Solve the inequality 47.75 + x Less-than-or-equal-to 50 to determine how much more weight can be added to Li’s suitcase without going over the 50-pound limit. What is the solution set?
x Less-than-or-equal-to 2.25
x Less-than-or-equal-to 2.75
x Greater-than-or-equal-to 2.25
x Greater-than-or-equal-to 2.75

Answer:

A 95​% confidence interval for the proportion of students who eat cauliflower on​ Jane's campus is [0.012, 0.270].

Step-by-step explanation:

We are given that Jane wants to estimate the proportion of students on her campus who eat cauliflower. After surveying 24 ​students, she finds 2 who eat cauliflower.

Firstly, the pivotal quantity for finding the confidence interval for the population proportion is given by;

                              P.Q.  =  [tex]\frac{\hat p-p}{\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex]  ~ N(0,1)

where, [tex]\hat p[/tex] = sample proportion of students who eat cauliflower

           n = sample of students

           p = population proportion of students who eat cauliflower

Here for constructing a 95% confidence interval we have used a One-sample z-test for proportions.

So, 95% confidence interval for the population proportion, p is ;

P(-1.96 < N(0,1) < 1.96) = 0.95  {As the critical value of z at 2.5% level

                                                   of significance are -1.96 & 1.96}  

P(-1.96 < [tex]\frac{\hat p-p}{\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex] < 1.96) = 0.95

P( [tex]-1.96 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex] < [tex]{\hat p-p}[/tex] < [tex]1.96 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex] ) = 0.95

P( [tex]\hat p-1.96 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex] < p < [tex]\hat p+1.96 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex] ) = 0.95

Now, in Agresti and​ Coull's method; the sample size and the sample proportion is calculated as;

[tex]n = n + Z^{2}__(\frac{_\alpha}{2})[/tex]

n = [tex]24 + 1.96^{2}[/tex] = 27.842

[tex]\hat p = \frac{x+\frac{Z^{2}__(\frac{\alpha}{2}_) }{2} }{n}[/tex] = [tex]\hat p = \frac{2+\frac{1.96^{2} }{2} }{27.842}[/tex] = 0.141

95% confidence interval for p = [ [tex]\hat p-1.96 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex] , [tex]\hat p+1.96 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex] ]

 = [ [tex]0.141 -1.96 \times {\sqrt{\frac{0.141(1-0.141)}{27.842} } }[/tex] , [tex]0.141 +1.96 \times {\sqrt{\frac{0.141(1-0.141)}{27.842} } }[/tex] ]

 = [0.012, 0.270]

Therefore, a 95​% confidence interval for the proportion of students who eat cauliflower on​ Jane's campus [0.012, 0.270].

The interpretation of the above confidence interval is that we are 95​% confident that the proportion of students who eat cauliflower on​ Jane's campus is between 0.012 and 0.270.

Answer:

Step-by-step explanation:

5x+30 is a corresponding angle with 4x-9 so set them equal to each other. 4x-9+2x+3 will equal 180

Answer:

no, the values would be above 180º

Step-by-step explanation:

if...

(4x - 9) + (2x + 3) + y = 180

(5x + 30) + y = 180

then...

(4x - 9) + (2x + 3) = 5x + 30

so...

6x - 6 = 5x + 30

x = 36

plug it in.

4(36) - 9 = 135

2(36) + 3 = 75

already you can see the sum of these two angles surpasses 180 which is not possible for a triangle.

Answer:

3.5

Step-by-step explanation:

I did the test, also, take the people multiply by score, u get 66 total, divided by 19=number of students, is 3.5-ish

The mean for gymnastic score is, 3.5

The process of combining two or more numbers is called the Addition. The 4 main properties of addition are commutative, associative, distributive, and additive identity.

Given that;

Zahara asked the students of her class their gymnastic scores and recorded the scores in the table shown in table.

