What is the length of the side opposite the 60° angle?

Hence, the required algebraic expression is 8([tex]x^2[/tex]+4x+4) + 17 -32

expression is a combination of numbers, variables, and functions (such as addition, subtraction, multiplication or division etc.). This math operation can be addition, subtraction, multiplication, or division. The structure of an expression is: Expression is (Number/Variable, Math Operator, Number/Variable)

We were given y = 8[tex]x^2[/tex]+32x+17

To convert to vertex form, We factor out the leading coefficient which is 8.

Next, we form a perfect square by adding and subtracting 32 to get,

[tex]y=8(x^2+4x)+8(4)+17-8(4)[/tex]

We factor and combine the first two terms with a common factor of 8

This simplifies to,

              8([tex]x^2[/tex]+4x+4) + 17 -32

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Answer:

Answer is y = 8(x2 + 4x +

4

) + 17 +

-32

Step-by-step explanation:

The fraction of 5 seconds in 1 minute or part of 5 seconds in 1 minute is 1/12.

The fraction of 5 seconds in 1 minute or part of 5 seconds in 1 minute is calculated as follows;

1 minute = 60 secs

Fraction = 5 / 60

Fraction = 1/12

Thus, the fraction of 5 seconds in 1 minute or part of 5 seconds in 1 minute is 1/12.

The complete question is below:

What is part of 1 minute is 5 seconds?

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Answer: y=40

Step-by-step explanation:

because a triangle adds up to 180 degrees, and you subtract 180-15-26.5-90[the right angle]=40

The probability that a person wins the game is 32.1%

Based on the information given, the following can be depicted. It should be noted that there are 6 sides as well as 4 cards.

Therefore, the numbers on the dice i.e from 1 - 6 will be represented 4 times each. This gives a total of (4 × 6) = 24. There are also 4 cards. The total in sample space will now be:

= 24 + 4 = 28

The frequency table will be such that 28 or more has a relative frequency of 9. Therefore, the probability that a person wins the game will be:

= 9/28 = 32.1%

When you win 25% of the time, this illustrates that the number of products picked will be:

= 25% × 28

= 7 products.

The probability of participants achieving a winning score of 36 or higher in four consecutive attempts will be:

= 1/6⁴

= 1/1296

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The length of a in the triangle to the nearest tenth is 8.1 units.

The side a of the triangle can be found using cosine formula.

Therefore,

a²= b² + c² - 2bc cos A

a² = 10² + 12² - 2 × 10 × 12 cos 42°

a² = 100 + 144 - 240cos 42

a² = 244 - 178.354758115

a = √65.6453

a = 8.10217871933

a = 8.1

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Answer:

[tex]\frac{1}{16}, \frac{1}{4}, \frac{3}{16}[/tex]

Step-by-step explanation:

Recall a probability: [tex]P=\frac{F}{T}[/tex] , where F is a number of favorable outcomes and T is a number of total outcomes.

The probability to get tail is [tex]\frac{1}{2}[/tex] as well as probability to get head.

The probability to choose number 7 of 8 numbers at total is equal to [tex]\frac{1}{8}[/tex].

Therefore, the probability to get number 7 and a tail is:

[tex]\frac{1}{8}\cdot \frac{1}{2}=\frac{1}{16}[/tex]

Prime numbers from 1 to 8 are: 2, 3, 5 and 7, so there are 4 numbers of 8 numbers in total, so the probability to get a prime number is  [tex]\frac{4}{8}=\frac{1}{2}[/tex].

The second probability is equal to [tex]\frac{1}{2}\cdot \frac{1}{2}=\frac{1}{4}[/tex].

The numbers greater than 5 are: 6,7,8, so there are 3 numbers of 8 in total, so the probability to get a number greater than 5 is [tex]\frac{3}{8}[/tex].

The third probability is equal to:  [tex]\frac{3}{8}\cdot \frac{1}{2}=\frac{3}{16}[/tex].

If the fraction of times an event happened in the past is used as the basis for assigning a probability to the event, this is Empirical probability.

If the events are mutually exclusive, special additional rules can be applied. -Additional general rules can be used if the events are not mutually exclusive. Events A and B must be mutually exclusive.

If the occurrence of one event is not completely affected by the occurrence of another event, such an event is probabilistically called an independent event, and the event affected by another event is a dependent event. Is called dependent events.

