I really need your help ASAP!

Only one triangle possible with angle 38.2° at C.

According to the given statement

we have to seek out that the measurement of m with the help of the a and c.

Then for this purpose, we all know that the

The ambiguous case occurs when one uses the law of sines to see missing measures of a triangle when given two sides and an angle opposite one in every of those angles (SSA).

According to the this law

The equation become

35/sin(60) = 25/sinC

sinC = 0.6185895741

C = 38.2, 141.8

Since 141.8+60 = 201.8 > 180

It will not form a triangle.

So, only 1 triangle possible with angle 38.2° at C

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Disclaimer: This question was incomplete. Please find the full content below.

Question:

Law of Sines and the Ambiguous Case.

In ∆ ABC, a =35, c = 25, and m < A = 60*

How many distinct triangles can be drawn given these measurements?

The function position of the particle is s(t) = (1 / 12) · t⁴ + (7 / 6) · t³ + 3 · t² + (63 / 4) · t.

By mechanical physics we know that the function velocity is the integral of function acceleration and the function position is the integral of function velocity. Hence, we need to integrate twice to obtain the function position of the particle:

Velocity

v(t) = ∫ t² dt - 7 ∫ t dt + 6 ∫ dt

v(t) = (1 / 3) · t³ - (7 / 2) · t² + 6 · t + C₁

Position

s(t) = (1 / 3) ∫ t³ dt - (7 / 2) ∫ t² dt + 6 ∫ t dt  + C₁ ∫ dt

s(t) = (1 / 12) · t⁴ + (7 / 6) · t³ + 3 · t² + C₁ · t + C₂

Now we find the values of the integration constants by solving the following system of linear equations:

0 = C₂

63 / 4 = C₁ + C₂

The solution of the system is C₁ = 63 / 4 and C₂ = 0. The function position of the particle is s(t) = (1 / 12) · t⁴ + (7 / 6) · t³ + 3 · t² + (63 / 4) · t.

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The two-column proof that shows that ΔEAB ≅ ΔDCB by SAS congruence theorem is explained below.

The Side-angle-side congruence theorem (SAS) that states that two triangles that are have two pairs of corresponding congruent sides and a pair of included corresponding congruent angles are congruent to each other.

Any triangle with two equal base angles is referred to as an isosceles triangle, The sides opposite these base angles are also congruent to each other.

Given the diagram below, the proof is expressed as follows:

Statement 1: ΔEAB and ΔDCB are two right triangles

Reason 1: Given

Statement 2: ∠EAB  ≅ DCB

Reason 2: Right angles

Statement 3: ∠BED ≅ BDE

Reason 3: Given

Statement 4: ΔBED is an isosceles triangle

Reason 4: Definition of isosceles triangle

Statement 5: BE ≅ BD

Reason 5:  Definition of isosceles triangle

Statement 6: ΔEAB ≅ ΔDCB

Reason 6: SAS

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Answer:

93.39

Step-by-step explanation:

So the sum of exterior angles of the convex octagon is: 360 degrees

This means if we add all the equations that represent each angle, we can set it equal to 360 and solve for x

[tex](x+14) + (2x-3) + (3x+8) + (3x+16) + (2x-17) + (3x-4) + (3x-12) + (6x)[/tex]

Group like terms

[tex](x+2x+3x+3x+2x+3x+3x+6x) + (14-3+8+16-17-4-12)[/tex]

Add like terms

[tex]23x+2[/tex]

Now let's set the sum of exterior angles to 360

[tex]23x+2 = 360[/tex]

Subtract 2 from both sides

[tex]23x=358[/tex]

Divide both sides by 23

[tex]x\approx 15.565[/tex]

So by looking at all these, it appears that 6x is the highest value, given that x is positive. The way I estimated, is approximately 15.5, whenever I saw an equation like x+14, I estimated it's about 2x, since 14 is not exactly, but close to 15.5. I did this with each polynomial given. You could also manually check each one

Original equation

6x

Subsitute

6(15.565)

Simplify

[tex]93.39[/tex]

It should be noted that Group A is a cluster of points with similar property or relationship and Point B is an outlier. This is the point outside of the common relationship in the scatterplot

It should be noted that scatter plots are the graphs that present the relationship between two variables in a data-set. It represents data points on a two-dimensional plane or on a Cartesian system.

