A height is labeled on the triangle below.
Which line segment shows the base that corresponds to the given height of the triangle
Option A,B,C

Answer:

[tex]3x^{2} +38x+80[/tex]

Step-by-step explanation:

Hello!

A trinomial is a expression consisting of three different terms

To turn this into a trinomial we multiply everything to each other

                    3x                    

3x * x = [tex]3x^{2}[/tex]

3x * 10 = 30x

                    8                      

8 * x = 8x

8 * 10 = 80

Now we put them all together in an equation

[tex]3x^{2} +30x+8x+80[/tex]

Combine like terms

[tex]3x^{2} +38x+80[/tex]

The answer is [tex]3x^{2} +38x+80[/tex]

Hope this helps!

The width of the gym will be W=60 feet for the area of 6,960 square feet.

Area is defines as the space covered by a surface in the two dimensional plane.

It is given that

Area of the gym =6960 square feet

Width of the gym = ?

Length of the gym=116 feet

The width of the gym will be calculated as

[tex]A=\L\times W\\\\\\6960=116\times W\\\\\\w=\dfrac{6960}{116}=60\ \ Feet[/tex]

hence the width of the gym will be W=60 feet for the area of 6,960 square feet.

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Step-by-step explanation:

a2=a1+1/2=-1

a3=a2+1/2=-1/2, then we have common difference 0.5

a9=a1+(n-1)d

a9=-3/2+(8)0.5=5/2

Answer:

Step-by-step explanation:

Adjacent angles are supplementary, so ...

  (y +x) +(y -x) = 180

  2y = 180 . . . . . . . . . simplify

  y = 90 . . . . . . . . . . . divide by 2

__

  2x +(y +x) = 180

  3x +90 = 180 . . . . substitute for y

  x + 30 = 60 . . . . . . divide by 3

  x = 30 . . . . . . . . . . subtract 30

__

With these values of x and y, the angle measures are ...

  2x° = 2(30)° = 60°

  (y+x)° = (90+30)° = 120°

  (y-x)° = (90-30)° = 60°

Answer:

The null hypothesis is rejected and  research hypotheses is supported

Step-by-step explanation:

From the question we are told that

    The population mean is  [tex]\mu = 30[/tex]

     The standard deviation is [tex]\sigma = 5[/tex]

      The sample size is  n =  1

      The  cutoff Z score for significance is  [tex]Z_{\alpha } = 1.96[/tex]

       The mean score is  [tex]\= x = 45[/tex]

Generally the test hypothesis is mathematically represented as

            [tex]t = \frac{\= x - \mu }{ \frac{ \sigma }{\sqrt{n} } }[/tex]

=>         [tex]t = \frac{45 - 30 }{ \frac{ 5}{\sqrt{1} } }[/tex]

=>         [tex]t = 3[/tex]

From the obtained value  we can see that [tex]t > Z_{\alpha }[/tex]

Hence the null hypothesis is rejected and  research hypotheses is supported

Answer

arrange the element in increasing order

-1.9, -1.3, -0.8, 2.3, 5.8, 7.4, 8.5, 9.9

interquatile = Q3 - Q1

[tex] = \frac{7.4 + 8.5}{2} - \frac{ - 1.3 - 0.8}{2} [/tex]

[tex] = 7.95 + 1.05[/tex]

[tex] = 9[/tex]

Answer:

9.0

Step-by-step explanation:

i took the quiz

Answer:

It's 8.3

Step-by-step explanation:

Answer:

8.3

Step-by-step explanation:

Answer:

[tex] \boxed{f(x) = 2 {x}^{9} - 4 {x}^{2} + 4}[/tex]

Option B is the correct option

Step-by-step explanation:

By looking at the end behavior , we can say that the degree of the polynomial must be odd and leading coefficient will be positive.

Thus , the correct choice is B.

Hope I helped!

Best regards!

The polynomial function that could have created the given curve on the xy-plane is [tex]f(x)= 2x^9-4x^2+4[/tex]

Polynomial functions aree function having a leading degrees of 3 and greater.

The nature of the curve on the xy-plane depends on its end behaviour. From the given graph, the end behaviour shows that the equivalnt function has a positive leading coefficient and an odd degree.

