Solve for x in the equation x squared + 11 x + 121/4 = 125/4.

Answer:

The  99%  confidence interval is

                     [tex]37.167< \= x < 44.833[/tex]

Step-by-step explanation:

From the question we are told that

  The sample size is  [tex]n = 29[/tex]

  The  sample mean is  [tex]\= x =[/tex]$41

  The  sample standard deviation is  [tex]\sigma =[/tex]$8

   The  level of confidence is [tex]C =[/tex]99%

Given that the confidence level id  99% the level of confidence is evaluated as

        [tex]\alpha = 100 - 99[/tex]

        [tex]\alpha = 1[/tex]%

Next we obtain the critical value of [tex]\frac{\alpha }{2}[/tex] from the normal distribution table which is  

      [tex]Z_{\frac{\alpha }{2} } = 2.58[/tex]

The reason we are obtaining values for  is because  is the area under the normal distribution curve for both the left and right tail where the 99% interval did not cover while   is the area under the normal distribution curve for just one tail and we need the  value for one tail in order to calculate the confidence interval

Next we evaluate the margin of error which is mathematically represented as

          [tex]MOE = Z_{\frac{\alpha }{2} } * \frac{\sigma }{\sqrt{n} }[/tex]

substituting values

         [tex]MOE = 2.58 * \frac{8 }{\sqrt{29} }[/tex]

           [tex]MOE = 3.8328[/tex]

The 99% confidence level is constructed as follows

      [tex]\= x - MOE < \= x < \= x + MOE[/tex]

substituting values

    [tex]41 - 3.8328 < \= x < 41 + 3.8328[/tex]

     [tex]37.167< \= x < 44.833[/tex]

Range is [tex]y\in[-3,+\infty)[/tex].

Hope this helps.

Answer:

3057.6 cm³

Step-by-step explanation:

You have a cylinder and a rectangular prism.  Solve for the area of each separately.

Cylinder

The formula for volume of a cylinder is V = πr²h.  The radius is 7, and the height is 7.

V = πr²h

V = π(7)²(7)

V = π(49)(7)

V = 343π

V = 1077.57 cm³

Rectangular Prism

The formula for volume of a rectangular prism is V = lwh.  The length is 20, the width is 11, and the height is 9.

V = lwh

V = (20)(11)(9)

V = (220)(9)

V = 1980 cm³

Add the areas of the two shapes.

1077.57 cm³ + 1980 cm³ = 3057.57 cm³

Round to the nearest tenth.

3057.57 cm³ ≈ 3057.6 cm³

Answer:

[tex]\huge\boxed{slope=\dfrac{1}{2}=0.5}[/tex]

Step-by-step explanation:

The formula of a slope:

[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]

We have the points

[tex](-5;\ 3)\to x_1=-5;\ y_1=3\\(7;\ 9)\to x_2=7;\ y_2=9[/tex]

Substitute:

[tex]m=\dfrac{9-3}{7-(-5)}=\dfrac{6}{7+5}=\dfrac{6}{12}=\dfrac{6:6}{12:6}=\dfrac{1}{2}[/tex]

Answer:

1/2

Step-by-step explanation:

We can use the slope formula since we have 2 points

m = ( y2-y1)/(x2-x1)

    = (9-3)/( 7 - -5)

    = (9-3) /( 7+5)

   = 6/ 12

  = 1/2

Answer: $2.95

Step-by-step explanation:

Given: Probability of losing the $7 = [tex]\dfrac{20}{38}[/tex]

Probability of winning $14  = [tex]\dfrac{18}{38}[/tex]

Then, the expected value = (- $7)  x ( Probability of losing the $7) + $14 x(Probability of winning $14)

= [tex](-\$ 7)\times\dfrac{20}{38}+(\$14)\times\dfrac{18}{38}[/tex]

= [tex]-\dfrac{70}{19}+\dfrac{126}{19}[/tex]

= [tex]\dfrac{56}{19}\times\approx\$2.95[/tex]

∴ If a doctor pays $7 that the outcome is an odd number, the doctor's

expected value is $2.95.

Triangle DAC is congruent to triangle BCA by SAS congruence theorem.