In this case, the independent variable or attribute is plotted on the X-axis, while the dependent variable is plotted on the Y-axis.

The association between students' test scores and the number of hours they exercise is that there is a negative tendency. As number of hours spent on computer games increase, the test scores decrease.

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ANSWER: 480 out of 1200 were taken at the Honolulu Zoo.

Answer:

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

Given series:

We notice that this is a geometric progression.

The common ratio is:

To find the next term multiply the last term by the common ratio:

The 4th term is:

If there are 23 students study Economics,6 students study both government and economics and 48 students study either government or economics or both then there are 31 students study government, 17 students study economics only and 25 students are there who study government only.

Given that in a secondary school class, 23 students study Economics, 6 students study both government and economics. 48 students study either government or Economics or both.

We are required to find :

Suppose E represents economics students and G students government students. In this way:

E=23

G∩E=6  (And represents intersection between sets)

G∪E=48 (Or represents union of sets)

G∪E=G+E-G∩E

48=G+23-6

G=48-17

G=31

Economics only=E-G∩E

=23-6

=17

Governments only=G-G∩E

=31-6

=25

Hence if there are 23 students study Economics,6 students study both government and economics and 48 students study either government or economics or both then there are 31 students study government, 17 students study economics only and 25 students are there who study government only.

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The amount invested in the first account is $1,500 and $6,500 was invested in the second account.

What is simple interest?

Simple interest is determined as the principal multiplied by the interest rate ,then multiplied by the duration of the investment.

The formula for simple interest on an investment is as shown below:

I=PRT

P=principal=$8,000

R=interest rates= 1% and 6%

T=duration of investment=1 year

Let assume that X was invested at 1% and that the remaining of $8000-X is invested at 6%.

Interest on the first account=X*1%*1

Interest on the first account=0.01X

Interest on second account=($8000-X)*6%*1

Interest on second account=480-0.06X

Total interest=0.01X+480-0.06X

Total interest=480-0.05X

Total interest=$405

405=480-0.05X

0.05X=480-405

0.05X=75

X=75/0.05

X=amount invested in the first account=$1,500

Amount invested in the second account=$8000-X

Amount invested in the second account=$8,000-$1,500

Amount invested in the second account=$6,500

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The length of the vine is 21 ft

what is the circumference of a circle?

the circumference is the perimeter of a circle

the perimeter of the circle = 2πr = 3 ft

the vine is 7 times the perimeter

length of vine = 7×3= 21 ft

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If the tree is 20 feet tall with circumference 3 feet then the length of  vince is around 21 feet.

Given the height of tree is 20 feet and the circumference of tree is 3 feet.

We have to find the length of vine.

Circumference is the perimeter of a circular object. Because the trunk of a tree is in shape of circle so the perimeter of the trunk is 2πr.

We have been given the circumference of tree be 3 feet.

Circumference=2πr

Because vine is 7 times the circumference so the length of vine being:

Length of vine=7*3

=21 feet.

Hence if the tree is 20 feet tall with circumference 3 feet then the vince is around 21 feet long.

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The equation of parabola is a [tex]\frac{-(x+ 3)^{2}}{64} + \frac{ (y-1)^{2}}{4} = 1[/tex] and the coordinates of center is (0,0) And asymptote is become 16.

According to the statement

we have to find the centers, foci, vertices and asymptotes of the hyperbola from the given equations.

So, For this purpose,

Hyperbola is a a plane curve generated by a point so moving that the difference of the distances from two fixed points is a constant.

