In ∆PQR, p=13 inches, q=18 inches and r= 12 inches. Find the area of ∆PQR to the nearest square inch.

Answer:

x=36

y=54

Step-by-step explanation:

tan(x) = 15/21

x=tan^-1(15/21)

x=35.537677792

x~36

To solve for y, either repeat the same process:

tan(y)=21/15

y=tan^-1(21/15)

y=54.462322208

y~=54

OR

180-90-x=y

180-90-36=54

y=54

Answer:

Step-by-step explanation:

A) Find the figure attached. According to the figure, since line PQ is parallel to line RS, then <CBQ = <DCS (corresponding angle)

Also <BCS + <DCS = 180° (sum of angles on a straight line)

Given

<BCS = (5a+14)° and <DCS = <CBQ =(2a-9)°

Substituting this values into the formula to calculate the value of a;

(5a+14)°+(2a-9)° = 180°

5a+2a+14-9 = 180

7a+5 = 180

7a = 180-5

7a = 175

a = 175/7

a = 25°

Hence the value of a is 25°

B) From the diagram <ABQ = <BCS = 5a+14 (corresponding angle)

Substitute a = 25 into the expression

<ABQ = 5(25)+14

<ABQ  = 125+14

<ABQ = 139°

C) To get <BCR, we will use the formula;

<BCR + <BCS = 180

Given <ABQ = <BCS = 139°

<BCR = 180 - <BCS

<BCR = 180 - 139

<BCR = 41°

Answer:

Part A: 25

Part B: 139

Part C: 41

Step-by-step explanation:

5a+14+2a-9

a=25

5(25)+14

=139

2(25)-9

=41

Answer:168

Step-by-step explanation:

274.32 is the answer. Tell me if I need to be more precise.

Answer: choice B

B would be the most logical answer showing that these 2 events are independent.

The cone that has the greatest volume is cone C

The given parameters in the question are

Cone A

Height = 10 cm

Diameter = 4 cm

Cone B

Height = 20 cm

Diameter = 4 cm

Cone C

Height = 10 cm

Diameter = 8 cm

The volume of a cone can be calculated using the following volume equation

Volume of a cone = 1/3π(d/2)²h

Where

h = height of the cone

r = radius of the cone

d = diameter of the cone

Using the above equations, we have the following computations

Volume of a cone A = 1/3π * (4/2)² * 10

Volume of a cone A = 40/3π

Volume of a cone B = 1/3π * (4/2)² * 20

Volume of a cone B = 80/3π

Volume of a cone C = 1/3π * (8/2)² * 10

Volume of a cone C = 160/3π

We can see that 160/3π is greater than 40/3π and 80/3π

Hence, cone C has the highest volume

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Answer:

In the explanation. :)

Step-by-step explanation:

608000

Work Shown:

Plug x = 4.3 into the equation given

ŷ = 2.6 − 3.1x

ŷ = 2.6 − 3.1(4.3)

ŷ = 2.6 − 13.33

ŷ = -10.73

Note: The symbol ŷ is read as "y hat". It's used to estimate the y value when it comes to regression equations.

The number of Jim's model car is 48

From the question, we have the following parameters that can be used in our computation:

Ratio of the number of model cars that Jim owns to the number of model cars Terrence owns is 8 : 6

This means that

Jim : Terrence = 8 : 6

Also from the question, we have

Terrence owns 36 models cars

This means that

Terrence = 36

Substitute the known values in the above equation, so, we have the following representation

Jim : 36 = 8 : 6

Multiply by 6

Jim : 36 = 48 : 36

So, we have

Jim = 48

Hence, the number of car is 48

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Answer:

First: 105

Second: 65

Third: 133

Fourth: 129

Fifth: 60

Answer:

Step-by-step explanation:

Well yes!.There are some numbers you can simplify to their lowest terms and will also give 1/4

Answer: hope that helps

Step-by-step explanation: To find equivalent fractions, just multiply the numerator and denominator of that reduced fraction (1/4) by any interger number, ie, multiply by 2, 3, 10, 30 ... and so on ... Equivalent fractions may look different, but when you reduce then to the lowest terms you will get the same value.