Now, We get;

The mean for gymnastic score is,

= ((1×0)+(1×1)+(2×2)+(6×3)+(4×4)+(3×5)+(2×6)) / 19

= 3.47

= 3.5

Thus, The mean for gymnastic score is, 3.5

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Answer:

Misty is the more consistent employee

Step-by-step explanation:

The given data are

Misty: 11, 13, 12, 14, 10, 16, 14

Brock: 8, 15, 10, 11, 16, 10, 9

The mean of Misty's successfully answered questions = ∑x/n = 90/7 = 12.86

Misty's data standard deviation = √(∑(x - μ)²/n) = 1.884

The mean of Brock's successfully answered questions = ∑x/n = 79/7 = 11.29

Brock's data  standard deviation = √(∑(x - μ)²/n) = 2.81

Therefore, based on the value of the standard deviation which is a measure of variability, whereby the standard deviation of Brock's number of successfully answered questions is larger than the standard deviation of Misty's number of tech supported successfully answered questions, Misty is the more consistent employee.

Answer        

6B+7X-9Y+19

Step-by-step explanation:

Answer:

Equation:-  [tex]x + y = 38.50[/tex]

Solution of x:-  [tex]x = 38.50 - y[/tex]

Step-by-step explanation:

Given

Total Purchase = $38.50

Required

Determine the equation for finding the cost of a bear

From the question; we understand that the cost of 1 bear is represented with x

Solving further; by representing the cost of 1 football uniform with y

So;

[tex]1\ bear + 1\ uniform = 38.50[/tex]

Substitute x for 1 bear and y for 1 uniform to give us an equation

[tex]x + y = 38.50[/tex]

Solving for x (Subtract y from both sides)

[tex]x +y - y = 38.50 - y[/tex]

[tex]x = 38.50 - y[/tex]

The equation can't be solved further

Answer:

48

Step-by-step explanation:

We have that the volume of a cylinder is given by:

 V = pi * (r ^ 2) * h

In this case we know the diameter, we know that the radius is half the diameter like this:

r = d / 2

r = 8/2

r = 4

Now we know that the V equals 768 pi

we replace and we have:

768 * pi = pi * (4 ^ 2) * h

768 = 16 * h

h = 768/16

h = 48

Therefore the value of x would be 48 cm

Answer:

The answer is below

Step-by-step explanation:

AD = X + 8 ∠D = 2y +13 ∠C = 16 - x CB = 5y+4

In a parallelogram, consecutive angles are supplementary and opposite sides are equal.

Therefore for parallelogram ABCD, AB = CD, CB = AD

Since AD = CB (opposite sides of a parallelogram are equal):

x + 8 = 5y + 4

5y - x = 8 - 4

5y - x = 4             (1)

∠C + ∠D= 180° (consecutive angles of a parallelogram are supplementary). Therefore:

16 - x + 2y + 13 = 180

2y - x + 29 = 180

2y - x = 180 -29

2y - x = 151             (2)

To find x and y, subtract equation 1 from equation 2:

3y = -147

y = -49

Put y = -49 in equation 2

2(-49) - x = 151

x = -98 - 151

x = -249

Answer with explanation:

After dilation about the origin(0,0) with the scale factor of 'k" , the image of the original point (x,y) becomes (kx,ky)

From the given graph, the coordinates of point C = (0,6)  [Since it lies on y-axis , the x-coordinate is zero]

After a dilation about the origin(0,0) with the scale factor of [tex]\dfrac{1}{2}[/tex], the new point will be [tex](\dfrac{1}{2}\times0,\dfrac{1}{2}\times6)=(0,3)[/tex]

Now plot this point on y-axis at y=3 as given in the attachment.

Answer:

83

Step-by-step explanation:

You're given two vertical angles, and vertical angles are congruent. This means that (6x - 7) = (4x + 23); x = 15. Plug it into ABC (which is (6x - 7)) to get 6(15) - 7 = 90 - 7 = 83

Answer:

158.73 yd

Step-by-step explanation:

A picture of the situation is needed, investigating I could find a related one, in the same way the important thing is the solution, the data can be exchanged. I attach the drawing.