So, The given equation is:

16y²-x² - 6x - 32y = 57

So, rearrange it then

-x² - 6x - 32y + 16y² = 57

-(x² + 6x) + (16y² - 32y ) = 57

-(x² + 6x) + 16(y² - 2y ) = 57

-(x² + 6x + 9) + 16(y² - 2y +1 ) = 57 +1(16) + 9(-1)

-(x+ 3)²  + 16 (y-1)²  = 64

-(x+ 3)²  + 16 (y-1)²  = 64

divide whole equation by 64 then

[tex]\frac{-(x+ 3)^{2}}{64} + \frac{16 (y-1)^{2}}{64} =\frac{64}{64}[/tex]

then equation become

[tex]\frac{-(x+ 3)^{2}}{64} + \frac{ (y-1)^{2}}{4} = 1[/tex]

This become the equation of hyperbola.

So,

here coordinates of center is (0,0)

And asymptote is become 16.

So, The equation of parabola is a [tex]\frac{-(x+ 3)^{2}}{64} + \frac{ (y-1)^{2}}{4} = 1[/tex] and the coordinates of center is (0,0) And asymptote is become 16.

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Using the monthly payment formula, it is found that:

It is given by:

[tex]A = P\frac{\frac{r}{12}\left(1 + \frac{r}{12}\right)^n}{\left(1 + \frac{r}{12}\right)^n - 1}[/tex]

In which:

Considering that she must pay 20% down, the parameters are given by:

P = 0.8 x 2900 = 2320, r/12 = 0.085/12 = 0.007083, n = 24.

Hence the monthly payments are found as follows:

[tex]A = P\frac{\frac{r}{12}\left(1 + \frac{r}{12}\right)^n}{\left(1 + \frac{r}{12}\right)^n - 1}[/tex]

[tex]A = 2320\frac{0.007083(1.007083)^{24}}{(1.007083)^{24} - 1}[/tex]

A = $105.46.

The total finance charge is composed by the down payment plus the 24 monthly payments, hence:

F = 0.2 x 2900 + 24 x 105.46 = $3,111.04.

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Answer: 1, 2, 5, 10

Step-by-step explanation:

1 x 30 = 30

1 x 20 = 20

2 x 15 = 30

2 x 10 = 20

5 x 6 = 30

5 x 4 = 20

10 x 3 = 30

10 x 2 = 20

Answer:

center:

(-0.25, 5)

foci :

(-0.25, 0.158771) | (-0.25, 9.84123)

vertices :

(-0.25, -0.59017) | (-0.25, 10.5902)

wolframramalpha

Using it's concept, the probability that the first coin is a nickel and the second coin is a quarter is:

2/39.

A probability is given by the number of desired outcomes divided by the number of total outcomes.

In this problem, we have that:

Hence the probability will be given as follows:

p = 4/13 x 2/12 = 4/13 x 1/6 = 2/13 x 1/3 = 2/39.

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The two ordered pairs that the mid point is (4,-10) are (4,-20),(4,0) & (4,0),(4,-20).

Given the coordinates of mid point be (4,-10).

We are required to find the ordered pairs that the mid point is (4,-20).

Coordinates show positions of points or something else on a surface.

There are various combinations whose mid point is (4,-10).

First are (4,-20),(4,0).

Mid point =[(4+4)/2,(-20+0)/2]

=(4,-10)

Second are (4,0) , (4,-20)

Mid point=[(4+4)/2,(0-20)/2]

=(4,-10)

Third are (8,-20),(0,0)

Mid point=[(8+0)/2,(-20+0)/2]

=(4,-10)

Fourth are (0,-20),(8,0)

Mid point =[(0+8)/2,(-10+0)/2]

=(4,-10)

Hence the ordered pairs that the mid point is (4,-10) are (4,-20),(4,0) & (4,0),(4,-20)& (8,-20),(0,0)&(0,-20),(8,0)&(0,0),(8,-20).etc.

