The area of a triangle is 474. Two of the side lengths are 87 and 19 and the included angle is acute. Find the measure of the included angle, to the nearest tenth of a degree.

The frequency of 1 is option (d) 973

Reselecting cases means selecting a subset of data that meets specific criteria. In this case, you will need to identify which cases to keep based on certain conditions. After reselecting cases, the next step is to define the variable TX + Y. This means that you will perform an operation on two existing variables, T and Y, and create a new variable that is the sum of T and Y. The result will be a numerical variable.

To summarize, you will need to follow these steps:

Reselect cases based on specific criteria.

Define the variable TX + Y as the sum of T and Y.

Recode the numerical variable into a categorical variable with two categories: G-1 İFT <= 10 and G=0 if T>10.

Calculate the frequency of category 1 in the new variable G.

Finally, to answer the question, you will need to calculate the frequency of category 1 in the variable G. This means that there are 973 cases where the value of TX + Y is less than or equal to 10.

The correct answer is option d. 973.

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To find the point on the surface 6x = y^2 + z^2 where its tangent plane is parallel to a given plane, we need to find a point on the surface and determine the normal vector of the surface at that point.

Then, we can compare the normal vector of the surface to the normal vector of the given plane to check if they are parallel.

Let's first find a point on the surface by substituting a value for either y or z and solving for x. Let's choose y = 0:

6x = 0^2 + z^2

6x = z^2

x = z^2/6

So, one point on the surface is (z^2/6, 0, z).

To find the normal vector of the surface at this point, we can calculate the partial derivatives with respect to x, y, and z:

∂/∂x (6x) = 6

∂/∂y (y^2 + z^2) = 0

∂/∂z (y^2 + z^2) = 2z

The normal vector is then N = (6, 0, 2z) = (6, 0, 2z) / ||(6, 0, 2z)||, where ||N|| represents the magnitude of N.

To determine if the tangent plane is parallel to a given plane, we compare the normal vector of the surface to the normal vector of the given plane. If they are parallel, their direction vectors should be proportional.

If the given plane is parallel to the xy-plane and has a normal vector N_1 = (0, 0, 1), we can compare it to the normal vector of the surface. In this case, we see that the z-component of N (2z) is not proportional to the z-component of N_1 (1). Therefore, the tangent plane of the surface at the chosen point is not parallel to the given plane.

To find a point on the surface where its tangent plane is parallel to the given plane, we would need to choose a different point on the surface such that the normal vector of the surface at that point is parallel to the given plane's normal vector.

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Answer:

If you roll two dices, you can get as results all numbers from 2 to 12. Among these, the prime numbers are 2, 3, 5, 7, 11. The probability you get each of them is: 2: you can get it only as 1+1, so one combination over 36 possibility. Probability: 1/36. 3: you can get it as 1+2 or 2+1, so two combinations over 36 possibility. Probability: 2/36. 5: you can get it as 1+4, 2+3, 3+2, 4+1, so four combinations over 36 possibility. Probability: 4/36. 7: you can get as 1+6, 2+5, 3+4, 4+3, 5+2, 6+1, so six combinations over 36 possibility. Probability: 6/36. 11: you can get it as 5+6 or 6+5 so two combinations over 36 possibility. Probability: 2/36. The total probability of getting a prime number is the sum of the probabilities, which is 15/36. So m=15, n=36 and 10m+n=150+36=186.

For this above box plot prompt, the answer are given below.

Part A

From the box plots, we can see that the Red Team has the least variability and spread of times, followed by the Blue Team and then the Green Team.

The Red Team's box is the smallest, indicating that their times are more tightly clustered together.

Blue Team:

Q1: 75

Q2: 82

Q3: 87

IQR: 12

Upper fence: Q3 + 1.5IQR = 87 + 1.512 = 105

There are no outliers

Green Team:

Q1: 70

Q2: 75

Q3: 80

IQR: 10

Upper fence: Q3 + 1.5IQR = 80 + 1.510 = 95

There is one outlier at 90

Red Team:

Q1: 80

Q2: 83

Q3: 87

IQR: 7

Upper fence: Q3 + 1.5IQR = 87 + 1.57 = 98.5

There are no outliers

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Answer:

The diagonal has to measure 10 meters

Step-by-step explanation:

The diagonal has to be based on the Pythagorean theorem (for right angle triangles) and that is:

\(diagonal^2=side_1^2+side_2^2\\diagonl^2=6^2+8^2\\diagonal ^2=36+64\\diagonal^2=100\\diagonal = 10 \,\,m\)

The difference of the means as a multiple of the MAD is approximately equal to 2.23

Given that,

Mrs. Huang found the mean and mean absolute deviation (MAD) of the latest test scores for two of her classes.