From the listed option, the function that satisfies both criteria is [tex]f(x)=2x^9-4x^2+4[/tex].

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Answer:

The probability that the assembly line will be shut down is 0.00617.

Step-by-step explanation:

We are given that a soda bottling company’s manufacturing process is calibrated so that 99% of bottles are filled to within specifications, while 1% is not within specification.

Every hour, 12 random bottles are taken from the assembly line and tested. If 2 or more bottles in the sample are not within specification, the assembly line is shut down for recalibration.

Let X = Number of bottles in the sample that are not within specification.

The above situation can be represented through binomial distribution;

[tex]P(X=r)=\binom{n}{r} \times p^{r}\times (1-p)^{n-r};x=0,1,2,3,.....[/tex]

where, n = number of trials (samples) taken = 12 bottles

             x = number of success  = 2 or more bottles

            p = probabilitiy of success which in our question is probability that  

                 bottles are not within specification, i.e. p = 0.01

So, X ~ Binom (n = 12, p = 0.01)

Now, the probability that the assembly line will be shut down is given by = P(X [tex]\geq[/tex] 2)

  P(X [tex]\geq[/tex] 2) = 1 - P(X = 0) - P(X = 1)

                 = [tex]1-\binom{12}{0} \times 0.01^{0}\times (1-0.01)^{12-0}-\binom{12}{1} \times 0.01^{1}\times (1-0.01)^{12-1}[/tex]

                 = [tex]1-(1 \times 1\times 0.99^{12})-(12 \times 0.01^{1}\times 0.99^{11})[/tex]

                 = 0.00617

Answer:

∠NMC  = 50°

Step-by-step explanation:

The interpretation of the information given in the question can be seen in the attached images below.

In ΔABC;

∠ A + ∠ B + ∠ C = 180°    (sum of angles in a triangle)

∠ A + 70°  + 50°  = 180°

∠ A = 180° - 70° - 50°

∠ A =  180° - 120°

∠ A =  60°

In ΔAMN ; the base angle are equal , let the base angles be x and y

So; x = y   (base angle of an equilateral  triangle)

Then;

x + x + 60° = 180°

2x +  60° = 180°

2x = 180° - 60°

2x = 120°

x = 120°/2

x = 60°

∴ x = 60° , y = 60°

In ΔBQC

∠a + ∠e + ∠b = 180°

50° + ∠e + 40° = 180°

∠e = 180° - 50° - 40°

∠e = 180° - 90°

∠e = 90°

At point Q , ∠e = ∠f = ∠g = ∠h = 90°  (angles at a point)

∠i  = 50° - 40° = 10°

In ΔNQC

∠f + ∠i   + ∠j = 180°

90° + 10° + ∠j = 180°

∠j  = 180° - 90°-10°

∠j  = 180° - 100°

∠j  = 80°

From  line AC , at point N , ∠y + ∠c + ∠j = 180°   (sum of angles on a straight line)

60° + ∠c + ∠80° = 180°

∠c  = 180° - 60°-80°

∠c  = 180° - 140°

∠c  = 40°

Recall that :

At point Q , ∠e = ∠f = ∠g = ∠h = 90°  (angles at a point)

Then In Δ NMC ;

∠d + ∠h + ∠c = 180°   (sum of angles in a triangle)

∠d + 90° + 40° = 180°

∠d  = 180° - 90° -40°

∠d  = 180° - 130°

∠d  = 50°

Therefore, ∠NMC = ∠d  = 50°

Answer:

3/500

Step-by-step explanation:

3/5 x 1%

=> 3/5 x 1/100

=> 3/500

Hope it helps you

Answer:

so first convert to fraction so

9 3/4 = 39/4

so it was spread among 3

so this is division so you do 39/4 divided by 3

so you keep switch flip

which is  39/4 *1/3

answer is 13/4

Answer:

Step-by-step explanation:

[tex]9\frac{3}{4}= \frac{(4 \times 9)+3}{4}= \frac{39}{4} \\\\\frac{39}{4} = 3 \:vegetable \: beds\\x \:\:\:= 1 \: vegetable \:bed\\\\3x = \frac{39}{4} \\\\\frac{3x}{3} = \frac{\frac{39}{4} }{3} \\\\x = \frac{13}{4} \\\\x = 3\frac{1}{4}[/tex]

Answer:

The mean age is 48

The standard deviation is 4

Step-by-step explanation:

The answer is, (a) mean age is 48.