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The nickels in the envelope is $0. 12

From the information given, we have that;

Dimes + nickels = $1. 20

1/4 dimes + dimes = $ 1. 35

Let dimes = d

Nickels = n

d + n = 1. 20    equation a

d/4 + d = 1. 35   equation b

Make 'd' subject from equation a

d = 1. 20 - n

Substitute into equation b

1. 20 - n/ 4 + 1. 20 - n = 1. 35

0. 3 - 0. 25n + 1. 20 - n = 1. 35

collect like terms

- 1. 25n = 1. 35 - 1. 5

- 1. 25 = - 0. 15

n = -0. 15/ -1. 25

n = 0. 12

Thus, the number of nickels in the envelope is $0. 12

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In conducting a​ goodness of fit test, a requirement is that​ the expected frequency must be at least ten for each category.

In relation to the statistical model, the test tells how well it fits a set of observations.

The measures of the goodness of fit summarize the discrepancy between observed values and the values expected under the model in question.

Also, when conducting a​ goodness of fit test, a requirement is that​ the expected frequency must be at least ten for each category.

Therefore, the Option B is correct,

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The expression which can be used to determine the algebraic sum of the given polynomials as in the task content is; -11x² +4x +14.

It follows from the task content that the polynomials whose sum are to be determined are; (9 - 3x2) + (-8x2 + 4x + 5).

Hence, the sum can be evaluated as follows;

= 9 - 3x² + -8x² + 4x + 5

= -11x² +4x +14.

Consequently, the required expression is; -11x² +4x +14.

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Answer:

Step-by-step explanation:

is 100 for the points

Answer
5/9 is the dividend

Step-by-step explanation:

The dimensions based on the area given are 15cm by 20cm.

From the information given about the rectangle, the area is given as 300cm² and the margins are given as 1.5 and 2.

Therefore, the dimensions will be:

(1.5 × x) × (2 × x) = 300

1.5x × 2x = 300

3x² = 300

x² = 300/3

x² = 100

x = 10

Therefore the dimensions will be:

= 1.5x = 1.5 × 10 = 15

= 2x = 2 × 10 = 20

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We minimize the total area of the sheet

[tex]S = xy[/tex]

constrained by

[tex](x-4)(y-3) = 300[/tex]

Solve the constraint equation for [tex]y[/tex].

[tex](x-4)(y-3) = 300 \implies y-3 = \dfrac{300}{x-4} \implies y = 3 + \dfrac{300}{x-4} = \dfrac{3x+288}{x-4}[/tex]

Substitute this into [tex]S[/tex] and find the critical points.

[tex]S = \dfrac{3x^2+288x}{x-4} = 3x + 300 + \dfrac{1200}{x-4}[/tex]

[tex]\dfrac{dS}{dx} = 3 - \dfrac{1200}{(x-4)^2} = 0[/tex]

[tex]\implies \dfrac{1200}{(x-4)^2} = 3[/tex]

[tex]\implies (x-4)^2 = 400[/tex]

[tex]\implies x-4 = \pm20[/tex]

[tex]\implies x=-16 \text{ or } x = 24[/tex]

Of course [tex]x[/tex] can't be negative, so the page dimensions that minimize [tex]S[/tex] are [tex]x=24[/tex] and [tex]y=18[/tex].

Using it's concept, the mean absolute deviation of the data-set is of 2 sundaes.

The mean for this problem is:

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

Hence the MAD is:

(|4-4| + |6-4| + |2-4| + |4-4|)/4 = 1

Since each unit represents 2 sundaes, the mean absolute deviation is of 2 sundaes.

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a. Central angle in the circle is: Angle BAC

b. A major arc is: Arc BEC

c. A minor arc is: Arc BC

d. measure of arc BEC is: 260°

e. m(BC) = 100°

A central angle has two of its sides as radii of the circle, forming an angle at the center of the circle, where the vertex is at the center of the circle.