Triangle congruence theorem or triangle congruence criteria help in proving if a triangle is congruent or not. The word congruent means exactly equal in shape and size no matter if we turn it, flip it or rotate it.

Given that, AD = BC and AD || BC.

AD = BC (Given)

AD || BC (Given)

AC = AC (Reflexive property)

∠DAC=∠BCA (Interior alternate angles)

By SAS congruence theorem, ΔDAC≅ΔBCA

By CPCT, AB=CD

Therefore, triangle DAC is congruent to triangle BCA by SAS congruence theorem.

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Answer:

97 m

Step-by-step explanation:

Perimeter = 2 * (length + width); perimeter = 344, width = 75 (solving for length)

344 = 2(length + 75)

172 = length + 75

length = 97

Answer:

a) Mean = 4.55

   Median = 4.7

   Mode = 1.9

b) S =  2.3952

   CV = 52.64 %

   Range = 6.3

c) Yes, since the average and median values are both over "acceptable" ranges.

Step-by-step explanation:

Explanation is provided in the attached document.

Answer:

Step-by-step explanation:

Using the following data:

H0:p=0.40 (null hypothesis)

Ha:p>0.40 (alternative hypothesis)

The p-value was determined to be 0.001.

a significance level of 5%

Since the p value (0.001) is less than the significance level (0.05), we will reject the null hypothesis and then we would conclude that the proportion of students that are nursing majors is greater than 0.4.

Answer:

p value= 0.131

Step-by-step explanation:

Since we have calculated the test statistic, we can now proceed to find the p-value for this hypothesis test.Using the test statistic and since the hypothesis test is a left tailed test, the p-value will then be the area under the standard normal curve to the left of the test statistic of -1.12.Using the Standard Normal table given above, the area under the standard normal curve to the left of the test statistic of -1.12 is 0.131 (rounded to 3 decimal places.Thus the p-value = 0.131.

Answer:

d ≈ 8.3

Step-by-step explanation:

This is kind of like the pythagorean theorem, but with one extra value.  Thus, [tex]d^2=l^2+w^2+h^2[/tex].

Plug in the values to get:

[tex]d^2=2^2+7^2+4^2\\d^2=4+49+16\\d^2=69\\d=\sqrt{69} \\[/tex]

Thus d ≈ 8.3

Answer:

[tex]4y - 7x - 1 = 0[/tex]

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

[tex]m = \frac{ - 5 - 2}{ - 6 - - 2?} [/tex]

[tex]m = \frac{ - 7}{ - 4} [/tex]

[tex]m = \frac{7}{4} [/tex]

[tex]y = m(x - x1) + y1[/tex]

[tex]y = \frac{7}{4} (x + 2) + 2[/tex]

[tex]y = \frac{7}{4} x + \frac{7}{2} + 2[/tex]

[tex]y = \frac{7}{4} x + \frac{11}{2} [/tex]

[tex]4y = 7x + 22[/tex]

[tex]4y - 7x - 22 = 0[/tex]

The equation of the line passing through the point (-2,2) and (-6,-5) is,

y = (-7/4)x +(11/2).

An equation of the line is defined as a linear equation having a degree of one. The equation of the line contains two variables x and y. And the third parameter is the slope of the line which represents the elevation of the line.

The general form of the equation of the line:-

y = mx + c

m = slope

c = y-intercept

Slope = ( y₂ - y₁ ) / ( x₂ - x₁ )

Given that the equation of a line that contains the points (−2,2) and (−6,−5).

Calculate the slope of the line,

Slope = ( y₂ - y₁ ) / ( x₂ - x₁ )

Slope = ( -5-2) / (-6 + 2 )

Slope= 7 / 4

The y-intercept is calculated as,

y = mx + c

2 = (-7/4) x 2 + c

c = 11 / 2

The equation will be written as,

y = mx + c

y = (7 / 4)x + (11/2)

Therefore, the equation of the line passing through the point (-2,2) and (-6,-5) is,

y = (-7/4)x +(11/2).

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Answer:

The value of the polynomial function at P(1) and P(-2) is 24 and 0 respectively.

Step-by-step explanation:

We are given with the following polynomial function below;

[tex]\text{P}(x) = 2x^{5} +9x^{4} +9x^{3} +3x^{2}+7x-6[/tex]

Now, we have to calculate the value of P(x) at x = 1 and x = -2.

