Watch the sign of the cosine function when using the cosign law. Cos 120 degrees for example, is in the second quadrant and therefore

The statement that is TRUE of the rectangle is AB + BD > AD. Option A

WE have that a diagonal divides the rectangle into two equal triangles

line AD is the length of the diagonal

With the diagonal drawn, we have

AD = hypotenuse

AB  and BD are the two other sides

From the Pythagorean theorem, we have that the square root of the square sum of the other two sides fives the hypotenuse. This mean that their sum is greater than the hypotenuse

Thus, the statement that is TRUE is AB + BD > AD. Option A

The complete question is;

Which of the following statements is TRUE about rectangle ABDC.

a. AB + BD > AD

b. AB + BD < AD

c. AB + BD = AD

d. (AB) (BD) = AD

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30 Jagged rocks are the same 3 shiny rocks using the exchange rates provided(i.e. option D)

What is an exchange rate?

Exchange rate means the rate at which one item exchanges hands with another, for instance, in this case, 6 jagged rocks are equivalent to 2 smooth pebbles.

6 jagged rocks=2 smooth pebbles

divide both sides by 2

6/2 jagged rocks=2/2 smooth pebbles

3 jagged rocks=1 smooth pebble

We can rewrite as below:

1 jagged rock=1/3 smooth pebble

30jagged rocks=1/3*30 smooth pebbles

30 jagged rocks=10 smooth pebbles

Now we need to convert 10 smooth pebbles to shiny rock equivalence

3 smooth pebbles=1 shiny rock

1 smooth pebble=1/3 shiny rock

10 smooth pebbles=1/3*10 shiny rocks

10 smooth pebbles=3 shiny rocks( even though it is 3.33, but the final answer should be rounded to a whole number)

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Answer:

70

Step-by-step explanation:

45+90=135

180-45=45

q=45

45+65=110

180-110=70

70-45=25

p=25

45+25=70

Answer: 70°

Step-by-step explanation:

We know that the sum of all 3 angles in a triangle is 180°. Hence, we can just set all measures to be equal to 180° and solve for the variables.

[tex]p+65+90=180\\p+155=180\\p=25[/tex]

[tex]45+90+q=180\\135+q=180\\q=45[/tex]

[tex]p+q=25+45=70[/tex]

The sum of p and q is 70°.

Answer:

152 units

Step-by-step explanation:

Two sides of the rectangle are 27 units long and the other two sides are 49 units wide. You just add all the numbers up (27+27+49+49). When you do that, you get 152. I hope this helps!

Step-by-step explanation:

the third option is the answer.

Let A, B, and W denote the sets of students apply to Addis Ababa Uni (A), Bahir Dar Uni (B), or Wachemo Uni (W). Let U denote the universal set of all students in the class.

We're given the cardinalities of several sets:

• total number of students: [tex]n(U) = 60[/tex]

• A applicants: [tex]n(A) = 30[/tex]

• B applicants: [tex]n(B) = 25[/tex]

• W applicants: [tex]n(W) = 24[/tex]

• A and B applicants: [tex]n(A\cap B) = 11[/tex]

• A and W applicants: [tex]n(A \cap W) = 6[/tex]

• B and W applicants: [tex]n(B\cap W) = 9[/tex]

• non-applicants: [tex]n(U \setminus (A\cup B\cup W)) = 4[/tex]

The last cardinality tells us [tex]n(A\cup B\cup W) = 60-4 = 56[/tex] students applied anywhere at all.

We want to find [tex]n(A\cap B\cap W)[/tex], the number of students that applied to each of the three universities.

By the inclusion/exclusion principle,

[tex]n(A\cup B\cup W) = n(A) + n(B) + n(W) \\\\~~~~~~~~~~~~~~~~~~~~~~~~ - n(A\cap B) - n(A\cap W) - n(B\cap W)\\ \\~~~~~~~~~~~~~~~~~~~~~~~~ + n(A\cap B\cap W)[/tex]

That is, we count up all the students in the sets A, B, and W, then subtract the number of students in each pairwise intersection to not double-count, then add back the number of students in the intersection of all three sets since it was removed in the previous step.

Now solve.