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No, there is significant difference in the use of e readers by different age groups.

Given sample 1 ( 29 years old) [tex]n_{1}[/tex]=628, [tex]p_{1}[/tex]=7%, sample 2( 30 years old)[tex]n_{2}[/tex]=2309, [tex]p_{2}[/tex]=0.11.

We have to first form hypothesis one null hypothesis and other alternate hypothesis.

[tex]H_{0}:[/tex]π1-π2=0

[tex]H_{1}:[/tex]π1-π2≠0

α=0.05

Difference between proportions [tex]p_{1}-p_{2} =-0.04[/tex]

[tex]p_{d}=0.07-0.11=-0.04[/tex]

The pooled proportion needed to calculate standard error is:

[tex]p=(X_{1} -X_{2} )/(n_{1} +n_{2} )[/tex]

=(44+254)/(628+2309)

=0.10146

The estimated standard error of difference between means is computed using the formula:

[tex]S_{p_{1} -p_{2} }=\sqrt{p(1-p)/m_{1}+p(1-p)/n_{2} }[/tex]

=[tex]\sqrt{0.101*0.899/628+0.101*0.899/2309}[/tex]

=[tex]\sqrt{0.000143+0.00003}[/tex]

=[tex]\sqrt{0.000173}[/tex]

=0.01315

Z= Pd-(π1-π2)/[tex]S_{p_{1} -p_{2} }[/tex]

=-0.04-0/0.013

=-3.0769

This test is a two tailed test so the p value for this test is calculated as (using z table)

p value:2 P(Z<-3.0769)

=2*0.002092

=0.004189

P value< significance level of 5%.

Hence there is enough evidence to show the claim that there is a significant difference in the use of e readers by different age groups.

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Question is incomplete as it also includes:

Significance level of 5%.

Hello and Good Morning/Afternoon

Let's take this problem step-by-step

The Line DF is '5x + 7' cm long

The Line DF is made up of two lines DE and EF

    ⇒ therefore

          [tex]DE + EF = \\ 7 + 4x + 3 = 5x + 7\\10+4x=5x+7\\5x-4x=10-7\\x=3[/tex]

Let's plug x's value into '5x + 7'

    [tex]\hookrightarrow DF = 5(3) +7=22[/tex]

Answer: 22cm

Hope that helps!

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The statement that are true about the dilation are:

A. M'N' is 18 units.

D. The dilation is an enlargement.

F. Scale factor is 3.

Given that rectangle LMNP is dilated using the rule Dp.3, it means that rectangle LMNN is enlarged times 3 to get rectangle L'M'N'P'.

This means that the scale factor is 3.

We would have the following:

M'N' = 6 × 3 = 18 units.

Therefore, the statements that are true are:

A. M'N' is 18 units.

D. The dilation is an enlargement.

F. Scale factor is 3.

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Answer:  A. The length of line segment M'N' is 18 units,  D. The dilation is an enlargement, & F. The scale factor is 3.

Step-by-step explanation:  TRUST ME!!! Answer is correct in Edge.  :)

Answers: A, D & F.  

Answer:

To show that 2 triangles are congruent, both triangles must have the same the same size and shape. Basically both triangles must have the same 3 angles and 3 sides.

Step-by-step explanation:

This means that the corresponding sides are equal and the corresponding angles are equal. We can tell whether two triangles are congruent without testing all the sides and all the angles of the two triangles.

Hope this helped! :D

Answer:

Step-by-step explanation:

Follow this rules

Work Shown:

[tex]b^2 = a^2 + c^2 - 2*a*c*\cos(B)\\\\b^2 = 150^2 + 30^2 - 2*150*30*\cos(150)\\\\b^2 \approx 31194.22863406\\\\b \approx \sqrt{31194.22863406}\\\\b \approx 176.618879608211\\\\b \approx 176.6\\\\[/tex]

Answer:

[tex]4\sqrt2[/tex]

Step-by-step explanation:

[tex]2\sqrt{2} +\sqrt{8}=2\sqrt{2}+2\sqrt{2}=4\sqrt{2}[/tex]

Step-by-step explanation:

i sent the solution in the photo pls check it

The graph of the linear equation can be seen in the image below.

Here we have the linear equation:

y = (2/5)*x - 6

To graph it, we just need to find two points on the line, and then connect them with a line.