For this, we will substitute the value of x in the given polynomial and find it's value.

At x = 1;

[tex]\text{P}(1) = 2(1)^{5} +9(1)^{4} +9(1)^{3} +3(1)^{2}+7(1)-6[/tex]

[tex]\text{P}(1) = (2\times 1) +(9\times 1)+(9 \times 1)+(3\times 1)+(7\times 1)-6[/tex]

[tex]\text{P}(1) = 2 +9+9+3+7-6[/tex]

P(1) = 30 - 6

P(1) = 24

At x = -2;

[tex]\text{P}(-2) = 2(-2)^{5} +9(-2)^{4} +9(-2)^{3} +3(-2)^{2}+7(-2)-6[/tex]

[tex]\text{P}(-2) = (2\times -32) +(9\times 16)+(9 \times -8)+(3\times 4)+(7\times -2)-6[/tex]

[tex]\text{P}(-2) = -64 +144-72+12-14-6[/tex]

P(-2) = 156 - 156

P(-2) = 0

Hence, the value of the polynomial function at P(1) and P(-2) is 24 and 0 respectively.

Answer:

C. μ = 3.60

Step-by-step explanation:

Two tables have been attached to this response.

One of the tables contains the given data and distribution with two columns: Houses Sold and Probability

The other table contains the analysis of the data with additional columns: Frequency and Fx

=> The Frequency(F) column is derived from the product of the probability of each item in the Houses sold column and the total number of houses sold (which is 28). For example,

When the number of houses sold = 0

F = P(0) x Total number of houses sold

F = 0.24 x 28 = 6.72

When the number of houses sold = 1

F = P(1) x Total number of houses sold

F = 0.01 x 28 = 0.28

=> The Fx column is found by multiplying the Frequency column by the Houses Sold column. For example,

When the number of houses sold = 0

Fx = F * x

F = 6.72 x 0 = 0

Now to get the mean, μ we use the relation;

μ = ∑Fx / ∑F

Where;

∑Fx = summation of the items in the Fx column = 100.8

∑F = summation of the items in the Frequency column = 28

μ = 100.8 / 28

μ = 3.60

Therefore, the mean of the given probability distribution is 3.60

The mean of the discrete probability distribution is given by:

C. μ = 3.60

The expected value of a discrete distribution is given by the sum of each outcome multiplied by it's respective probability.

In this problem, the table x - P(x) gives each outcome and their respective probabilities, hence, the mean is:

[tex]E(X) = 0(0.24) + 1(0.01) + 2(0.12) + 3(0.16) + 4(0.01) + 5(0.14) + 6(0.11) + 7(0.21) = 3.6[/tex]

Hence option C is correct.

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Answer:

[tex]\large \boxed{\sf \ \ x = -\dfrac{\sqrt{33}+1}{4} \ \ or \ \ x = \dfrac{\sqrt{33}-1}{4} \ \ }[/tex]

Step-by-step explanation:

Hello, please find below my work.

[tex]2x^2+x-4=0\\\\\text{*** divide by 2 both sides ***}\\\\x^2+\dfrac{1}{2}x-2=0\\\\\text{*** complete the square ***}\\\\x^2+\dfrac{1}{2}x-2=(x+\dfrac{1}{4})^2-\dfrac{1^2}{4^2}-2=0\\\\\text{*** simplify ***}\\\\(x+\dfrac{1}{4})^2-\dfrac{1+16*2}{16}=(x+\dfrac{1}{4})^2-\dfrac{33}{16}=0[/tex]

[tex]\text{*** add } \dfrac{33}{16} \text{ to both sides ***}\\\\(x+\dfrac{1}{4})^2=\dfrac{33}{16}\\\\\text{**** take the root ***}\\\\x+\dfrac{1}{4}=\pm \dfrac{\sqrt{33}}{4}\\\\\text{*** subtract } \dfrac{1}{4} \text{ from both sides ***}\\\\x = -\dfrac{1}{4} -\dfrac{\sqrt{33}}{4} \ \ or \ \ x = -\dfrac{1}{4} +\dfrac{\sqrt{33}}{4}[/tex]

Hope this helps.