[tex]56 = 30 + 25 + 24 - 11 - 6 - 9 + n(A\cap B\cap W)[/tex]

[tex]\implies n(A\cap B\cap W) = \boxed{3}[/tex]

Answer: [tex]m\angle BAM=30^{\circ}[/tex]

Step-by-step explanation:

[tex]AD=x\sqrt{3}[/tex] (Pythagorean theorem)

[tex]m\angle ACD=60^{\circ}[/tex] (30-60-90 triangle)

[tex]m\angle MCA=30^{\circ}[/tex] (angle subtraction)

[tex]m\angle MAC=30^{\circ}[/tex] (base angles theorem)

[tex]m\angle CAD=30^{\circ}[/tex] (30-60-90 triangle)

[tex]m\angle BAM=30^{\circ}[/tex] (angle subtraction)

Answer:

108

Step-by-step explanation:

When the lines cut through by a transversal are parallel, alternate interior angles are congruent. angle 4 = angle 6 = 108

Answer:

C) The volume of the prism is equal to the volume of the cylinder.

Step-by-step explanation:

volume of triangular prism = area of base × height

volume of cylinder = area of base × height

The cross sectional area are equal, so the bases have the same area.

The heights are also equal.

The volumes must be equal.

Answer: C) The volume of the prism is equal to the volume of the cylinder.

Answer:

C) The volume of the prism is equal to the volume of the cylinder.

Step-by-step explanation:

If the cross-sectional areas of the triangular prism and the right cylinder are congruent, it means that when you look at their shapes from the top or bottom, they have the same size and shape.

Since both the triangular prism and the right cylinder have a height of 5 units, and their cross-sectional areas are the same, it implies that they have the same volume as well. So, the volume of the triangular prism is equal to the volume of the cylinder.

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it would take Janis 14 minutes to complete a package alone

From the information given,

Let's say that

Carol working time = x = 30 minutes

Janis working time = y

x + y = 16 minutes

Let's make 'y' the subject

30 - 16 = y

y= 14 minutes

Thus, it would take Janis 14 minutes to complete a package alone

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Answer:

6.2 rounds

Step-by-step explanation:

since 1 kilometer is 0.62 miles

10 kilometers is 6.2 miles

so about 6 and 1/5 rounds

Using right triangle, the length of the ramp is 10.44 ft.

The situation forms a right angle triangle.

The length of the ramp is the hypotenuse side of the right triangle.

Therefore, using Pythagoras theorem,

c² = a² + b²

where

Therefore,

c² = 10² + 3²

c² = 100 + 9

c = √109

c = 10.4403065089

c = 10.44 ft

Therefore, the length of the ramp is 10.44 ft.

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a)

b) Conditions:[tex]\sigma[/tex] is understood to have a regular distribution of weights

c) Interpretation: 80 percent of the time, this range will include the actual average weight of Allen's hummingbirds, hence its reliability may be counted on

d) sample size [tex]n \approx 27[/tex].

Generally,
Here n = 17

T= 3.15

[tex]\sigma=0.40[/tex]

confidence level =c = 0.80

Here we will usethe  z critical value.

z critical value for (1+c) /2 = (1+0.80)/2

z critical value for (1+c) /2= 0.9

Zc = 1.28

Critical value = 1.28

a) Margin of error (E) :

[tex]E = Zc*\frac{\sigma}{\sqrt{n}}\\\\\E = 1.28*\frac{0.40}{\sqrt{17}}[/tex]

E =0.124

Margin of error = E =0.124

Lower limit = x-E

L= 3.15 - 0.124

L= 3.026

Lower limit =3.026

Upper limit = x + E

U= 3.15 + 0.124

U= 3.274

Upper limit =  3.274

The following is a confidence interval with a value of 80 percent for the mean weights of Allen's hummingbirds in the area under study: (3.02,3.28)

b) Conditions:[tex]\sigma[/tex] is understood to have a regular distribution of weights

c) Interpretation: 80 percent of the time, this range will include the actual average weight of Allen's hummingbirds, hence its reliability may be counted on.

d) When is already known, the following equation may be used to determine the appropriate number of samples, n:

[tex]n=(\frac{z_c*\sigma }{E})^2[/tex]

Margin of error = 0.13

Sample size (n):

[tex]n= (\frac{z_c*\sigma }{E})^2[/tex]

[tex]n=(\frac{ 1.28*0.36}{0.09})^2[/tex]

n = 26.21

[tex]n \approx 27[/tex]

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Answer:

g(-1) = 3, g(2) = 6, g(5) = 4

Step-by-step explanation:

Please refer to attached photo. (Apologies for the terrible handwriting.)