                          (b)  standard deviation is 4.

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Answer:

cos 60° = 1/2 because the angles are complements.

Step-by-step explanation:

Answer:

y = 8x + 70

Step-by-step explanation:

Start with the third line.

x = 3, y = 94

Subtract 1 from x and 8 from y:

x = 2, y = 86; this is the second line

Subtract 1 from x and 8 from y:

x = 1, y = 78; this is the first line

Subtract 1 from x and 8 from y:

x = 0; y = 70

For selling 0 games, she earns $70.

y = mx + b

y = mx + 70

For each game she sells, her commission is $8.

y = 8x + 70

Answer:

P(C|Y) = 0.5.

Step-by-step explanation:

We are given the following table below;

               X             Y               Z             Total

A             32           10             28              70

B              6             5              25              36

C             18            15              7                40

Total       56           30            60              146

Now, we have to find the probability of P(C/Y).

As we know that the conditional probability formula of P(A/B) is given by;

                    P(A/B) =  [tex]\frac{P(A \bigcap B)}{P(B)}[/tex]

So, according to our question;

P(C/Y) =  [tex]\frac{P(C \bigcap Y)}{P(Y)}[/tex]

Here, P(Y) = [tex]\frac{30}{146}[/tex] and P(C [tex]\bigcap[/tex] Y) =  [tex]\frac{15}{146}[/tex]  {by seeing third row and second column}

Hence, P(C/Y) =  [tex]\frac{\frac{15}{146} }{\frac{30}{146} }[/tex]

                       =  [tex]\frac{15}{30}[/tex]  = 0.5.

Answer: 0.5

Step-by-step explanation:

edge

Answer:

Tran family's sprinkler was used for 20 hours

Green's  family's sprinkler was used for 30 hours

Step-by-step explanation:

Let the hours for which Tran family's sprinkler used is x hours

water output rate for the Tran family's sprinkler = 35L per hour

water output from  Tran family's sprinkler in x hours = 35*x L = 35x

Let the hours for which Green family's sprinkler used is y hours

water output rate for the Green family's sprinkler = 40L per hour

water output from  Green family's sprinkler in x hours = 40*y L = 40y

Given

The families used their sprinklers for a combined total of 50 hours

thus

x + y = 50 -------------------equation 1

y = 50-x

total water output of 1900L

35x+40y = 1900  -------------------equation 1

using  y = 50-x in equation 2, we have

35x + 40(50-x) = 1900

35x + 2000 - 40x = 1900

=> -5x = 1900 - 2000 = -100

=> x = -100/-5 = 20

y = 50-20 = 30

Thus,

Tran family's sprinkler was used for 20 hours

Green's  family's sprinkler was used for 30 hours

Answer:

Step-by-step explanation:

[tex]3h\left(2\right)+2k\left(3\right)\\\\\mathrm{Remove\:parentheses}:\quad \left(a\right)=a\\\\=3h\times \:2+2k\times \:3\\\\\mathrm{Multiply\:the\:numbers:}\:3\times \:2=6\\\\=6h+2\times \:3k\\\\\mathrm{Multiply\:the\:numbers:}\:2\times \:3=6\\\\=6h+6k[/tex]

Answer:

Answers for E-dge-nuityyy

Step-by-step explanation:

(h + k)(2) = 5

(h – k)(3) = 9

Evaluate 3h(2) + 2k(3) = 17

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

Explanation:

The piecewise function shows that we have two cases. Either x = 1 or [tex]x \ne 1[/tex].

If x = 1, then g(x) = 3 as shown in the bottom row. This is why g(1) = 3.

If [tex]x \ne 1[/tex], then g(x) = (1/4)x^2-4

Plug x = -5 into this second definition

g(x) = (1/4)x^2-4

g(-5) = (1/4)(-5)^2-4

g(-5) = (1/4)(25)-4

g(-5) = 25/4 - 4

g(-5) = 25/4 - 16/4

g(-5) = 9/4

Repeat for x = 4

g(x) = (1/4)x^2-4

g(4) = (1/4)(4)^2-4

g(4) = (1/4)(16)-4

g(4) = 4-4

g(4) = 0

The value of the function at x = -5, x = 1, and x = 4 will be 2.25, 3, and 0, respectively.