Do not hesitate if you need further explanation.

Thank you

Answer:

x1= -4, x2 = 7

Step-by-step explanation:

Move expression to the left-hand side:

1/4x-3/4-7/x=0

Write all the numerators above a common denominator:

x^2 - 3x - 28 /4x =0

When the quotient of expressions equal 0, the numerator has to be 0

x^2 + 4x - 7x - 28 = 0

x(x+4) - 7(x+4) =0

(x+4) × (x-7) =0

Separate into possible cases:

x+4=0

x-7=0

Answer: -9

Step-by-step explanation:

Answer:

Step-by-step explanation:

Given the following geometric progression; 1/2 + 1/10 + ( 1/50) + (1/250 ) + ... + (1/31,250),the sum of the arithmetic geometric progression is expressed using the formula below;

Sn = a(1-rⁿ)/1-r  for r less than 1

r is the common ratio

n is the number of terms

a is the first term of the series

In between the mid-line ellipsis there are 2 more terms, making the total number of terms n to be 7]

common ratio = (1/10)/(1/2) =  (1/50)/(1/10) =  (1/250)/(1/50) = 1/5  

a = 1/2

Substituting the given values into the equation above

S7 = 1/2{1 - (1/5)⁷}/1 - 1/5

S7 = 1/2(1- 1/78125)/(4/5)

S7 = 1/2 (78124/78125)/(4/5)

S7 = 78124/156,250 * 5/4

S7 = 390,620/625000

S7 = 39062/62,500

Hence the geometric sum is 39062/62,500

Answer:

Step-by-step explanation:

Given,

Perpendicular ( p ) = 9x

Base ( b ) = 10

Hypotenuse ( h ) = x + 10

Now, let's find the value of x

Using Pythagoras theorem:

[tex] {h}^{2} = {p}^{2} + {b}^{2} [/tex]

Plug the values

[tex] {(x + 10)}^{2} = {(9x)}^{2} + {(10)}^{2} [/tex]

Using [tex] {(a + b)}^{2} = {a}^{2} + 2ab + {b}^{2} [/tex] , expand the expression

[tex] {x}^{2} + 20x + 100 = {(9x)}^{2} + {10}^{2} [/tex]

To raise a product to a power , raise each factor to that power

[tex] {x}^{2} + 20x + 100 = 81 {x}^{2} + {10}^{2} [/tex]

Evaluate the power

[tex] {x}^{2} + 20x + 100 = 81 {x}^{2} + 100[/tex]

Cancel equal terms on both sides of the equation

[tex] {x}^{2} + 20x = 81 {x}^{2} [/tex]

Move x² to R.H.S and change its sign

[tex]20x = 81 {x}^{2} - {x}^{2} [/tex]

Calculate

[tex]20x = 80 {x}^{2} [/tex]

Swap both sides of the equation and cancel both on both sides

[tex]80x = 20[/tex]

Divide both sides of the equation by 80

[tex] \frac{80x}{80} = \frac{20}{80} [/tex]

Calculate

[tex]x = \frac{20}{80} [/tex]

Reduce the numbers with 20

[tex]x = \frac{1}{4} [/tex]

The value of X is [tex] \frac{1}{4} [/tex]

Now, let's replace the value of x to find the approximate value of hypotenuse

Hypotenuse = [tex] \frac{1}{4} + 10[/tex]

Write all numerators above the common denominator

[tex] \frac{1 + 40}{4} [/tex]

Add the numbers

[tex] \frac{41}{4} [/tex]

[tex] = 10.25[/tex] inches

Hope this helps..

best regards!!

Answer:

10.25

Step-by-step explanation:

because I said so ya skoozie

Answer:

Step-by-step explanation:

You haven't answered any questions, yet…

Answer:

( 2A - kn) /k = m

Step-by-step explanation:

A = k/2(m+n)

Multiply each side by 2/k

2/k *A =2/k * k/2(m+n)

2A /k = m+n

Subtract n from each side

2A /k - n = m+n -n

2A /k - n = m

Getting a common denominator

2A/k - kn/k = m

( 2A - kn) /k = m

Answer:

Step-by-step explanation:

[tex]A=\frac{k(m+n)}{2}\\2A=k(m+n)\\\frac{2A}{k} =m+n\\\frac{2A}{k}-n=m\\2A-kn=km\\\frac{(2A-kn)}{k}=m[/tex]

Answer:

(a) H0:μ1=μ2; Ha:μ1≠μ2, which is a two-tailed test.

