample size (n) = 49,
Sample means (μ) = 8.5,
Standard deviation (σ) = 1.5, and the significance level of 0.01.
To determine whether the population means is equal to 9.2 and also the value of sample test statistic t.

The T - statistic is the ratio of the predictive value of a parameter from its hypothesized value to its standard disputable values.

Let to prove the claim let's assume the population means is not equal to 9.2.
Now

Z = (x - μ)/σ

Z = (8.5 - 9.2) / 1.5

  = -0.7 / 1.5

  = -0.467

The probability(P) of z of -0.467 is 0.67975.

Since the value of P is more than 0.01 so it implies that the assumption that population means is not equal to 9.2.

\(t = \frac{x - \mu}{\sigma/\sqrt{n} }\\ t = \frac{8.5 - 9.2}{1.5/\sqrt{49} } \\ t = -1.02\)

Thus, the claim is false that the population means 9.2. and the required value of the t statistic is -1.02.

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The surface area of the right cone is 602.88 inch².

Given,

        length of radius of the base is = 8 inches

                          the slant height is  =16 inches.

Now using formula ,

the surface area of right circular cone is a right circular cone = πr(r + l)

So,    r = 8 inches  l = 16 inches

put values in  the formula ,

             surface area of right circular cone = 3.14 × 8 ( 8 + 16 )

                                                                       = 3.14 × 8 × 24

                                                                       = 602.88 inch²

Therefore, the surface area of the right cone is 602.88 inch².

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Answer:

X=10

Step-by-step explanation:

1. Subtract 10 from both sides

2. Simplify

3. Divide both sides by the same factor

4. Simplify

Answer:

Answer: 39.7  

∘

 and 140.3  

∘

Step-by-step explanation:

All possible values of ∠O, to the nearest 10th of a 39.7degrees and 140.3 degrees.

We have given that,

In ΔNOP, o = 3.5 inches, n = 3.3 inches and ∠N=37°.

A triangle is a polygon with three edges and three vertices. It is one of the basic shapes in geometry. A triangle with vertices A, B, and C is denoted \triangle ABC.

We have to determine all possible values of ∠O, to the nearest 10th of a degree.

All possible values of ∠O, to the nearest 10th of a 39.7degrees and 140.3 degrees.

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The tangent function is defined as the ratio of the sine function to the cosine function. It is periodic with a period of pi and has vertical asymptotes at odd multiples of pi/2. An equation for a tangent function with a domain of all real numbers and n as an integer is given by the following equation:
y = tan(x + n(pi))


The tangent function is defined as the ratio of the sine function to the cosine function, and it is periodic with a period of pi. It has vertical asymptotes at odd multiples of pi/2.
The tangent function can be represented by the following equation:
y = tan(x)
Where x is the angle measured in radians.
If we want to shift the graph of the tangent function by a certain amount, n, in the horizontal direction, we can use the following equation:
y = tan(x + n(pi))
Where n is an integer.
For example, if n = 2, then the graph of the tangent function would be shifted 2pi units to the left, and the equation would be:
y = tan(x - 2pi)
If n = 3, then the graph of the tangent function would be shifted 3pi units to the left, and the equation would be:
y = tan(x - 3pi)
And so on for any integer value of n.

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Using the fact that P is the midpoint of the segment AB, we will see that its y-value is -4.

We know that point P partitions directed segment AB in the part to part ratio of 4:4.

Notice that the ratio is equivalent to 1:1

So point P is just the midpoint of the segment, remember that for a segment whose endpoints are (a, b) and (c, d), the midpoint is:

M= ( [a+ c]/2, [b + d]/2)

P is the midpoint of (5,-7) and (1,-1), then the value of the y-coordinate of P is:

y = (-7 + (-1))/2

y = (-7 - 1)/2

y = -4

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Answer:

speed of James is: 3.75 miles/hour.

Step-by-step explanation:

We need to find the speed of James in miles per hour(mi/hr)

we know that 1 mile=5280 feet

James takes 120 steps in 1 minute so he will cover 120×60 steps in 1 hour.

i.e. he takes 7200 steps in 1 hour.

also each step of James=2.75 feet

total distance covered by James in 1 hour=2.75×7200 feet=19800 feet

\(19800feet=\frac{19800}{5280} miles=3.65miles\)

hence speed of James= (distance covered by james in 1 hour)/1 hour

speed of James=3.75 miles/hour.

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Answer:

We need to find the speed of James in miles per hour(mi/hr)

we know that 1 mile=5280 feet

James takes 120 steps in 1 minute so he will cover 120×60 steps in 1 hour.

i.e. he takes 7200 steps in 1 hour.

also each step of James=2.75 feet

total distance covered by James in 1 hour=2.75×7200 feet=19800 feet

19800feet=\frac{19800}{5280} miles=3.65miles19800feet=

5280

19800

miles=3.65miles

hence speed of James= (distance covered by james in 1 hour)/1 hour

The value of the union of sets A and B is, P(A ∪ B) is 0.64.

The union of two sets means the total elements in both the sets combined.

Given: sets P(A) = 0.38, P(B) = 0.83, and  intersection P(A ∩ B) = 0.57

We need to find the union of P(A ∪ B).

P(A ∪ B) = P(A) + P(B) - P(A ∩ B)

Let us substitute the given values in the formula.

P(A ∪ B) = P(A) + P(B) - P(A ∩ B)

=0.38+0.83-0.57

=1.21-0.57

=0.64

Therefore, the value of union of sets P(A ∪ B) is 0.64.

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Problem 1

a = 6

b = \(6\sqrt{3}\)

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

Reason:

The short leg is opposite the smallest angle. For any 30-60-90 triangle, the short leg is half the hypotenuse. This means the short leg is 12/2 = 6 units long. That's why a = 6.

