Solve the following equation, answer as a reduced, mixed number. Then place the correct number in the box provided.

15(2 - x) = 13(3 - x)

[tex]Answer ☘️[/tex]

★ Important points to know

[tex] {\boxed{ \bold{Exterior \: Angle \: Theorem : - }}}[/tex]

★ Let's solve :-

[tex] \sf ↪\angle \: 65 \degree + \angle \: 30 \degree =\angle \:B\\ \\ \sf ↪\angle \: 95 \degree = \angle \:B[/tex]

Hence option A 95⁰ is the right ans ✓

[tex]\sf{\:мѕнαcкεя\: ♪...}[/tex]

[tex]\sf\large \green{\underbrace{\red{Answer⋆}}}:[/tex]

To find :-

The angle ∠ABC = ?

Given :-

∠BCD = 65°

∠BDC = 30°

Solution :-

Firstly we have to find ∠CBD, with the help of ∠CBD, we will able to find ∠ABC.

To find ∠CBD, we will use angle sum formula

(=> The sum of angles of all 3 sides of triangle is equal to 180°).

∠CBD + ∠BCD + ∠BDC = 180° (angle sum property)

∠CBD + 65° + 30° = 180°

∠CBD + 95° = 180°

∠CBD = 180° - 95°

∠CBD = 85°

Now we have ∠CBD, and in the diagram ∠CBD and ∠ABD lies on the same line but it is seperated by line BC, it means they are linear pair and the sum of both angles (∠CBD and ∠ABC) is equal to 180°.

∠ABC + ∠CBD = 180° (linear pair)

∠ABC + 85° = 180°

∠ABC = 180° - 85°

∠ABC = 95°

Result :-

The ∠ABC is 95° by using the above method.

Choose the first option

(A) 95°

The term used to describe the process of assigning values to responses in a research instrument and grouping them is called: coding.

In data analysis, before raw data can be processed, the researcher groups and assigns values to each response in the research instrument for easy collation and analysis.

This is referred to as coding, in research analysis.

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Answer: 1/10, 1/7, 2/9, 2/5, 7/11, 1/4, 1/10, 1/7,  1/9, 1/2 , 1/8, 1/12, 0/1, 0/0
1/13, 1/3, 1/4

Step-by-step explanation: i think i know all the answers

Answer: 14.5

Step-by-step explanation: (1½ ×3 ) + (2½ ×4)² = 4.5 + 10

Answer:

the value of k is 27.

Step-by-step explanation:

find by using formula y2-y1/x2-x1

Answer:

6%

Step-by-step explanation:

3/20=4/x

It is a indirect proportion so we reciprocal,

Then,

3/20=x/40

3×40=20×x

120=20x

x=120/20

x=6

The required probability for the given case is 0.4779.

The binomial distribution is based on the binomial theorem which can be written as (a + b)ⁿ = ⁿC₀aⁿb⁰ +  ⁿC₁aⁿ⁻¹b¹ + ⁿC₂aⁿ⁻²b²+ ....+  ⁿCₙa₀bⁿ.

In order to use in the probability, there should be events independent of each other and the sum of there probabilities is 1.

Given that,

The total number of students are 20.

And, the probability that a student cheats is 3/20 = 0.15.

The number of students chosen by the teacher is 4.

Thus, the probability that at least one student cheats can be found by binomial distribution as,

P(at least one student cheats) = ⁴C₁(0.15)¹(0.85)³ + ⁴C₂(0.15)²(0.85)² +  ⁴C₃(0.15)³(0.85)¹ + ⁴C₄(0.15)⁴(0.85)⁰

= 4 × 0.15 × 0.6141 + 6 × 0.0225 × 0.7225 + 4 × 0.003375 × 0.85 + 1 × 0.00050625

= 0.4779

Hence, the probability that at least one student selected by the teacher does cheating is 0.4779.

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Answer:

$30

Step-by-step explanation:

if something is 50% off that is the same as saying half off.

so you simply do 60 divided by 2 and you get 30

Answer:

$30

Step-by-step explanation:

You get this anaswer by multiplying 60 (the cost of the suitcase) by 0.50 (50 percent as a decimal) and get 30 then subtract 30 by 30 to get the total cost.

Answer:

v=3,m=2

Step-by-step explanation:

You can find the complete solution in given attachment

I hope it helped you

Answer:

A and C

Step-by-step explanation:

1) -5(4x-6)-14=-4x+16

-20x+30-14+4x-16=0

-16x=0

x=16

3)4x-8(x-2)=-4x+16

-4x+16=-4x+16

Answer:

3.14     (or pi )  feet  

Step-by-step explanation:

Entire circle circumference  = pi *d  = 8 pi    feet

45 degrees is a fraction of the entire 360 degrees of the circle

   45 / 360  *  8 pi = pi =  3.14 ft

Using the vertex of the quadratic equation, it is found that the ball reaches it's maximum height after 2.1 seconds.