(ii) 3% of students failed all three courses, 12% failed economics and mathematics, 9% in math and business, and 10% in econ and business. In other words, the students in these groups failed at least the two mentioned courses. Then 12% - 3% = 9% failed only econ and math but not business; 9% - 3% = 6% failed math and business but not econ; and 10% - 3% = 7% failed econ and business but not math. These groups are mutually exclusive, so the total percentage of students that failed exactly two courses is (ii) 9% + 6% + 7% = 22%.

32% failed econ, which means 32% - 12% - 10% + 3% = 13% failed only econ. Similarly, 46% failed business, so 46% - 9% - 10% + 3% = 30% failed only business. But we don't know how many students failed math, so we can't determine how many failed only math... And consequently we can't determine the proportion of students that make up the other categories.

Answer:

The area of the original piece of paper is 60cm

Answer:

the answer is 60

hope it helps :D

Step-by-step explanation:

Answer: 0.04848

Step-by-step explanation:

Given : There are 4 sophomores, 4 juniors and 3 seniors.

Total choices = 4+4+3 = 11

Number of people needed to be chosen for committee = 4

Number of ways to select 3 people out of 11 (without replacement)=  \(^{11}P_4\)

\(=\dfrac{11!}{(11-4)!}\ \ \ \ [^nP_r=\dfrac{n!}{(n-r)!}]\)

\(=\dfrac{11\times10\times9\times8\times7!}{7!}\\\\= 7920\)

Number of ways to select at least one representative from all three groups of students =  \(^4P_2\times ^4P_1\times ^3P_1+^4P_1\times ^4P_2\times ^3P_1+^4P_1\times ^4P_1\times ^3P_2\)

\(=\dfrac{4!}{2!}\times4\times3+4\dfrac{4!}{2!}\times3+4\times4\times\dfrac{3!}{2!}\\\\= 144+144+96=384\)

Required probability = \(\dfrac{384}{7920}=0.04848\)

Hence, the probability the committee thus formed will have at least one representative from all three groups of students = 0.04848

Draven use 1 (3/4) (option d) ounces of tomato paste to make marinara sauce.

Given,

The quantity of tomato paste = 4 (3/8) ounce jar

The quantity of tomato paste used to make marinara sauce = 2/5 of the jar

We have to find the quantity of tomato paste in ounces used to make marinara sauce:

Here,

4(3/8) = (4 × 8 + 3) / 8 = (32 + 3) / 8 = 35 / 8 = 4.375

2/5 of the jar = 2/5 of 4.375 = 4.375 × 2/5 = 1.75 = 1 (3/4)

That is, Draven use 1 (3/4) (option d) ounces of tomato paste to make marinara sauce.

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Answer:

a) 5.37% probability that an individual distance is greater than 210.9 cm

b) 75.80% probability that the mean for 15 randomly selected distances is greater than 196.00 cm.

c) Because the underlying distribution is normal. We only have to verify the sample size if the underlying population is not normal.

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal probability distribution

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean \(\mu\) and standard deviation \(\sigma\), the zscore of a measure X is given by:

\(Z = \frac{X - \mu}{\sigma}\)

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 pvalue, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean \(\mu\) and standard deviation \(\sigma\), the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean \(\mu\) and standard deviation \(s = \frac{\sigma}{\sqrt{n}}\).

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

In this question, we have that:

\(\mu = 197.5, \sigma = 8.3\)

a. Find the probability that an individual distance is greater than 210.9 cm

This is 1 subtracted by the pvalue of Z when X = 210.9. So

\(Z = \frac{X - \mu}{\sigma}\)

\(Z = \frac{210.9 - 197.5}{8.3}\)

\(Z = 1.61\)

\(Z = 1.61\) has a pvalue of 0.9463.