A function is an assertion, concept, or principle that establishes an association between two variables. Functions may be found throughout mathematics and are essential for the development of significant links.

The functions are given below.

g(x) = (1/4)x² - 4, x ≠ 1

g(x) = 3, x = 1

The value of the function at x = -5 will be given as,

g(-5) = (1/4)(-5)² - 4

g(-5) = 25 / 4 - 4

g(-5) = 6.25 - 4

g(-5) = 2.25

The value of the function at x = 4 will be given as,

g(4) = (1/4)(4)² - 4

g(4) = 16 / 4 - 4

g(4) = 4 - 4

g(4) = 0

The value of the function at x = 1 will be given as,

g(1) = 3

The value of the function at x = -5, x = 1, and x = 4 will be 2.25, 3, and 0, respectively.

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Answer:  3.79 litres

Step-by-step explanation:

1 litre is equivalent to about ‭1.05668821‬ American quarts.

4 quarts would therefore be;

= 4/‭1.05668821‬

= 3.78541178

= 3.79 litres

Answer:

Step-by-step explanation:

1. The sum of one-third of a number and 27

= [tex]\frac{1}{3}\times x +27\\= 1/3x +27[/tex]

2. The product of a number squared and 4

[tex]Let\:the\:unknown\: number\: be \:x\\\\x^2\times4\\\\= 4x^2[/tex]

3.Write a verbal expression for 5n^3 +9.

The sum of the product and of 5 and a cubed number and 9

Rewrite f in terms of the unit step function:

[tex]f(t)=\begin{cases}5&\text{for }0\le t<7\\-3&\text{for }t\ge7\end{cases}[/tex]

[tex]\implies f(t)=5(u(t)-u(t-7))-3u(t-7)=5u(t)-8u(t-7)[/tex]

where

[tex]u(t)=\begin{cases}1&\text{for }t\ge0\\0&\text{for }t<0\end{cases}[/tex]

Recall the time-shifting property of the Laplace transform:

[tex]L[u(t-c)f(t-c)]=e^{-cs}L[f(t)][/tex]

and the Laplace transform of a constant function,

[tex]L[k]=\dfrac ks[/tex]

So we have

[tex]L[f(t)]=L[5u(t)-8u(t-7)]=5L[1]-8e^{-7s}L[1]=\boxed{\dfrac{5-8e^{-7s}}s}[/tex]

In this exercise you have to find the laplace transform:

[tex]L[f(t)]=\frac{5-8e^{-7s}}{s}[/tex]

Rewrite f in terms of the unit step function:

[tex]f(t)=\left \{ {{5, for 0\leq t\leq 7} \atop {-3, for t\geq 7}} \right. \\f(t)= 5(u(t)-u(t-7)-3u(t-7)=5u(t)-8u(t-7)[/tex]

Where:

[tex]u(t)= \left \{ {{1, t\geq 0} \atop {0, t<0}} \right.[/tex]

Recall the time-shifting property of the Laplace transform:

[tex]L[u(t-c)f(t-c)]= e^{-cs}L[f(t)][/tex]

and the Laplace transform of a constant function,

[tex]L[k]=\frac{k}{s}[/tex]

So we have:

[tex]L[f(t)]= L[5u(t)-8u(t-7)]= 5L[1]-8e^{-7s}L[1]= \frac{5-8e^{-7s}}{s}[/tex]

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Answer:

-16

Step-by-step explanation:

8q

Let q = -2

8*-2

-16

Hi there! :)

Answer:

x = 1/2 or -7.

Step-by-step explanation:

(I'm assuming the expression is 2x² + 13x - 7 = 0)

Factor the equation to solve for the possible values of "x":

2x² + 13x - 7 = 0

When factored, we get:

(2x - 1) ( x + 7) = 0

Use the Zero-Product property to solve for the roots:

2x - 1 = 0

2x = 1

x = 1/2.

-----------

x + 7 = 0

x = -7.

Therefore, possible values of x are x = -1/2, 7.