A quadratic equation is modeled by:

[tex]y = ax^2 + bx + c[/tex]

The vertex is given by:

[tex](x_v, y_v)[/tex]

In which:

[tex]x_v = -\frac{b}{2a}[/tex]

[tex]y_v = -\frac{b^2 - 4ac}{4a}[/tex]

Considering the coefficient a, we have that:

In this problem, the equation is given by:

h(t) = -5t² + 21t + 120.

Meaning that the coefficients are a = -5, b = 21, c = 120.

Hence, the time at which the maximum height is reached is given by:

[tex]t_v = -\frac{b}{2a} = -\frac{21}{-10} = 2.1[/tex]

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Answer:

B

Step-by-step explanation:

because 30÷3=10

Answer:

Your answer is B

Step-by-step explanation:

Answer:

range: 70

Step-by-step explanation:

range is the difference between the highest and lowest values.

Answer: a= -18

              b= -28 inches      c=30 pounds

Step-by-step explanation:

4a.4²x +3=1

Slotuion:

4²x + 3=1 : x= -⅛ (Decimal:x= -0.125)

Steps

4² x +3=1

4²=16

16x + 3=1

Subract 3 from borh sides

16x +3-3=1-3

Simplify

16x=-2

Divides both sides by 16

[tex] \frac{16 \times }{16} =

[tex] \frac{ - 2}{16} [/tex]

[/tex]

Simplitfy

[tex] \frac{16 \times }{16} : x[/tex]

Simplify

[tex] \frac{ - 2}{16}: -⅛ [/tex]

x = -⅛

therefore the answer is x= -⅛

4b.ex-1 -5 =5

x~=3.30258

explanation:

e^(x-1)-5=5

e^(x-1)=10

x-1=ln 10

x-1~=2.30258

x~=3.30258

[tex] \large \pink{ \overbrace{ \underbrace{ \tt{ \color{red}{ \: \: \: \: \: \: \: hope \: it \: help \: you \: \: \: \: \: \: \: \: }}}}}[/tex]

You have writing errors may be

[tex]\\ \rm\Rrightarrow 4x²+3=1[/tex]

[tex]\\ \rm\Rrightarrow 4x²=1-3[/tex]

[tex]\\ \rm\Rrightarrow 4x²=-2[/tex]

[tex]\\ \rm\Rrightarrow x^2=-1/2[/tex]

[tex]\\ \rm\Rrightarrow logx²=-log0.5[/tex]

[tex]\\ \rm\Rrightarrow 2logx=-log0.5[/tex]

[tex]\\ \rm\Rrightarrow logx=0.15[/tex]

[tex]\\ \rm\Rrightarrow x=10^{0.15}[/tex]

[tex]\\ \rm\Rrightarrow x=1.412[/tex]

#2

[tex]\\ \rm\Rrightarrow e^{x-1}-5=5[/tex]

[tex]\\ \rm\Rrightarrow e^{x-1}=10[/tex]

[tex]\\ \rm\Rrightarrow x-1=ln10[/tex]

[tex]\\ \rm\Rrightarrow x-1=2.3[/tex]

[tex]\\ \rm\Rrightarrow x=2.3+1[/tex]

[tex]\\ \rm\Rrightarrow x=3.3[/tex]

Answer:

D. 11/9

Step-by-step explanation:

Which of the following fractions is the largest?

A. 5/81

B. 75/81

C. 10/9

D. 11/9

To make things easier, convert the fractions to decimals:

A. 5/81 = 0.062

B. 75/81 = 0.93

C. 10/9 = 1.11

D. 11/9 = 1.22

As we can see, 11/9 or 1.22, is the largest of all the values.

Hope this helps!

To make the denominators of the given fractions equivalent, we need to determine the LCM of the denominators. Clearly, the denominators of the set of fractions are 81, 81, 9, and 9 respectively.

LCM = 81 (81 × 1 = 81 and 9 × 9 = 81)

Multiply the denominators such that the denominator is equivalent to 81. Keep in mind that if we are multiplying a number (x), the numerator must be multiplied by the same number (x) .

   ⇒ 5/81, 75/81, 10/9, 11/9

   ⇒ (5 × 1)/(81 × 1), (75 × 1)/(81 × 1), (10 × 9)/(9 × 9), (11 × 9)/(9 × 9)

   ⇒ (5)/(81), (75)/(81), (90)/(81), (99)/(81)

   ⇒ 5/81, 75/81, 90/81, 99/81

Since 99 > 90 > 75 > 5, we can tell that 99/81 is the largest as:

Therefore, 11/9 is the largest fraction in the set.