From here we can see,

g(x) = x + 4 applies for values x less than or equal to 2.

g(x) = 9 - x applies for values x more than 2 (which does not include 2.)

g(-1):

Since -1 < 2,

g(-1) = -1 + 4 = 3

g(2) = 2 + 4 = 6

g(5):

Since 5 > 2,

g(5) = 9 - 5 = 4

75 percent of the stock are sleeveless

The given parameters are:

Blouse = 120

Sleeveless = 90

The percentage is calculated as:

Percentage = Sleeveless/Blouse * 100%

So, we have:

Percentage = 90/120* 100%

Evaluate the expression

Percentage = 75%

Hence, 75 percent of the stock are sleeveless

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Answer:

[tex]\text{f}^{-1}(x)=\dfrac{x-15}{12}[/tex]

Step-by-step explanation:

[tex]\text{f}^{-1}(x)[/tex] is the notation for the inverse of a function.  

The inverse of a function is a reflection in the line y = x.

Given function:

[tex]\text{f}(x)=15+12x[/tex]

To find the inverse of the given function:

Step 1

Replace f(x) with y to get an equation for y in terms of x:

[tex]\implies y=15+12x[/tex]

Step 2

Rearrange the equation to make x the subject:

[tex]\implies y-15=15+12x-15[/tex]

[tex]\implies y-15=12x[/tex]

[tex]\implies \dfrac{y-15}{12}=\dfrac{12x}{12}[/tex]

[tex]\implies x=\dfrac{y-15}{12}[/tex]

Step 3

Replace x with [tex]\text{f}^{-1}(x)[/tex] and y with x → this is the inverse function:

[tex]\implies \text{f}^{-1}(x)=\dfrac{x-15}{12}[/tex]

Step 4 (if necessary)

The domain of the function is the range of the inverse function.

The range of the function is the domain of the inverse function.

Therefore, as the domain and range of the given function are unrestricted, so too are the domain and the range of the inverse function:

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[tex]\\ \rm\leadsto y=15+12x[/tex]

Interchange x and y

[tex]\\ \rm\leadsto x=15+12y[/tex]

Solve for y

[tex]\\ \rm\leadsto 12y=x-15[/tex]

[tex]\\ \rm\leadsto y=\dfrac{x-15}{12}[/tex]

That's the inverse

The number π (pi) is a mathematical constant which is equal to the ratio of a circle's circumference to its diameter. It has a value of π = 22/7

An equation is an expression that shows the relationship between two or more variables and numbers.

The number π (pi) is a mathematical constant which is equal to the ratio of a circle's circumference to its diameter. It is given by:

π = 22/7

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Answer:

  G.  24

Step-by-step explanation:

The perimeter of the figure is the sum of its side lengths. The given dimensions tell us all of the side lengths.

Triangle BCX is given as an isosceles triangle with a base angle of 60° and side lengths of 4. Such a triangle is equilateral, so all side lengths will have a measure of 4.

The given information tells us all sides that appear parallel are parallel, so the figure consists of 4 equilateral triangles. Every short line segment has length 4.

The perimeter is the length of 6 short line segments, so is ...

  P = 6×4 = 24

The perimeter of parallelogram ABCD is 24 units.

Answer:

12705

Step-by-step explanation:

The problem could be solved in two different methods:

1:

231×(55)=12705

2.

231×40+231×15=9240+3465=12705

Answer:

6.2 pounds

Step-by-step explanation:

$5.58 / $.9 = 6.2 pounds of carrots bought

Answer:

what is the monthly payment or ask for the mileage use for the car

Answer:

1±2i.

Step-by-step explanation:

1. if to evaluate the expression given, it can be written

(x-5)(x²-2x+5)=0;

2. where the nonreal roots are 1±2i.

[tex] {\qquad\qquad\huge\underline{{\sf Answer}}} [/tex]

Information : The given ellipse is a horizontal ellipse, and it's centre lies on origin, as the foci are given on x - axis.