To find the points we just evaluate in two values of x.

if x = 0.

y = (2/5)*0 - 6 = -6

Then we have the point (0, -6)

If x = 5.

y = (2/5)*5 - 6 = 2 - 6 = -4

Then we have the point (5, - 4)

Now we can graph these two points and connect them with a line. The graph of the line can be seen below.

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The correct expression for the inverse proportion is k/7 = 3/1

Given the inequality xy = k

If y is inversely proportional to x, then;

y = k/x

Given that y = 3, and  x = 7, then;

3 = k/7

Swap

k/7 = 3

k/7 = 3/1

Hence the correct expression for the inverse proportion is k/7 = 3/1

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Answer: Option 4

Step-by-step explanation:

Each value of x maps onto only one value of y.

Answer:

(x + 4)(x - 2) = x · x

(option L)

Step-by-step explanation:

we know that area = length × width

So, can write out the lengths and widths that we know:

(note: I will use the square as the reference point, because we can simply say "x" for both of its side lengths--you'll see why this is easier later)

Rug A:

length = x

width = x

Rug B:

length: x + 4

(4 feet greater than rug A length)

width: x - 2

(2 feet less than rug A width)

we can now set these areas to be equal to each other:

(rug A) = (rug B)

(length · width of A) = (length · width of B)

(x · x) = [ (x + 4)(x - 2) ]

So, the equation:

(x + 4)(x - 2) = x · x

can be used to find x (the length in feet) of rug A

hope this helps!! have a lovely day :)

Answer:

10 . 44 ft

Step-by-step explanation:

sin 50 = opposite leg / hypotenuse = 8 / x

8 / sin 50 = x    = 10 .44  ft

Answer:

10.433cm

Step-by-step explanation:

Using SOH from TOACAHSOH,

[tex]sin50deg = \frac{opposite}{hypotenuse} [/tex]

From here we know there the opposite is 8ft (height of the ring) and hypotenuse is what we want to find, distance between you and the ring.

[tex]sin(50) = \frac{8}{x} \\ x \sin(50) = 8 \\ x = \frac{8}{ \sin(50) } \\ x = 10.443cm(rounded \: to \: 5sf)[/tex]

Answer: What you picked

Step-by-step explanation:

I can't see the dropdown menus, but those answers make sense.

Answer:

The bottom part of the chest is best modeled by rectangular prism because each face is a rectangle The top part of the chest is best modeled by part of a cylinder because some faces are curved

Using the together rate, it is found that it will take 18 hours for Erick to build the garden box himself.

The together rate is given by the sum of each separate rate.

In this problem, the rates are given as follows:

Hence:

[tex]\frac{1}{x} + \frac{2}{x} = \frac{1}{6}[/tex]

[tex]\frac{3}{x} = \frac{1}{6}[/tex]

x = 18.

Hence, it will take 18 hours for Erick to build the garden box himself.

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Answer:

Option D

Step-by-step explanation:

Looking at the graph each jump is 2 units on the x-axis and y-axis :

We are looking for a quadratic with x values of 3 and 6 when y=0  

Solving the last quadratic gives us :

(x-3)(x-6)=0

x = 3 , x = 6

Our answer will be Option D

Hope this helped and have a good day  

Answer:

D: [tex]y=x^{2} -9x+18\\[/tex]

Step-by-step explanation:

x intercept of the curve is 3 and 6

meaning that when y=0, x is either 3 or 6

mathematically stated:

0 = (x - 3)  (x - 6)

0=x(x-6)-3(x-6)

[tex]0=x^{2} -6x-3x+18\\therefore \ y=x^{2} -9x+18\\[/tex]

If the order does not matter, cars can be arranged in 20 ways

If an order is important, cars can be arranged in 120 ways

The probability that the three newest cars end up parked in the driveway is 0.167

1. If the order does not matter, combination is used

[tex]\left ({n} \atop {r}} \right.)=\frac{n!}{r!(n-r)!}[/tex]

Here, n=6 r=3

using formula,we get

[tex]\left ( {{6} \atop {3}} \right)=\frac{6!}{3!3!} =5*4=20[/tex]

2. If an order is important, Permutation will be applicable

[tex]^{n}P_{r} = \frac{n!}{(n-r)!} \\[/tex]