Let use the formula of the law of cosine:

c ^ 2 = a ^ 2 + b ^ 2 - 2 * a * b * cos C, to solve the problem

Let the third side be c, we replace:

c ^ 2 = 375 ^ 2 + 240 ^ 2 - 2 * 375 * 240 * cos 16 °

c ^ 2 = 198225 - 173027.10

c ^ 2 = 25197.9

c = 158.73

So the distance is 158.73 yd

Answer: the right answer is 195.4

Step-by-step explanation: this guy does not what's happening

Answer:

Yes, the ordered pair is correct.

Explanation:

You can check the if the ordered pair by substituting the values into the equation. If you substitute the ordered pair (1, 3), then you can make sure the ordered pair is correct. The equation with the substitution will be 3 = 1 + 2, which results in the true equation 3 = 3, therefore the ordered pair is correct.

Answer:

first option

Step-by-step explanation:

Given

[tex]\frac{15}{x}[/tex] + 6 = [tex]\frac{9}{x^2}[/tex]

Multiply through by x² to clear the fractions

15x + 6x² = 9 ( subtract 9 from both sides )

6x² + 15x - 9 = 0 ( divide through by 3 )

2x² + 5x - 3 = 0 ← in standard form

Consider the factors of the product of the coefficient of x² and the constant term which sum to give the coefficient of the x- term.

product = 2 × - 3 = - 6 and sum = + 5

The factors are + 6 and - 1

Use these factors to slit the x- term

2x² + 6x - x - 3 = 0 ( factor the first/second and third/fourth terms )

2x(x + 3) - 1(x + 3) = 0 ← factor out (x + 3) from each term

(x + 3)(2x - 1) = 0 ← in factored form

Equate each factor to zero and solve for x

x + 3 = 0 ⇒ x = - 3

2x - 1 = 0 ⇒ 2x = 1 ⇒ x = 0.5

Solution set is { - 3, 0.5 }

Answer:

Inclusive means that we'll use the signs ≤ and ≥. Let's call the variable in our inequality as x. Therefore, the answer is -5 ≤ x ≤ -1.

Answer:

[tex]f(x) = (x+1)^2 +2[/tex]

Step-by-step explanation:

Well you complete the square and get,

[tex]x^2 + 2x + 1 ^2 - 1^2 +3[/tex]

Then you use the binomial formula to get,

(x + 1)^2 + 2

Thus,

f(x) = x^2 + 2x + 3 is f(x) = (x + 1)^2 + 2.

Hope this helps :)

Answer:  3.2 yd

Step-by-step explanation:

Notice that TWV is a right triangle.  

Segment TU is not needed to answer this question.

∠V = 32°, opposite side (TW) is unknown, hypotenuse (TV) = 6

[tex]\sin \theta=\dfrac{opposite}{hypotenuse}\\\\\\\sin 32=\dfrac{\overline{TW}}{6}\\\\\\6\sin 32=\overline{TW}\\\\\\\large\boxed{3.2=\overline{TW}}[/tex]

Answer:

What is the question

Step-by-step explanation:

Answer:

x=1.94

x = - 1.94

Step-by-step explanation:

8x² + 5 = 35

Subtract 5 from each side

8x² + 5-5 = 35-5

8x²  = 30

Divide each side by 8

8x² /8 = 30/8

x² = 15/4

Take the square root of each side

sqrt( x²) = ±sqrt(15/4)

x = ±sqrt(15/4)

x=1.93649

x = - 1.93649

To the nearest hundredth

x=1.94

x = - 1.94

Answer:

1.94

Step-by-step explanation:

[tex]8x^2+5=35\\8x^2=30 \\x^2=30/8\\x^2=3.75\\\sqrt{3.75} \\[/tex]

≈ ±1.94

Answer:

Step-by-step explanation:

                +2d+30    +2d+30

                    ÷(-15)      ÷(-15)

my mistake it's actually d= -30/19 sometimes I forget you put them in fractions

a+b+c=68

b-3=a

c-5=b

now just solve the system of equations, substitue so that there are only b's in the equation:

a+b+c=68

(b-3) + b + (b+5) = 68

3b=66

b=22

Therefore Barbara is 22

The required age of barbar is 22 years.