The long leg is \(\sqrt{3}\) times longer compared to the short leg.

\(\text{long leg} = (\text{short leg})*\sqrt{3}\\\\\text{long leg} = 6\sqrt{3}\)

This template applies to 30-60-90 triangles only.

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

Problem 2

Answer:

a = 7

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

Reason:

We use the same idea mentioned in problem 1. The short leg is half as long as the hypotenuse. It works for 30-60-90 triangles only.

Answer:

12

Step-by-step explanation:

You need to use the pythagorean theorem. a^2 +b^2=c^2. Label the sides with a, b, and c. The longest side is c, but it does not matter for the other two sides.

Answer:

y = 12

Step-by-step explanation:

\(c^{2}\) = \(a^{2}\) - \(b^{2}\)

\(c^{2}\) = \(35^{2}\) - \(37^{2}\)

\(35^{2}\) = 1,225

\(37^{2}\) = 1,369

1,369 - 1,225 = 144

\(\sqrt{144}\) = \(c^{2}\)

\(\sqrt{144}\) = 12

The diagonals of a Rhombus are congruent and perpendicular bisectors of each other​

If a parallelogram contains a pair of consecutive sides that are called congruent, then it is considered a rhombus, or if a parallelogram bisects two angles of the same, then it is a rhombus.

If the diagonals of a quadrilateral are perpendicular bisectors to each other, then the quadrilateral is a rhombus.

There are  general properties of a Rhombus are:

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Answer:

Step-by-step explanation:

300 grams of shrimp food

10 shrimp

get 300 and divide by 10

300/10=30

Answer: 7 3/4 pounds

Step-by-step explanation:

Here's the correct question:

Last year, Bob's Market ordered 15 1/2 pounds of plums from a local orchard. This year, the market plans to order 1 1/4 times as many pounds of plums as were ordered last year. They want 2/5 of this order to be red plums. What is the total amount, in pounds, of red plums the market plans to order this year?

The amount of pounds of plum that is ordered this year will be:

= 15 1/2 × 1 1/4

= 31/2 × 5/4

= 19 3/8

Since they want 2/5 to be red plums, the total amount of red plums will then be:

= 2/5 × 19 3/8

= 2/5 × 155/8

= 310/40

= 7 3/4 pounds

Answer:

x=20

Step-by-step explanation:

Answer:

23%

Step-by-step explanation:

Answer:

23 %

Step-by-step explanation:

The total money earned:

124+ 30+ 46 =200

Percent earned babysitting

money earned babysitting / total * 100%

46/200 * 100 = 23 %

Answer:

twice a day

Step-by-step explanation:

morning and bed time

The given problem involves finding the inverse Laplace transform of a given function. Specifically, we are asked to find the time-domain function that corresponds to the Laplace transform of the function 0.250 s + 0.707 s + 0.250.To find the inverse Laplace transform, we need to use the properties of the Laplace transform and the inverse Laplace transform.

We can use tables of Laplace transforms to find the inverse Laplace transform of each term in the given function, and then combine these terms to obtain the overall inverse Laplace transform.The inverse Laplace transform involves finding the time-domain function that corresponds to a given Laplace transform. It is the inverse operation of the Laplace transform, which converts a time-domain function into its Laplace transform. The Laplace transform is a useful tool in engineering, physics, and mathematics, as it allows us to analyze linear systems and differential equations in the frequency domain.

Overall, the problem involves applying the principles of Laplace transforms and inverse Laplace transforms to find the time-domain function that corresponds to a given Laplace transform. It also requires an understanding of tables of Laplace transforms and the properties of the Laplace transform and the inverse Laplace transform.

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Answer:

56a+40b

Step-by-step explanation:

43a plus 13a is 56a, -12b + 52b is 40b, together it's 56a+40b

Answer:

8

Step-by-step explanation:

The weight of an object with a mass of 2 kg would be 6 N on this planet, assuming the direct variation relationship holds.According to the given information, the weight of an object varies directly with its mass.

This implies that there is a constant of proportionality between weight and mass. Let's denote this constant as k.

From the given data, we have:

Mass = 5 kg

Weight = 15 N

Using the direct variation equation, we can write:

Weight = k * Mass

Substituting the given values, we have:

15 N = k * 5 kg

To find the value of k, we divide both sides of the equation by 5 kg:

k = 15 N / 5 kg = 3 N/kg

Now that we know the constant of proportionality, we can find the weight of an object with a mass of 2 kg:

Weight = k * Mass = 3 N/kg * 2 kg = 6 N.

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The given rational function is 2x / ((x)(x-1)(x-2)(x-3)). By using partial fraction decomposition, we can rewrite the expression as a sum of simpler fractions, with each denominator being a factor of the original expression.

To perform partial fraction decomposition, we start by factoring the denominator of the rational function. In this case, the denominator is (x)(x-1)(x-2)(x-3). We can rewrite the original expression as a sum of fractions with simpler denominators.

Let's denote the unknown coefficients as A, B, C, and D. Then the partial fraction decomposition of the given rational function is:

2x / ((x)(x-1)(x-2)(x-3)) = A/x + B/(x-1) + C/(x-2) + D/(x-3).

Each term on the right side has a simpler denominator that matches one of the factors of the original denominator. The coefficients A, B, C, and D are constants that we need to determine by equating the numerators on both sides of the equation and solving the resulting system of equations.

Note that the given prompt specifically asks not to solve for the coefficients, so we stop here with the partial fraction decomposition.

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Answer:

variable =A (x)

Constant= C (5)

operation=B (+)

Answer:

A C B

Step-by-step explanation: