In the expression 3x2 + y − 5, which of the following choices is the exponent in the term 3x2?

First pair of equations :

[tex]\dfrac{1}{2}x+y=15\ ..(i)\\\\-x-\dfrac{1}{3}y=-6\ ..(ii)[/tex]

Multiply 2 to equation (i), we get

[tex]x+2y=30\ ..(iii)[/tex]

By Elimination Method, Add (i) and (ii) (term with x eliminate), we get

[tex]2y-\dfrac{1}{3}y=30-6\\\\\Rightarrow\ \dfrac{5}{3}y=24\\\\\Rightarrow\ y=\dfrac{24\times3}{5}=14.4[/tex]

put y= 14.4 in (iii), we get

[tex]x+2(14.4)=30\Rightarrow\ x=30-28.8=1.2[/tex]

hence, x=1.2 and y =14.4

Second pair of equations :

[tex]\dfrac{5}{6}x+\dfrac13y=0\ ..(i)\\\\ \dfrac12x-\dfrac{2}{3}y=3\ ..(ii)[/tex]

Multiply 2 to equation (i), we get

[tex]\dfrac{5}{3}x+\dfrac{2}{3}y=0\ ..(iii)[/tex]

Elimination Method, Add (i) and (ii) (term with y eliminate) , we get

[tex]\dfrac53x+\dfrac12x=3\Rightarrow\ \dfrac{10+3}{6}x=3\\\\\Rightarrow\ \dfrac{13}{6}x=3\\\\\Rightarrow\ x=\dfrac{18}{13}[/tex]

put [tex]x=\dfrac{18}{13}[/tex]   in (i), we get

[tex]\dfrac{5}{6}(\dfrac{18}{13})+\dfrac{1}{3}y=0\\\\\Rightarrow\ \dfrac{15}{13}+\dfrac{1}{3}y=0\\\\\Rightarrow\ \dfrac{1}{3}y=-\dfrac{15}{13}\\\\\Rightarrow\ y=-\dfrac{45}{13}[/tex]

hence, [tex]x=\dfrac{18}{13}[/tex]   and [tex]y=\dfrac{-45}{13}[/tex] .

Complete Question

Assume that adults have IQ scores that are normally distributed with a mean μ=100 and a standard deviation σ=15. Find the probability that a randomly selected adult has an IQ between 81 and 119.

Answer:

The probability is  [tex]P( x_1 < X < x_2) = 0.79474[/tex]

Step-by-step explanation:

From the question we are told that

   The standard deviation is  σ = 15.

    The mean μ= 100

     The range we are considering is [tex]x_1 = 81 , \ x_2 = 119[/tex]

Now given that IQ scores are normally distributed

    Then the probability that a randomly selected adult has an IQ between 81 and 119 is mathematically represented as

               [tex]P( x_1 < X < x_2) = P(\frac{x_1 - \mu }{\sigma } <\frac{X - \mu }{\sigma } < \frac{x_2- \mu }{\sigma } )[/tex]

 Generally

                [tex]\frac{X - \mu }{\sigma } = Z(The \ standardized \ value \ of \ X )[/tex]

So

              [tex]P( x_1 < X < x_2) = P(\frac{x_1 - \mu }{\sigma } <Z < \frac{x_2- \mu }{\sigma } )[/tex]

substituting values

               [tex]P( x_1 < X < x_2) = P(\frac{81 - 100 }{15 } <Z < \frac{119- 100 }{15 } )[/tex]

               [tex]P( x_1 < X < x_2) = P( -1.2667 <Z <1.2667 )[/tex]

               [tex]P( x_1 < X < x_2) = P(Z <1.2667 )-P( Z < -1.2667 )[/tex]

From the standardized Z table

               [tex]P(Z <-1.2667 ) = 0.10263[/tex]

And        [tex]P(Z <1.2667 ) = 0.89737[/tex]

So

            [tex]P( x_1 < X < x_2) = 0.89737 - 0.10263[/tex]

            [tex]P( x_1 < X < x_2) = 0.79474[/tex]

Answer:

Step-by-step explanation:

probabilty distribution= interval of x/total area of the distribution

OR  P(x)= frequency of x/total frequency(N)*the interval of x(w)

x                   f                   probabilty f/N*w

16                 10                  0.2

17                  16                  0.32

18                  20                  0.4

19                    4                   0.08

w is the width of the bar( interval) 17-16=1

N=10+16+20+4=50

( only need to draw histogram)

33/64 cups of sugar does snoopy scoop out.

The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.