Alice, Barbara, and Carol are sisters. Alice is 3 years younger than Barbara, and Barbara is 5 years younger than Carol. Together the sisters are 68 years old.  How old is Barbara to be determined.

In mathematics, it deals with numbers of operations according to the statements.

Let the age of Alice, Barbara and Carol are a, b and c.

Age Alice is 3 years younger than Barbara,

a = b - 3     - - - -(1)

Age Barbara is 5 years younger than Carol

b = c - 5

c = b + 5     - - - -(2)

Together the sisters are 68 years old i.e.

a + b +c =68

From equation 1 and 2

b - 3 + b + b +5 = 68

3b + 2 = 68

3b = 66

b  = 33

Thus, the required age of barbar is 22 years.

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Answer:

1131 cubic inches.

Step-by-step explanation:

The front side of the figure contains a rectangle and a semicircle.

Area of rectangle is

[tex]A_1=length\times breadth[/tex]

[tex]A_1=11\times 12[/tex]

[tex]A_1=132\text{ in}^2[/tex]

Radius of semicircle is

[tex]r=17-11=6\text{ in}[/tex]

Area of semicircle is

[tex]A_2=\dfrac{1}{2}\pi r^2[/tex]

[tex]A_2=\dfrac{1}{2}\pi (6)^2[/tex]

[tex]A_2\approx 56.55[/tex]

Area of front side is

[tex]A=A_1+A_2=132+56.55=188.55\text{ in}^2[/tex]

Let front side is the base of prism and height is 6 in. So, volume of given figure is

[tex]V=\text{Base area}\times height[/tex]

[tex]V=188.55\times 6[/tex]

[tex]V=1131.3[/tex]

[tex]V\approx 1131\text{ in}^3[/tex]

Therefore, the required volume is 1131 cubic inches.

Answer:

[tex]\dfrac{1}{x^{48}y^{36}z^{6}}[/tex]

Step-by-step explanation:

[tex] (\dfrac{(x^2y^3)^{-2}}{(x^6y^3z)^{2}})^3 = [/tex]

[tex] = (\dfrac{1}{(x^6y^3z)^{2}(x^2y^3)^{2}})^3 [/tex]

[tex] = (\dfrac{1}{x^{12}y^6z^{2}x^4y^6})^3 [/tex]

[tex]= (\dfrac{1}{x^{16}y^{12}z^{2}})^3[/tex]

[tex]= \dfrac{1}{x^{48}y^{36}z^{6}}[/tex]

Answer:

[tex]\displaystyle \frac{1}{x^{48}y^{36}z^6}[/tex]

Step-by-step explanation:

[tex]\displaystyle[\frac{(x^2 y^3)^{-2}}{(x^6 y^3 z)^2 } ]^3[/tex]

[tex]\displaystyle \frac{(x^2 y^3)^{-6}}{(x^6 y^3 z)^6 }[/tex]

[tex]\displaystyle \frac{(x^{-12} y^{-18})}{(x^{36} y^{18}z^6 ) }[/tex]

[tex]\displaystyle \frac{x^{-48} y^{-36}}{z^6 }[/tex]

[tex]\displaystyle \frac{1}{x^{48}y^{36}z^6}[/tex]

Answer:

[tex]2\sqrt{2} +2\sqrt{5}[/tex]