1 - 0.9463 = 0.0537

5.37% probability that an individual distance is greater than 210.9 cm.

b. Find the probability that the mean for 15 randomly selected distances is greater than 196.00 cm.

Now \(n = 15, s = \frac{8.3}{\sqrt{15}} = 2.14\)

This probability is 1 subtracted by the pvalue of Z when X = 196. Then

\(Z = \frac{X - \mu}{\sigma}\)

By the Central Limit Theorem

\(Z = \frac{X - \mu}{s}\)

\(Z = \frac{196 - 197.5}{2.14}\)

\(Z = -0.7\)

\(Z = -0.7\) has a pvalue of 0.2420.

1 - 0.2420 = 0.7580

75.80% probability that the mean for 15 randomly selected distances is greater than 196.00 cm.

c. Why can the normal distribution be used in part​ (b), even though the sample size does not exceed​ 30?

The underlying distribution(overhead reach distances of adult females) is normal, which means that the sample size requirement(being at least 30) does not apply.

Answer:

P(success at first attempt) = 0.1353

Step-by-step explanation:

This question follows poisson distribution. Thus, the formula is;

P(k) = (e^(-G) × (G)k)/k!

where;

G is number of frames generated in one frame transmission time(or frame slot time)

Let's find G.

To do this, we need to find number of frames generated in 1 slot time which is given as 50 ms.

Now, in 1000 ms, the number of frames generated = 50

Thus; number of frames generated in 50 ms is;

G = (50/1000) × 50

G = 2.5

To find the chance of success on the first attempt will be given by;

P(success at first attempt) = P(0) = e^(-G) = e^(-2) = 0.1353

Step-by-step explanation:

here is your answer hope it helps you plaz mark me as brainlist

Answer:

False

Step-by-step explanation:

Given

\(XLIV = 64\)

Required

True or False

The above numeral can be split as follows:

\(XLIV = XL + IV\)

X means 10 and L means 50.

But because X (10) which is smaller comes before L (50), XL is executed as:

\(XL = -10 + 50\)

\(XL = 40\)

In Roman numerals;

\(IV = 4\)

Substitute 40 for XL and 4 for IV.

\(XLIV = 40 + 4\)

\(XLIV = 44\)

Hence;

\(XLIV = 64\) is false

Answer:

AC = 12

Step-by-step explanation:

If BC is parallel to DE then ∠D ≅ ∠B and ∠E ≅ ∠C. Therefore

ΔABC is similar to ΔADE.

The sides of smaller triangle are in proportion with sides of bigger triangle.

Therefore we have the equation:

AC/AE = AB/AD

Substitute the given numbers:

x/x+15 =8/18

18x= 8(x+15)

18x = 8x+120

10x = 120

x = 12

AC=12

Since I don't see the graphs:

 ⇒ I am going to answer by the general format of what you should see

The function has zeros at -3, 4:

 ⇒ which means that the function must interest the x-axis at x = -3 and

      x = 4

Hope that helps!

      ⇒look at the image I uploaded which shows a possible answer

Using the concept of word problems and quadratic equation it will take 1 year until the sum of square of their ages be 45.

Word problems are mathematical problems that are delivered in ordinary words, instead of mathematical symbols.