The amount of sugar needed = 2 3/4 cups

Amount of sugar per scoop = 5 1/3 cups/scoop

So, number of cups of sugar scoops

= cups of sugar needed/ cups of sugar per scoop                                                                              

                                   =11/4 /16/3

                                     =11/4 *3/16

                                     =33/64

Hence, 33/64 cups of sugar does snoopy scoop out.

Learn more about this concept here:

https://brainly.com/question/25936585

#SPJ1

Answer:

or,x2-x=6

or,x2-x-6=0

or,x2-3x+2x-6=0

or,x(x-3)+2(x-3)=0

or,(x-3)(x+2)=0

so either x=3

or x=-2

Answer:

Step-by-step explanation:

A right angled triangle is a triangle that has one of this angles to be 90°. According to the ΔABC, the angle at B is 90°.

Area of a triangle = 1/2 * base * height

According to the diagram shown, the base is BC and the height is AB which is the required side.

Area of the triangle = 1/2 * BC * AB

Given area of the triangle = 10 square units

BC = 4 units

AB is the required length.

Substituting this values into the formula above;

10 = 1/2 * 4 * AB

10 = 2AB

Dividing both sides by 2

2AB/2 = 10/2

AB = 5 units

Hence the length of AB is 5 units.

Answer:

x=20

Step-by-step explanation:

Since this is a right triangle, we can use the Pythagorean theorem

a^2 + b^2 = c^2

21 ^2 + x^2 = 29^2

441+x^2 =841

Subtract 441 from each side

x^2 = 841-441

x^2 = 400

Take the square root of each side

sqrt(x^2) = sqrt(400)

x = 20

Answer:

[tex]\boxed{x = 20}[/tex]

Step-by-step explanation:

Hey there!

Well to find x we need to use the Pythagorean Theorem, which is.

[tex]a^2 + b^2 = c^2[/tex]

We have a which is 21 and 29 which is c.

[tex](21)^2 + x^2 = (29)^2[/tex]

[tex]441 + x^2 = 841[/tex]

[tex]-441[/tex]

[tex]x^2 = 400[/tex]

[tex]x = 20[/tex]

So the missing side "x" is 20.

Hope this helps :)

Answer:

False

Step-by-step explanation:

the answer is false because

year 1 to 2 is $18

year 2 to 3 is $17

year 3 to 4 is $18

year 4 to 5 is $17

false because simple interest always has the same money not a pattern

Answer:

[tex](-\infty,1/4)\cup(1/4,\infty)[/tex]

The answer is C.

Step-by-step explanation:

We are given the rational function:

[tex]\displaystyle f(x) = \frac{x-3}{4x-1}[/tex]

In rational functions, the domain is always all real numbers except for the values when the denominator equals zero. In other words, we need to find the zeros of the denominator:

[tex]\displaystyle \begin{aligned}4x -1 & = 0 \\ \\ 4x & = 1 \\ \\ x & = \frac{1}{4} \end{aligned}[/tex]

Therefore, the domain is all real number except for x = 1/4.

In interval notation, this is:

[tex](-\infty,1/4)\cup(1/4,\infty)[/tex]

The left interval represents all the values to the left of 1/4.The right interval represents all the values to the right of 1/4. The union symbol is needed to combine the two. Note that we use parentheses instead of brackets because we do not include the 1/4 nor the infinities.  

In conclusion, our answer is C.

Answer:

The third one

Step-by-step explanation:

Answer:

L = 13.3649

Step-by-step explanation:

We are given;

x = t − 2 sin(t)

dx/dt = 1 - 2 cos(t)

Also, y = 1 − 2 cos(t)

dy/dt = 2 sin(t)

0 ≤ t ≤ 2π

The arc length formula is;

L = (α,β)∫√[(dx/dt)² + (dy/dt)²]dt

Where α and β are the boundary points. Thus, applying this to our question, we have;

L = (0,2π)∫√((1 - 2 cos(t))² + (2 sin(t))²)dt

L = (0,2π)∫√(1 - 4cos(t) + 4cos²(t) + 4sin²(t))dt

L = (0,2π)∫√(1 - 4cos(t) + 4(cos²(t) + sin²(t)))dt

From trigonometry, we know that;

cos²t + sin²t = 1.

Thus;

L = (0,2π)∫√(1 - 4cos(t) + 4)dt

L = (0,2π)∫√(5 - 4cos(t))dt

Using online integral calculator, we have;

L = 13.3649

Answer:

The variance is  [tex]\sigma ^2 =25[/tex]

Step-by-step explanation:

From the question we are told that

    The sample size is  n =  21

     The sum of squares is [tex]SS = 500[/tex]

Generally the variance is mathematically represented as

           [tex]\sigma ^2 = \frac{SS}{n- 1}[/tex]

substituting values

          [tex]\sigma ^2 = \frac{ 500}{21- 1}[/tex]

          [tex]\sigma ^2 =25[/tex]

Answer:

A. 1

B. -1

C. -1.67

D. 0.67

E. 3.33

Step-by-step explanation:

Mathematically;

z-score = (x-mean)/SD

From the question, mean = 20 , SD = 3 while x represents the individual values

A. 23

Z = (23-20)/3 = 3/3 = 1

B. 17

z = (17-20)/3 = -3/3 = -1

C. 15

z = (15-20)/3 = -5/3 = -1.67

D. 22

z = (22-20)/3 = 2/3 = 0.67

E. 30

z = (30-20)/3 = 10/3 = 3.33

Answer: 4150

Step-by-step explanation:

You take the 50, becuse the amount earned increases once you surpass 40 you do 40 x 10 and that = 4000 then you take the remaining 10 and times that by 15 (becuse after 40 it is 1.5 of what you where earning before you hit 40 hours and half of ten is 5 so you do 10 plus 5 and times that by 10) then add both numbers together and you have 4150! Hope that helped!

Answer:

Step-by-step explanation:

Given sinα=−2/3, before we can get secα, we need to get the value of α first from  sinα=−2/3.

[tex]sin \alpha = -2/3[/tex]

Taking the arcsin of both sides

[tex]sin^{-1}(sin\alpha) = sin^{-1} -2/3\\ \\\alpha = sin^{-1} -2/3\\ \\\alpha = -41.8^0[/tex]

Since sin is negative in the 3rd and 4th quadrant. In the 3rd quadrant;

α = 180°+41.8°

α = 221.8° which is between the range 270°<α<360°

secα = sec 221.8°

secα = 1/cos 221.8

secα = 1.34

Let the largest integer equal x, the 3rd number ( smallest-number) would be x - 2

The sum of the two would be:

X + 5(x-2) = -244

Simplify:

X + 5x -10

Combine like terms

6x -10 = -244

Add 10 to both sides:

6x = -234

Divide both sides by 6

X = -234/6

X = -39

The smallest number is x-2 = -39-2 = -41

The answer is -41

Hi

35/100= 140/ X

X = 100*140 /35

X= 14000/35

X= 400

There are 400 computer in the compagny.

Answer:

0.9938

Step-by-step explanation:

We can find this probability using a test statistic.

The test statistic to use is the z-scores

Mathematically;

z-score = (x-mean)/SD/√n

from the question, x = 119 , mean = 117 , SD = 6.4 and n = 64

Plugging these values in the z-score equation above, we have;

z-score = (119-117)/6.4/√64

z-score = 2/6.4/8

z-score = 2.5

The probability we want to find is;

P(z < 2.5)

we can get this value from the standard normal distribution table

Thus; P(z < 2.5) = 0.99379

Which to four decimal places = 0.9938

Answer:

120%

Step-by-step explanation:

Answer:

-1 and 1

Step-by-step explanation:

Reciprocal means "one divided by...".

1/-1 = -1 and 1/1 = 1

Answer:

The  condition  are

           The  Null hypothesis is  [tex]H_o : \mu = 5[/tex]

           The  Alternative hypothesis is  [tex]H_a : \mu < 5[/tex]

The  check revealed that

             There is sufficient evidence to support the claim that in a small city renowned for its music school, the average child takes at least 5 years of piano lessons

Step-by-step explanation:

From the question we are told that

     The  population mean is  [tex]\mu = 5 \ year[/tex]

      The sample size is  n =  20

      The sample mean is  [tex]\= x = 4.6 \ years[/tex]

       The  standard deviation is [tex]\sigma = 2.2 \ years[/tex]

   The  Null hypothesis is  [tex]H_o : \mu = 5[/tex]

   The  Alternative hypothesis is  [tex]H_a : \mu < 5[/tex]

So i will be making use of  [tex]\alpha = 0.05[/tex] level of significance to test this claim

    The critical value of  [tex]\alpha[/tex] from the normal distribution table is  [tex]Z_\alpha = 1.645[/tex]

Generally the test statistics is mathematically evaluated as

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

substituting values

                 [tex]t = \frac{ 4.6 - 5}{ \frac{2.2}{\sqrt{20} } }[/tex]

                [tex]t = -0.8131[/tex]

Looking at the value of  t and [tex]Z_{\alpha }[/tex] we see that  [tex]t < Z_{\alpha }[/tex] so we fail to reject the null hypothesis  

  This implies that there is sufficient evidence to support the claim that in a small city renowned for its music school, the average child takes at least 5 years of piano lessons.