The proportionality shows the relation between two values.  The value of the constant of variation is 5.

The proportionality shows the relation between two values.

As given in the question the quantity q varies inversely with the square of m and directly with the product of r and x. Therefore, the proportionality can be written as,

[tex]q \propto \dfrac{rx}{m^2}[/tex]

Now to remove the proportionality add a constant to the equation which is the constant of variation.

[tex]q =k\dfrac{rx}{m^2}[/tex]

When m is 4 and the product of r and x is 8 then the value of q is 2.5. Therefore, the value of k can be written as,

[tex]q =k\dfrac{rx}{m^2}\\\\2.5 = k\dfrac{8}{4^2}\\\\\dfrac{2.5 \times 16}{8}=k\\\\k=5[/tex]

Thus, the value of the constant of variation is 5.

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Answer :-

Let the side of the square measure a cm, thus, according to the question,

We know that,

➭ Area ( Square ) = a²

Thus, the area of the square with normal length i.e. a cm, will be,

⤳ Area = a x a

⤳ Area = a²

Now, by taking the new length, the area will become,

⤳Area = 3a x 3a

⤳ Area = 9a²

Now,

We observe that, if we divide these, we get,

➤ 9a²/a²

( a² will get canceled since its common )

Thus, the ratio becomes,

➭ 9 : 1 = Area square with tripled length : Area of square

Thus, the area will increase by 9 times, and not 3.

Hence, Ashley's assumptions are wrong.

The annual premium result in an annual out-of-pocket expense that is about the same as her current plan is $0.28 per $100 of value.

Insurance premiums are paid for policies that cover all the basic needs such as healthcare, home, and life insurance.

We are given Amount of insurance policy for Stephanie = $ 355,000

Annual premium = $ 0.42 per $100

Deductible amount = $ 500

Total Annual out of pocket expense

= [($355,000/100) x $0.42] + $500

= $1,991  

Now, the New Deductible amount that Stephanie wants is $ 1000

So, Let the annual premium be x

To find the annual premium in an annual out-of-pocket expense that is about the same as her current plan when the deductible amount increases to $1000

355,000x / 100 + 1000 = 1991

3550x + 1000 = 1991

3550x = 1991 - 1000

3550x = 991

x = 991/3550

x = 0.279≈0.28

Hence the annual premium result in an annual out-of-pocket expense that is about the same as her current plan is $0.28 per $100 of value.

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Answer:

Pink is the least likely to be chosen because it has the lowest frequency.

Step-by-step explanation:

Step-by-step explanation:

90 degrees rotation, clockwise

Answer:

0.733 repeating

Step-by-step explanation:

use your calculator

Answer:

OPTION D

Step-by-step explanation:

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

[tex]6x + y = - 8[/tex]

[tex]y = - 6x - 8[/tex]

I hope it helped you

The number of laps around the lake did Heather run last week when the Ken ran 10 laps around the lake is 20/3.

Fraction number is the number which is a part of a whole number. It is written with a numerator and denominator. Fraction number are written as,

[tex]\dfrac{a}{b}[/tex]

Here (a) is the numerator and (b) is the denominator.

Last week, Ken ran 10 laps around the lake. Heather ran 2/3 as many laps around the lake as Ken did. Thus, the number of laps heather ran is,

[tex]x=\dfrac{2}{3}\times10\\x=\dfrac{20}{3}[/tex]

Hence, the number of laps around the lake did Heather run last week when the Ken ran 10 laps around the lake is 20/3.

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A) no property

B) distributive property of multiplication

C) no property

D) no property

E) no property

     [tex]\downarrow[/tex]

     [tex]no\ property[/tex]

____________________________________

    [tex]\downarrow[/tex]

    [tex]distributive\ property\ of\ multiplication[/tex]

____________________________________

    [tex]\downarrow[/tex]

    [tex]no\ property[/tex]

____________________________________

    [tex]\downarrow[/tex]

    [tex]no\ property[/tex]

____________________________________

    [tex]\downarrow[/tex]

    [tex]no\ property[/tex]

I hope this helps you

:)

Answer:

D and E

Step-by-step explanation:

i took the quiz on usa test prep

Answer:

x=11.1

Step-by-step explanation:

we can use the sine function: (opposite/hypotenuse)

sin(46)=8/x

x=8/(sin46)

11.1

Answer:

A

Step-by-step explanation:

8% = .08 in decimal form

10 000 ( 1 + .08)^10 =