Answer:

x = 1/2     x=-7

Step-by-step explanation:

2 x^2  + 13 x − 7 = 0

Factor

(2x-1)(x+7)=0

Using the zero product property

2x-1 =0   x+7=0

2x=1       x =-7

x = 1/2     x=-7

Answer:

14 + 25l + 6l^2

Step-by-step explanation:

(7 + 2i) (2 + 3i)

=> 14 + 4l + 21l + 6l^2

=> 14 + 25l + 6l^2

This is the correct answer

Answer:

[tex]\Large \boxed{\sf \bf \ \ 2(x-4)^3(x+2)^2 \ \ }[/tex]

Step-by-step explanation:

Hello, please consider the following.

Construct a polynomial function with the following properties...

... fifth degree

It means that the polynomial can be written as below.

[tex]a_5x^5+a_4x^4+a_3x^3+a_2x^2+a_1x+a_0 \ \text{ with }a_5\text{ different from 0}\\\\\text{ or } k(x-x_1)(x-x_2)(x-x_3)(x-x_4)(x-x_5) \\\\ \text{ with k different from 0 and } (x_i)_{1\leqi\leq 5 } \text { are the roots.}[/tex]

... 4 is a zero of multiplicity 3

We can write the polynomial as below.

[tex]k(x-4)(x-4)(x-4)(x-x_4)(x-x_5)=k(x-4)^3(x-x_4)(x-x_5)[/tex]

... −2 is the only other zero

Because this is the only other zero, we can deduce that -2 is a zero of multiplicity 2.

[tex]k(x-4)(x-4)(x-4)(x-x_4)(x-x_5)\\\\=k(x-4)^3(x-(-2))(x-(-2))\\\\=k(x-4)^3(x+2)^2[/tex]

... leading coefficient is 2.

Finally, it means that k = 2 and then the polynomial function is:

[tex]\large \boxed{2(x-4)^3(x+2)^2}[/tex]

Hope this helps.

Do not hesitate if you need further explanation.

Thank you

Answer:

0.1587

Step-by-step explanation:

Given the following :

Mean (m) of distribution = 64 inches

Standard deviation (sd) of distribution = 2 inches

Probability that a randomly selected woman is taller than 66 inches

For a normal distribution :

Z - score = (x - mean) / standard deviation

Where x = 66

P(X > 66) = P( Z > (66 - 64) / 2)

P(X > 66) = P(Z > (2 /2)

P(X > 66) = P(Z > 1)

P(Z > 1) = 1 - P(Z ≤ 1)

P(Z ≤ 1) = 0.8413 ( from z distribution table)

1 - P(Z ≤ 1) = 1 - 0.8413

= 0.1587

Answer:

x = sqrt(50) = 5sqrt(2) = 7.071 ft (to 3 decimals)

Step-by-step explanation:

referring to the diagram

theta (x) = atan(10/x) - atan(5/x)

differentiate with respect to x

theta'(x) = 5/(x^2+25) - 10/(x^2+100)

For x to have an extremum (max. or min)

theta'(x) = 0  ="

5/(x^2+25) - 10/(x^2+100) = 0

transpose and cross multiply

10(x^2+25) -5(x^2+100) = 0

expand and simplify

10x^2+250 - 5x^2-500 = 0

5x^2 = 250

x^2=50

x = sqrt(50) = 5sqrt(2) = 7.071 ft (to 3 decimals)

Since we know that if x becomes large, theta will decrease, so

x = 5sqrt(2) is a maximum.

Answer:

[tex]Probability = 0.35[/tex]

Step-by-step explanation:

Given

Probability of success free throw = 90%

Number of throw = 10

Required

Determine the probability of 10 consecutive free throws

Let p represents the given probability

[tex]p = 90\%[/tex]

Convert to decimal

[tex]p = 0.9[/tex]

Let n represents the number of throw

[tex]n = 10[/tex]

Provided that each throw is independent;

The probability of n consecutive free throw is

[tex]p^n[/tex]

Substitute 0.9 for p and 10 for n

[tex]Probability = 0.9^{10}[/tex]

[tex]Probability = 0.3486784401[/tex]

[tex]Probability = 0.35[/tex] (Approximated)