Part of the problem with dealing with word problems that they first need to be translated into mathematical equations, and then the equations need to be solved.In this problem;

let x represent the number of years from now when the sum of square of their respective age will be

45.(x + 2)² + (x + 5)² = 45

Expanding the brackets;

x² + 4x + 4 + x² + 10x + 25 = 45

2x² + 14x + 29 = 45

2x² + 14x + 29 - 45 = 0

2x² + 14x - 16 = 0

Solving the quadratic equation for x;

x = 1, x = -8

Taking the positive value, the value of x is 1

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Answer:

6

Step-by-step explanation:

Simplifying the expression (2+1)2, we can first perform the operation within the parentheses, which gives us:

(2+1)2 = 3 x 2

Then, we can multiply 3 by 2, which gives us:

3 x 2 = 6

Therefore, the simplified expression for (2+1)2 is 6

Answer

i´m  not sure what the answer is but hopefully these tips helped you

Step-by-step explanation:

first, sum up all sides of the lengths then simplify

The surface area of the base ball to the nearest whole number is 26 in²

A sphere is defined as the set of all points in three-dimensional Euclidean space that are located at a distance.

The area occupied by a three-dimensional object by its outer surface is called the surface area.

The surface area of a sphere is expressed as;

SA = 4πr²

where r is the radius and it's calculated as;

C = 2πr

9 = 2πr

r = 4.5/π =

SA = 4 π × (4.5/π)²

SA = 81/π

SA = 26 in²( nearest whole number)

Therefore the surface area of the sphere is 26 in²

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The general solution to the given differential equation is:

y = (x/12) - (1/288)

How to solve the Differential Equation?

We want to solve the differential equation given as: y' - 24xy = -2x

The integrating factor is given by the exponential of the integral of the coefficient of y, which in this case is -24x. Therefore, the integrating factor is e^(-24x).

Multiplying the entire equation by the integrating factor, we get:

e^(-24x)y' - 24xe^(-24x)y = -2xe^(-24x)

The left side of the equation is the derivative of (e^(-24x)y) with respect to x:

(d/dx)(e^(-24x)y) = -2xe^(-24x)

Integrating both sides with respect to x, we have:

e^(-24x)y = ∫(-2xe^(-24x))dx

Integrating the right side, we get:

e^(-24x)y = -∫(2xe^(-24x))dx

To evaluate the integral on the right side, we can use integration by parts. Let's differentiate -2x and integrate e^(-24x):

u = -2x (differential of u = -2dx)

dv = e^(-24x) (integral of dv = -1/24e^(-24x)dx)

Using the integration by parts formula:

∫uv dx = uv - ∫v du

We can compute the integral as follows:

-∫(2xe^(-24x))dx = -[(-2x)(-1/24e^(-24x)) - ∫(-1/24e^(-24x))(-2dx)]

= -[x/12e^(-24x) + 1/12∫e^(-24x)dx]

= -[x/12e^(-24x) + 1/12(-1/24)e^(-24x)]

= -[x/12e^(-24x) - 1/(12*24)e^(-24x)]

= -[x/12e^(-24x) - 1/(288e^(-24x))]

= -[x/12 - 1/288]e^(-24x)

Substituting this back into the previous equation, we have:

e^(-24x)y = -[-(x/12 - 1/288)e^(-24x)]

Simplifying further:

e^(-24x)y = (x/12 - 1/288)e^(-24x)

Canceling out e^(-24x) on both sides:

y = x/12 - 1/288

Therefore, the general solution to the given differential equation is:

y = x/12 - 1/288

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Answer: \(-\frac{1}{2}\)

Step-by-step explanation:

To find the slope, let's turn the equation into slope-interept form. In slope intercept form, y=mx+b, we know that m=slope.

\(x+2y=16\)             [subtract both sides by x]

\(2y=-x+16\)          [divide both sides by 2]

\(y=-\frac{1}{2}x+8\)

Now, we know that \(m=-\frac{1}{2}\). That tells us \(-\frac{1}{2}\) is the slope.

Step-by-step explanation:

x+2y=16

-× -×

2y=-x+16

÷2. ÷2

y=-1/2x+8

slope is -1/2

Answer:

41 meters

Step-by-step explanation:

\(\frac{31}{64}\) = \(\frac{19.8}{x}\)

31x = (19.8)(64)

31x = 1267.2  Divide both sides by 31 and round

x = 41