∴[tex]^{6} P_{3} =\frac{6!}{3!(6-3)!}=\frac{6!}{3!} =120[/tex]

3. the probability that the three newest cars end up parked in the driveway

P=[tex]\frac{No. of possible outcomes for 3 cars}{total possibilities}[/tex]

=[tex]\frac{6*4*5}{6!}[/tex]

=[tex]\frac{120}{720}[/tex]

=[tex]\frac{1}{6}[/tex] ≈ 0.167

Hence, If the order does not matter, cars can be arranged in 20 ways

If an order is important, cars can be arranged in 120 ways

The probability that the three newest cars end up parked in the driveway is 0.167

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Using linear function concepts, a system of equations with no solutions is created when:

[tex]m = -2, b \neq \frac{3}{2}[/tex]

A linear function is modeled by:

y = mx + b

In which:

The intersection of two lines is the solution of a system of equations. If two lines have the same slope and different intercepts, they will never intercept, that is, the system will not have a solution.

The lines are given as follows:

Hence, for a system with no solution, we need that:

[tex]m = -2, b \neq \frac{3}{2}[/tex]

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An equivalent situation, in which the binomial distribution could be used, is given by:

Flip a fair coin four times, with heads representing teenagers who prefer watching a movie at a theater and tails representing those who do not.

The formula is:

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

The parameters are:

For this problem, the parameters are:

p = 0.5, n = 4;

The other situation that would represent a binomial distribution with the same parameters is given by:

Flip a fair coin four times, with heads representing teenagers who prefer watching a movie at a theater and tails representing those who do not.

The other situations have different values of p, hence they are not equivalent.

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The utilization rate is 83.33

The Poisson distribution is a discrete probability distribution that expresses the probability of a given number of events occurring in a fixed interval of time or space if these events occur with a known constant mean rate and independently of the time since the last event.

An average of 10 cars per hour are expected to arrive according to a Poisson distribution. They will be served at an average rate of 12 cars per hour, with exponential service times,

Then, the utilization rate is 83.33.

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The equation of the line passing through the point (3, 0) and parallel to the y axis is x = 3.

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

The graph passes through the point (3, 0) and parallel to the y axis, the equation of this line is x = 3.

The equation of the line passing through the point (3, 0) and parallel to the y axis is x = 3.

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Answer:

Option no. B is a unit tile in that tesselation

i.e rectangular shape

Step-by-step explanation:

Well, it's because we all know that tesselation

only use one shape and it's sum is always 360°

meanwhile sum of rectangle=360°

as each side of rectangle are 90°

90°*4=360°##

I hope it helped you to understand more clearly...

The value of m and n that shows that point p(m,5-n) when reflected on line y=0 is m = 3, n = 3.

Transformation is the movement of a point from its initial point to a new location. Types of transformation are reflection, rotation, translation and dilation.

The rule for the reflection over the line y = 0 (x axis) is (x, y) ⇒ (x, -y)

If the point p(m,5-n) is reflected on line y=0, this would give (m, -(5 - n)) = p'(2m-3,2n-8). Hence:

2m - 3 = m

m = 3

Also:

-(5 - n) = 2n - 8

-5 + n = 2n - 8

n = 3

The value of m and n that shows that point p(m,5-n) when reflected on line y=0 is m = 3, n = 3.

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Step-by-step explanation:

the circumference of a circle is

2×pi×r

with r being the radius, which is always half of the diameter.

r = 1.8 / 2 = 0.9 cm

circumference :

2×pi×0.9 = 1.8×pi = 1.8 × 3.142 = 5.6556 cm ≈ 5.7 cm

Answer:

5.7cm

Step-by-step explanation:

circumference = π · d

(2πr)

{note: "d" is diameter; "r" is radius; "π" is pi}

we know our diameter (d) to be 1.8

let's plug this into our cicumference formula! :

π · d = circumference

(3.142) · (1.8)

3.142 · 1.8 = 5.6556

let's round our answer to 1 decimal place,

remember, if the next digit is ≥5 we round up; < 5 we keep the same

so, our answer is 5.7 cm

hope this helps!! have a lovely day :)

Answer:

distributive property

Step-by-step explanation:

(3x + 7) + (2x + 8)

each of the parenthesis has a multiplier of 1 , placed outside the parenthesis.

then multiplying the terms inside the parenthesis by 1 gives

3x + 7 + 2x + 8