A major arc has a measure that is greater than 180 degrees. That is, it is more than half a circle (semicircle). Thus, measure of major arc > 180 degrees.

A minor arc has a measure that is less than 180 degrees. That is, it is not more than half a circle (semicircle). Thus, measure of minor arc < 180 degrees.

a. Central angle in the circle is: Angle BAC

b. A major arc in circle A is: Arc BEC

c. A major arc in circle A is: Arc BC.

d. Measure of arc BEC = 360 - 100 [according to the central angle theorem]

Measure of arc BEC = 260°.

e. Measure of angle BAC = 100°  [given]

Measure of arc BC = angle BAC [according to the central angle theorem]

Measure of arc BC = 100°

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The standard deviation for the number of people with the genetic mutation is 3.77

The given parameters are:

Sample size, n = 300

Proportion that has the particular genetic mutation, p = 5%

The standard deviation for the number of people with the genetic mutation is calculated as:

Standard deviation = √np(1 - p)

Substitute the known values in the above equation

Standard deviation = √300 * 5% * (1 - 5%)

Evaluate the product

Standard deviation = √14.25

Evaluate the exponent

Standard deviation = 3.77

Hence, the standard deviation for the number of people with the genetic mutation is 3.77

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Answer:

Hi, to find the surface area of a cone is πrl

if your radius and length is given.

hope this helps (•‿•)

Answer:

200

Step-by-step explanation:

If 40% are roses than 60% must be sunflowers (40% + 60% = 100%)

We are trying to find 60% of some number is 120.

Let n = the total number of flowers

.6n = 120  Divide both sides by .6

n = 200

The given triangle has three angles with measurements: ∠A = 69°, ∠B = 52°, and ∠C = 59° respectively. Using the law of cosines, these angles are calculated from the given lengths of the triangle.

The law of cosines gives the relationship between the lengths of sides and the angles of the triangle ABC.

According to the law of cosines:

Cos A = (b² + c² - a²)/2bc

Cos B = (a² + c² - b²)/2ac

Cos C = (a² + b² - c²)/2ab

For the given triangle ABC,

a = 75, b = 63, and c = 69

So, using the law of cosines,

Cos A = (b² + c² - a²)/2bc

⇒ Cos A = (63² + 69² - 75²)/2×63×69

⇒ Cos A = 5/14

⇒ A = Cos⁻¹(5/14) = 69.07

∴ ∠A = 69°

Similarly,

Cos B = (a² + c² - b²)/2ac

⇒ Cos B = (75² + 69² - 63²)/2×75×69

⇒ Cos B = 31/50

⇒ B = Cos⁻¹(31/50) = 51.6 ≅ 52

∴ ∠B = 52°

Cos C = (a² + b² - c²)/2ab

⇒ Cos C = (75² + 63² - 69²)/2×75×63

⇒ Cos C = 179/350

⇒ C = Cos⁻¹(179/350) = 59.2

∴ C = 59°

Thus, the angles of the triangle ABC are 69°, 52°, and 59° respectively.

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Step-by-step explanation:

volume = area of circle × hight of cylinder ....

V = πr² × h

so V = πr²h

Answer:

  10831 mm³

Step-by-step explanation:

The volume of any solid figure with a uniform cross section parallel to the base can be found using the volume formula ...

  V = Bh

where B is the area of the base, and h is the height perpendicular to the base.

The base of this cylindrical stack of pennies is a circle of diameter 19.05 mm. The area formula for a circle in terms of diameter is ...

  A = (π/4)d²

The stack of pennies has a base area of ...

  A = (π/4)(19.05 mm)² ≈ 285.023 mm²

The volume formula tells us the stack of pennies has a volume of ...

  V = Bh

  V = (285.023 mm²)(38 mm) ≈ 10830.9 mm³

The volume of the stack of pennies is approximately 10831 mm³.