Step-by-step explanation:

i just got this one right

the kite has two pairs of congruent sides. using the distance formula, the two shorter sides=[tex]\sqrt{2}[/tex] (since there are two of those length sides, you multiply it by two). Again with the distance formula, the two longer sides=[tex]\sqrt{5}[/tex] (also multiply this by two).this gives the answer c or [tex]2\sqrt{2}+2\sqrt{5}[/tex]

Answer:

The answer is c [tex]\sqrt[2]{2}[/tex] + [tex]\sqrt[2]{5}[/tex] units. just took the test

Step-by-step explanation:

Answer:

y = - 49

Step-by-step explanation:

Given

7x - 2y = 35 ← substitute x = - 9 into the equation

7(- 9) - 2y = 35, that is

- 63 - 2y = 35 ( add 63 to both sides )

- 2y = 98 ( divide both sides by - 2 )

y = - 49

Answer:

[tex]\boxed{y = -49}[/tex]

Step-by-step explanation:

=> [tex]7x-2y = 25[/tex]

Given that x = -9

=> [tex]7(-9)-2y = 35[/tex]

=> [tex]-63 -2y = 35[/tex]

Adding 63 to both sides

=> [tex]-2y = 35+63[/tex]

=> [tex]-2y = 98[/tex]

Dividing both sides by -2

=> [tex]y = 98/-2[/tex]

=> [tex]y = -49[/tex]

By the factor theorem,

[tex]3x^2+5x+7=3(x-u)(x-v)\implies\begin{cases}uv=\frac73\\u+v=-\frac53\end{cases}[/tex]

Now,

[tex](u+v)^2=u^2+2uv+v^2=\left(-\dfrac53\right)^2=\dfrac{25}9[/tex]

[tex]\implies u^2+v^2=\dfrac{25}9-\dfrac{14}3=-\dfrac{17}9[/tex]

So we have

[tex]\dfrac uv+\dfrac vu=\dfrac{u^2+v^2}{uv}=\dfrac{-\frac{17}9}{\frac73}=\boxed{-\dfrac{17}{21}}[/tex]

The value of [tex]\frac{u}{v} +\frac{v}{u}[/tex] is [tex]\frac{-17}{21}[/tex].

A quadratic equation is an algebraic equation of the second degree in x. The quadratic equation in its standard form is[tex]ax^{2} +bx+c=0[/tex], where a and b are the coefficients, x is the variable, and c is the constant term.

If [tex]ax^{2} +bx+c = 0[/tex] be the quadratic equation then

Sum of the roots = [tex]\frac{-b}{a}[/tex]

And,

Product of the roots = [tex]\frac{c}{a}[/tex]

According to the given question.

We have a quadratic equation [tex]3x^{2} +5x+7=0..(i)[/tex]

On comparing the above quadratic equation with standard equation or general equation [tex]ax^{2} +bx+c = 0[/tex].

We get

[tex]a = 3\\b = 5\\and\\c = 7[/tex]

Also, u and v are the solutions of the quadratic equation.

⇒ u and v are the roots of the given quadratic equation.

Since, we know that the sum of the roots of the quadratic equation is [tex]-\frac{b}{a}[/tex].

And product of the roots of the quadratic equation is [tex]\frac{c}{a}[/tex].

Therefore,

[tex]u +v = \frac{-5}{3}[/tex] ...(ii) (sum of the roots)

[tex]uv=\frac{7}{3}[/tex]   ....(iii)       (product of the roots)

Now,

[tex]\frac{u}{v} +\frac{v}{u} = \frac{u^{2} +v^{2} }{uv} = \frac{(u+v)^{2}-2uv }{uv}[/tex]                    ([tex](a+b)^{2} =a^{2} +b^{2} +2ab[/tex])

Therefore,

[tex]\frac{u}{v} +\frac{v}{u} =\frac{(\frac{-5}{3} )^{2}-2(\frac{7}{3} ) }{\frac{7}{3} }[/tex]         (from (i) and (ii))

⇒ [tex]\frac{u}{v} +\frac{v}{u} =\frac{\frac{25}{9}-\frac{14}{3} }{\frac{7}{3} }[/tex]