The foci of the ellipse can be written in form :

[tex]\qquad \sf  \dashrightarrow \: ( \pm ae , 0)[/tex]

So,

[tex]\qquad \sf  \dashrightarrow \: ae = 5[/tex]

and Vertex of the ellipse can be written as

[tex]\qquad \sf  \dashrightarrow \: (\pm a,0)[/tex]

Now, plug the value in first equation ~

[tex]\qquad \sf  \dashrightarrow \: ae = 5[/tex]

[tex]\qquad \sf  \dashrightarrow \: 11e = 5[/tex]

[tex]\qquad \sf  \dashrightarrow \: e = \cfrac{5}{11} [/tex]

Now, we have to find b (length of semi minor axis)

we can use the formula ~

[tex]\qquad \sf  \dashrightarrow \: b {}^{2} = {a}^{2} (1 - {e}^{2} )[/tex]

[tex]\qquad \sf  \dashrightarrow \: b {}^{2} = 121(1 - \frac{25}{121} )[/tex]

[tex]\qquad \sf  \dashrightarrow \: b {}^{2} = 121( \frac{121 - 25}{121} )[/tex]

[tex]\qquad \sf  \dashrightarrow \: b {}^{2} = 96[/tex]

Now, we can write the equation of ellipse as :

[tex]\qquad \sf  \dashrightarrow \: \cfrac{ {x}^{2} }{ {a}^{2} } + \cfrac{ {y}^{2} }{ {b}^{2} } = 1[/tex]

[ plug the values ]

[tex]\qquad \sf  \dashrightarrow \: \cfrac{ {x}^{2} }{ {121}^{} } + \cfrac{ {y}^{2} }{ {96}^{} } = 1[/tex]

Answer:

[tex]\dfrac{x^2}{121}+\dfrac{y^2}{96}=1[/tex]

Step-by-step explanation:

General equation of an ellipse:

[tex]\dfrac{(x-h)^2}{a^2}+\dfrac{(y-k)^2}{b^2}=1[/tex]

where:

If a > b the ellipse is horizontal, a is the major radius, and b is the minor radius.

If b > a the ellipse is vertical, b is the major radius, and a is the minor radius.

Given:

Therefore, the ellipse is horizontal with its center at (0, 0):

⇒ h = 0 and k = 0

⇒ a = 11

⇒ c = 5

To find b², use  c² = a² − b²:

⇒ 5² = 11² − b²

⇒ b² = 11² − 5²

⇒ b² = 96

Therefore, the standard form of the equation of the ellipse is:

[tex]\implies \dfrac{(x-0)^2}{11^2}+\dfrac{(y-0)^2}{96}=1[/tex]

[tex]\implies \dfrac{x^2}{121}+\dfrac{y^2}{96}=1[/tex]

Answer:

Same side interior angles

x=10

Step-by-step explanation:

The angles are same side  interior angles

The add to 180 degrees

6x+10 + 110 = 180

Combine like terms

6x+120 =180

Subtract 120 from each side

6x = 180-120

6x= 60

Divide by 6

6x/6 = 60/6

x = 10

Answer:

Same-Side Interior Angles

Equation: 6x + 10 + 110 = 180

x = 10

Step-by-step explanation:

Hello!

The sum of the two given angles is 180°, as they are same-side interior angles.

Equation: 6x + 10 + 110 = 180

The value of x is 10°.

Distance formula ds = v(dx² + dy²) s = ? v(1 + (dy/dx)²) dx ......... s = the arc length y = 171 - x²/45

chegg

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Answer:

3+37

11+29

17+23

20+20

Step-by-step explanation:

It's 20

(20+20 = 40)

Hope this helps!

The quantity of product that would result in the same profit is 1 thousand. Option A

Given the polynomial function as;

P(t) = –2t³ + 8t² + 2t

Where;

Let's equate the values

–2t³ + 8t² + 2t = 8

–2t³ + 8t² + 2t - 8 = 0

Factorize the expression

(-2t³ + 8t²) + ( 2t -8) = 0

- t² ( 2t - 8) + (2t -8) = 0

We take the similar factor

2t - 8 = 0

2t = 8

t = 8/2

t = 4

But we have that the company produced 4 thousand products for $8 million profit, so we have

= 4/ 4

= 1 thousand

Thus, the quantity of product that would result in the same profit is 1 thousand. Option A

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Step-by-step explanation:

Ig by dividing 12.50 and 250