Answer:

A typical example would be when a statistician wishes to estimate the ... by the standard deviation ó) is known, then the standard error of the sample mean is given by the formula: ... The central limit theorem is a significant result which depends on sample size. ... So, the sample mean X/n has maximum variance 0.25/ n.

Step-by-step explanation:

This is a sum of squares, which cannot be factored over the real numbers. You'll need to involve complex numbers to be able to factor, though its likely your teacher hasn't covered that topic yet (though I could be mistaken and your teacher has mentioned it).

Choice B can be factored through the difference of squares rule. Therefore, choice B is not prime.

Choice C and D can be factored by pulling out the GCF and then use the difference of squares rule afterward. So we can rule out C and D as well.

Answer:

A

Step-by-step explanation:

because it has a + sign

Answer:

g = [tex]\frac{1}{24}[/tex]

Step-by-step explanation:

Given

[tex]\frac{5}{2}[/tex] + 6g = [tex]\frac{11}{4}[/tex]

Multiply through by 4 to clear the fractions

10 + 24g = 11 ( subtract 10 from both sides )

24g = 1 ( divide both sides by 24 )

g = [tex]\frac{1}{24}[/tex]

Answer:

h = 5 cm

Step-by-step explanation:

Given that,

The volume of ice-cream in the cone is half the volume of the cone.

Volume of cone is given by :

[tex]V_c=\dfrac{1}{3}\pi r^2h[/tex]

r is radius of cone, r = 3 cm

h is height of cone, h = 6 cm

So,

[tex]V_c=\dfrac{1}{3}\pi (3)^2\times 6\\\\V_c=18\pi\ cm^3[/tex]

Let [tex]V_i[/tex] is the volume of icecream in the cone. So,

[tex]V_i=\dfrac{18\pi}{2}=9\pi\ cm^3[/tex]

Let H be the depth of the icecream.

Two triangles formed by the cone and the icecream will be similiar. SO,

[tex]\dfrac{H}{6}=\dfrac{r}{3}\\\\r=\dfrac{H}{2}[/tex]

So, volume of icecream in the cone is :

[tex]V_c=\dfrac{1}{3}\pi (\dfrac{h}{2})^2(\dfrac{h}{3})\\\\9\pi=\dfrac{h^3}{12}\pi\\\\h^3=108\\\\h=4.76\ cm[/tex]

or

h = 5 cm

So, the depth of the ice-cream is 5 cm.

Answer:

(x+4)/3. When x is 5 the answer is 3

Step-by-step explanation:

Answer:

y - 5 = -1/4(x - 4)

Step-by-step explanation:

Point slope form is y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope.

To find the point slope form, plug in the point given and the slope.

y - y1 = m(x - x1)

y - 5 = -1/4(x - 4)

Answer:

The first option is not the same point in polar coordinates as (-3, 1.236). This proves that inverting the signs of r and θ does not generally give the same point in polar coordinates.

Step-by-step explanation:

Let's think about the position of this point. As you can tell it lies in the 4th quadrant, on the 3rd circle of this polar graph.

Remember that polar coordinates is expressed as (r,θ) where r = distance from the positive x - axis, and theta = angle from the terminal side of the positive x - axis. Now there are two cases you can consider here when r > 0.

Given : (- 3, 1.236), (3,5.047), (3, - 7.518), (- 3, 1.906)

We know that :

7.518 - 1.236 = 6.282 = ( About ) 2π

5.047 + 1.236 = 6.283 = ( About ) 2π

1.236 + 1.906 = 3.142 = ( About ) 2π

Remember that sin and cos have a uniform period of 2π. All of the points are equivalent but the first option, as all of them ( but the first ) differ by 2π compared to the given point (3, - 1.236).

Answer:

x = 1, y = -1

Step-by-step explanation:

If we have the two equations:

[tex]4x+3y=1[/tex] and [tex]-3x - 6y = 3[/tex], we can look at which variable will be easiest to eliminate.

[tex]y[/tex] looks like it might be easy to get rid of, we just have to multiply [tex]4x+3y=1[/tex]  by 2 and y is gone (as -6y + 6y = 0).

So let's multiply the equation [tex]4x+3y=1[/tex]  by 2.

[tex]2(4x + 3y = 1)\\8x + 6y = 2[/tex]

Now we can add these equations

[tex]8x + 6y = 2\\-3x-6y=3\\[/tex]

------------------------

[tex]5x = 5[/tex]

Dividing both sides by 5, we get [tex]x = 1[/tex].

Now we can substitute x into an equation to find y.

[tex]4(1) + 3y = 1\\4 + 3y = 1\\3y = -3\\y = -1[/tex]

Hope this helped!