Class A had a mean of 73.5 and Class B had a mean of 82.4. Both classes had a MAD about 4. We need to calculate the difference of the means as a multiple of the MAD.

Steps involved in finding the difference of the means as a multiple of the MAD are as follows:

Step 1: Calculate the difference of the means

The difference of the means of the two classes can be calculated as follows:

Difference of means = Mean of Class B - Mean of Class A= 82.4 - 73.5= 8.9

Step 2: Calculate the difference of the means as a multiple of the MAD

The difference of the means as a multiple of the MAD can be calculated by dividing the difference of the means by the MAD of the two classes:

Difference of the means as a multiple of the MAD= (Mean of Class B - Mean of Class A) / MAD= 8.9 / 4= 2.225 ≈ 2.23

Therefore, the difference of the means as a multiple of the MAD is approximately equal to 2.23, when rounded to two decimal places.

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Where a and b are determined by the value of D.

A parabola is a type of graph, or curve, that is represented by an equation of the form y = ax² + bx + c. The vertex of a parabola is the point where the curve reaches its maximum or minimum point, depending on the direction of the opening of the parabola. In this case, the vertex of the parabola is at (-4,-1).
To find the equation of the parabola, we need to know two more points on the graph. We are given that when the y-value is 0, the x-value is 10-D. We can use this information to find another point on the graph.
When the y-value is 0, we have:
0 = a(10-D)² + b(10-D) + c
Simplifying this equation gives:
0 = 100a - 20aD + aD² + 10b - bD + c
Since the vertex is at (-4,-1), we know that:
-1 = a(-4)² + b(-4) + c
Simplifying this equation gives:
-1 = 16a - 4b + c
We now have two equations with three unknowns (a,b,c). To solve for these variables, we need one more point on the graph. Let's use the point (0,-5) as our third point.
When x = 0, y = -5:
-5 = a(0)² + b(0) + c
Simplifying this equation gives:
-5 = c
We can now substitute this value for c into the other two equations to get:
0 = 100a - 20aD + aD² + 10b - bD - 5
-1 = 16a - 4b - 5
Simplifying these equations gives:
100a - 20aD + aD² + 10b - bD = 5
16a - 4b = 4
We now have two equations with two unknowns (a,b). We can solve for these variables by using substitution or elimination. For example, we can solve for b in the second equation and substitute it into the first equation:
16a - 4b = 4
b = 4a - 1
100a - 20aD + aD² + 10(4a-1) - D(4a-1) = 5
Simplifying this equation gives:
aD² - 20aD - 391a + 391 = 0
We can now use the quadratic formula to solve for D:

D = [20 ± sqrt(20² - 4(a)(391a-391))]/2a
D = [20 ± sqrt(400 - 1564a² + 1564a)]/2a
D = 10 ± sqrt(100 - 391a² + 391a)/a
There are two possible values for D, depending on the value of a. However, since we don't have any information about the sign of a, we cannot determine which value of D is correct. Therefore, the final equation of the parabola is:
y = ax² + bx - 5

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The composite function g(h(8)) when evaluated is 94.

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

g(a) = 4a - 2

h(a) = 3a

To find g(h(8)), we need to first evaluate h(8), and then plug that result into g(a) and simplify.

h(a) is defined as 3a, so h(8) = 3(8) = 24.

Now we can plug in 24 for a in g(a) and simplify:

g(a) = 4a - 2

g(h(8)) = g(24) = 4(24) - 2 = 94

Therefore, g(h(8)) = 94.

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Answer:

42 ducks remain in the pond

Step-by-step explanation:

First, find the number of white ducks

28*2=56

Add them to the brown ducks

56+28= 84

Then divide by 2 because half flew away

84/2=42

So 42 ducks remain in the pond. Hope this helps :)

Answer:

Jorge needs 1/2 apple to make the snack.

Answer:

OOOOOOOOHHH SHUTE BROTHER SORRY WISHED I COULD HELP but im blonde so sowwy

Explanation : As you can see, \(\sqrt{-16}\) is not a real number, and hence should be expressed as 4\(i\), \(i\) being an imaginary number. Respectively \(\sqrt{-64}\) will be 8\(i\). Therefore this expression boils down to \(\left(3+4i\right)\left(6-8i\right)\). All we have to do from now on is expand this expression.

Apply the rule \(\left(a+bi\right)\left(c+di\right)=\left(ac-bd\right)+\left(ad+bc\right)i\), in this case where \(a=3,\:b=4,\:c=6,\:d=-8\),

\(\left(3\cdot \:6-4\left(-8\right)\right)+\left(3\left(-8\right)+4\cdot \:6\right)i\)

Let's simplify each part, \(3\cdot \:6-4\left(-8\right)\) and \(3\left(-8\right)+4\cdot \:6\). Afterwards we can add \(i\), and refine.