⇒ [tex]\frac{u}{v} +\frac{v}{u} = \frac{\frac{25-42}{9} }{\frac{7}{3} }[/tex]

⇒ [tex]\frac{u}{v} +\frac{v}{u} = \frac{\frac{-17}{9} }{\frac{7}{3} }[/tex]

⇒ [tex]\frac{u}{v} +\frac{v}{u} =\frac{-17}{21}[/tex]

Therefore, the value of [tex]\frac{u}{v} +\frac{v}{u}[/tex] is [tex]\frac{-17}{21}[/tex].

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Answer:

pretty sure this is right

Answer:

[tex]\displaystyle \sin \theta = \frac{4}{5}[/tex] if [tex]\displaystyle \cos\theta = -\frac{3}{5}[/tex] and [tex]\theta[/tex] is in the second quadrant.

Step-by-step explanation:

By the Pythagorean Trigonometric Identity:

[tex]\left(\sin \theta\right)^2 + \left(\cos\theta)^2 = 1[/tex] for all real [tex]\theta[/tex] values.

In this question:

[tex]\displaystyle \left(\cos\theta\right)^2 = \left(-\frac{3}{5}\right)^2 = \frac{9}{25}[/tex].

Therefore:

[tex]\begin{aligned} \left(\sin\theta\right)^2 &= 1 -\left(\cos\theta\right)^2 \\ &= 1 - \left(\frac{3}{5}\right)^2 = \frac{16}{25}\end{aligned}[/tex].

Note, that depending on [tex]\theta[/tex], the sign [tex]\sin \theta[/tex] can either be positive or negative. The sine of any angles above the [tex]x[/tex] axis should be positive. That region includes the first quadrant, the positive [tex]y[/tex]-axis, and the second quadrant.

According to this question, the [tex]\theta[/tex] here is in the second quadrant of the cartesian plane, which is indeed above the [tex]x[/tex]-axis. As a result, the sine of this

It was already found (using the Pythagorean Trigonometric Identity) that:

[tex]\displaystyle \left(\sin\theta\right)^2 = \frac{16}{25}[/tex].

Take the positive square root of both sides to find the value of [tex]\sin \theta[/tex]:

[tex]\displaystyle \sin\theta =\sqrt{\frac{16}{25}} = \frac{4}{5}[/tex].

Answer:

Option C is the correct option.

Step-by-step explanation:

Let the points be A and B

A ( -2 , 7 ) -----> ( x1 , y1 )

B ( 2 , 3 )-------> ( x2 , y2)

Now, let's find the slope:

Slope = [tex] \frac{y2 - y1}{x2 - x1} [/tex]

plug the values

[tex] = \frac{3 - 7}{2 - ( - 2)} [/tex]

Calculate the difference

[tex] = \frac{ - 4}{2 - (2)} [/tex]

When there is a ( - ) in front of an expression in parentheses, change the sign of each term in the expression

[tex] = \frac{ - 4}{2 + 2} [/tex]

Add the numbers

[tex] = \frac{ - 4}{4} [/tex]

Any expression divided by its opposite equals -1

[tex] = - 1[/tex]

Hope this helps..

Best regards!!

Answer:

both the equation and it's inverse are functions

Answer:

70° and 110°

Step-by-step explanation:

If two angles forms a linear pair, this means that the sum of the angles is 180°. If the measure of one angle is x and the measure of the other angle is 1.4 times x plus 12∘

Let A be the first angle = x°

Let B be the second angle = (1.4x+12)°

Since they form a linear pair, then

A+B = 180°

x + 1.4x+12 = 180°

2.4x = 180-12

2.4x = 168

x = 168/2.4

x = 70°

The measure of angle A = 70°

The measure if angle B = 1.4x+12

B = 1.4(70)+12

B = 98+12

B = 110°

The measure of both angles are 70° and 110°