\(3\cdot \:6-4\left(-8\right) = 50\) ; \(3\left(-8\right)+4\cdot \:6 = 0\)

Therefore our simplified expression will be \(50+0i\), otherwise known as just 50. That is our solution.

Answer:

Step-by-step explanation:

Answer: 0.137.

Step-by-step explanation:

Let p be the population proportion of musicians that are left-handed.

Given: Sample size : n= 2690   [subset of population]

Number of musicians that are left-handed: x= 368

Then the sample proportion: \(\hat{p}=\dfrac{368}{2690}\approx0.137\)

Since sample proportion is the best point estimate of the population proportion.

Hence, a point estimate for p, the population proportion of musicians that are left-handed is 0.137.

Answer:

x=-6/8 (i think)

Step-by-step explanation:

\(5x^{2} - 17x = -6\\25x-17x=-6\\8x=-6\\x=-6/8\)

The roots of the quadratic equation 0 = 2x² + 12x-14 is (C) x=-7 and x=1.

Any equation in algebra that can be written in the standard form where x stands for an unknown value and a, b, and c stand for known values is said to be a quadratic equation.

In general, it is assumed that a > 0; equations with a = 0 are regarded as degenerate since they become linear or even simpler.

So, the roots of 0 = 2x² + 12x-14 are:

2x² + 12x-14  = 0

2x² + 14x - 2x -14

2x(x + 7) - 2(x + 7)

(2x - 2) (x + 7)

Now, use the zero product property as follows:

2x - 2 = 0

2x = 2

x = 2/2

x = 1

And

x + 7 = 0

x = -7

Therefore, the roots of the quadratic equation 0 = 2x² + 12x-14 is (C) x = -7 and x = 1.

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Correct question:

What are the roots of the quadratic equation 0 = 2x² + 12x-14?

a. 1,6, -7

b. 2,12,-14

c. -7,1

d. -1,7

The train has 12 carriages

Step-by-step explanation:

The total no. of seats =876

No. of seats per carriage =73

It is given that each carriage has equal seats

So,

Let the total no. of carriages be x

According to the given information,

\(73 \times x = 876\)

\(x = 876 \div 73\)

x = 12

Hence the number of carriages is 12

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(2, 2), (3, 1), (4, 2) are ordered pairs are in the solution set of the system of linear inequalities.

What are linear inequalities, exactly?

A mathematical expression that compares two expressions using the inequality symbol is known as a linear inequality. The expression may be either a numerical or an algebraic expression, or it may be both.

                               x - 5 > 3x - 10 is an illustration of a linear inequality. Since greater than is utilized in this inequality, the LHS is indubitably greater than the RHS. The inequality is represented by the formula 2x 5 x (5/2).

y >-1/3x+2

y < 2x + 3

The answer is "None" of the given choices satisfy the linear inequality. Each choice has a point (2,2) which dissatisfy the equation.

(2, 2), (3, 1), (4, 2)

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Moon Software Inc. must issue approximately 3,927 OID bonds to raise $3,000,000.

The par bonds have a coupon rate of 10% and a par value of $1,000. To raise $3,000,000, Moon Software Inc. needs to issue 3,000 par bonds since $3,000,000 divided by $1,000 equals 3,000.

The OID bonds have a semiannual coupon rate of 7.75% and a par value of $1,000. Since these bonds need to provide investors with the same effective yield as the par bonds, they must be offered at a discount. To calculate the number of OID bonds required, we need to determine the discount needed to match the effective yield of the par bonds.

The effective yield of the par bonds is 10%. The OID bonds have a coupon rate of 7.75%, so the discount needed to match the effective yield is 10% - 7.75% = 2.25%.

To raise $3,000,000 with OID bonds, we divide the amount by the discount rate: $3,000,000 / 2.25% = $133,333,333.33.

Since each OID bond has a par value of $1,000, we divide the total amount by $1,000: $133,333,333.33 / $1,000 = approximately 133,333.33 bonds.

Since we need a whole number of bonds, we round up to the nearest whole number, which gives us 133,334 bonds.

Therefore, Moon Software Inc. must issue approximately 133,334 OID bonds to raise $3,000,000.

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Answer:

find the probaillity of each one.

Step-by-step explanation:

The equation is formed and solved below.

What is an equation?

A weighing scale, balance, or seesaw is equivalent to an equation. Each equation relates to a single side of the balance. Different quantities can be placed on either side: if the weights on both sides are equal, the scale balances, and the equality that displays the balance is balanced as well (if not, then the lack of balance corresponds to an inequality represented by an inequation). If two equations or two systems of equations have the same set of solutions, they are equivalent. The operations listed below convert an equation or a system of equations into an equivalent one, assuming that the operations are meaningful for the expressions to which they are applied.

The equation is 6(x)² + 5x = 4, which is solved below as

6x² - 5x - 4 = 0

or, 6x² - 8x + 3x - 4 = 0

or, 2x(3x-4) + 1(3x-4) = 0

or, (2x+1)(3x-4) = 0

either 2x + 1 = 0 => x = -1/2

or 3x - 4 = 0 => x = 4/3

The values could be -1/2 or 4/3

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Answer:

Step-by-step explanation:

If triangle equilateral, then h = 3 × 4√3 = 12√3

If side of triangle is "x" , then length of the base is

x² - ( \(\frac{x}{2}\) )² = ( 4√3 )²

4x² - x² = 192

x² = 64

x = 8

\(A_{triangle}\) = 8 × 12√3 = 96√3

Answer:

60/8 = 7.5 mins per mile

Step-by-step explanation:

Answer:

hey mate

surface area of cuboid is 2(lh+bh+hl)

doing for first cuboid

h = 20

l = 6

b = 5

surface area for this cuboid on calculating u get 500 sq.cm

now

second cuboid

h = 12

l = 6

b = 4

calculaye it by formula and u get 288 sq.cm

so total surface area is 500 + 288 = 788 but in this one side is getting counted 2 times which is rectangle with length 6 and 12 so it's area is 12×6 = 72

final ans = 788-72 = 716 cm2

as per me that's ans

brinliest pls

Answer:

Female: 93/328

Adult: 103/328

Baby: 61/328

Step-by-step explanation:

71 + 93 + 103 + 61 = 328

Male: 71/328

Female: 93/328

Adult: 103/328

Baby: 61/328

X would be the number of lawns he mows. We dont know that answer.

Y would be the amount he is paid. So i think it would be

Y=35 + X

Trying my best here im not good with algebra. I know that Y goes with the 35$

Answer:

H = F + 35  

Step-by-step explanation:

If Felix has 35 less than Helen, then adding 35 to Felix's amount should equal Helen's amount

Answer:

10, 3

Step-by-step explanation:

We want to find the common difference in this arithmetic sequence.

31 - 24 = 7 and 24 - 17 = 7, so 7 is the common difference.

The fourth term is then 17-7 = 10. The fifth term is 10-7 = 3.

Answer:

The sequence would now look like this:  31, 24, 17, 10, 3

The next two terms are 10 and 3.

Step-by-step explanation:

Look for a pattern among these numbers:

31         24           17

31 comes down to 24, meaning it went down 7 units.

24 comes down to 17, meaning this, too, went down 7 units.

So, what's' the pattern? The numbers are being subtracted by 7.

17 – 7 = 10

10 – 7 = 3

Thus, 10 and 3 are the next terms.

A translation is a congruent transformation along a vector such that each segment joining a point and its image has the same length as the vector and is parallel to the vector.

A translation is a type of congruent transformation in geometry that involves shifting an object or shape along a specific vector.

In a translation, every point and its corresponding image are connected by a segment, which has the same length as the vector and is parallel to the vector. The term you are looking for to fill the blank is "image."

During a translation, the object or shape maintains its size, shape, and orientation, ensuring that it remains congruent to its original form. This transformation moves the object without changing any of its properties, except for its position in the coordinate plane. Since the segment joining each point and its image is parallel to the vector and has the same length, this ensures that the entire shape is shifted uniformly along the vector's direction.

In summary, a translation is a congruent transformation that shifts an object or shape along a vector, preserving its size, shape, and orientation. The segments connecting each point and its image have the same length as the vector and are parallel to it, ensuring a uniform shift in the object's position.

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Answer:

Step-by-step explanation:

3a > 6

a > 2

According to Zaller's Receive-Accept-Sample (RAS) model, individuals who are most susceptible to the message of a political action committee launching a new advertisement aimed at expanding health insurance to low-income Americans through increased government funding would be those who both receive and accept the message.

The RAS model suggests that individuals have varying levels of political knowledge and are exposed to different sources of information. Those who are more likely to receive the message are individuals who are politically interested and engaged, while those who are more likely to accept the message are individuals who have limited political knowledge and are less critical of the information presented to them.

Therefore, in the context of the advertisement aiming to expand health insurance to low-income Americans, the most susceptible individuals would be those who are politically interested but have limited political knowledge. These individuals may be more likely to accept the message without critically evaluating its content.

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