Step-by-step explanation:

We formulate the

H0: μ1=μ2; null hypothesis that the two means are equal and alternate hypothesis that the two mean are not equal.

Ha:μ1≠μ2 Two tailed test

Test statistic used is

t= x1`-x2` / s√n as the variances are equal and sample size is same

T value for 9 degrees of freedom for two tailed test at α = 0.05 is 2.26

P- value for t test for 9 degrees of freedom is 0.125 from the table.

Hence only a is correct .

Answer:  Focus = (-2, 3)

Step-by-step explanation:

[tex]y=-\dfrac{1}{4}x^2-x+3\\\\\rightarrow a=-\dfrac{1}{4},\ b=-1[/tex]

First let's find the vertex. We do that by finding the Axis-Of-Symmetry:

[tex]AOS: x=\dfrac{-b}{2a}\quad =\dfrac{-(-1)}{2(\frac{-1}{4})}=\dfrac{1}{-\frac{1}{2}}=-2[/tex]

Then finding the maximum by inputting x = -2 into the given equation:

[tex]y=-\dfrac{1}{4}(-2)^2-(-2)+3\\\\y=-1+2+3\\\\y=4[/tex]

The vertex is: (-2, 4)

Now let's find p, which is the distance from the vertex to the focus:

[tex]a=\dfrac{1}{4p}\\\\\\-\dfrac{1}{4}=\dfrac{1}{4p}\\\\\\p=-1[/tex]

The vertex is (-2, 4) and p = -1

The focus is (-2, 4 + p) = (-2, 4 - 1) = (-2, 3)

Answer:

k ≥ 24

Step-by-step explanation:

ᵏ⁄₄ ≥ 6

Multiply each side by 4

ᵏ⁄₄ *4 ≥ 6*4

k ≥ 24

Answer:

k≥24

Step-by-step explanation:

k/4≥6

Use the multiplication property of equality by multiplying both sides by 4 to get

k≥24

If this is wrong or if I did something wrong, please tell me so I can learn the proper way, I am just treating this like a normal problem

Thank you

Step-by-step explanation:

the common ratio is -4

Gn=2 (-4)^n-1

Answer:

38.68 cm

Step-by-step explanation:

Perimeter of an equilateral triangle : P = 3a

Area of an equilateral triangle : A = [tex]\frac{\sqrt{3} }{4}a^2[/tex]

a = side length

The area is given, solve for a.

[tex]72= \frac{\sqrt{3} }{4}a^2[/tex]

[tex]a = 12.894839[/tex]

The side length is 12.894839 centimeters.

Find the perimeter.

P = 3a

P = 3(12.894839)

P = 38.684517 ≈ 38.68

The perimeter is 38.68 centimeters.

Answer:

(a) $7/ticket

(b) 3 cats/dog

(c) 10 ft/sec

(d) 16 cups/gal

Step-by-step explanation:

(a) $35 for 5 tickets

$35/(5 tickets) = $7/ticket

(b) 21 cats and 7 dogs

21 cats/(7 dogs) = 3 cats/dog

(c) 40 ft in 4 seconds

40 ft/(4 sec) = 10 ft/sec

(d) 48 cups for 3 gallons

48 cups/(3 gal) = 16 cups/gal

Looks like the function on the right hand side is

[tex]f(t)=\begin{cases}1&\text{for }t<4\\-1&\text{for }t\ge4\end{cases}[/tex]

We can write it in terms of the Heaviside function,

[tex]h(t-a)=\begin{cases}1&\text{for }t\ge a\\0&\text{for }t>a\end{cases}[/tex]

as

[tex]f(t)=h(t)-2h(t-4)[/tex]

Now for the ODE: take the Laplace transform of both sides:

[tex]y'(t)+y(t)=f(t)[/tex]

[tex]\implies s Y(s)-y(0)+Y(s)=\dfrac{1-2e^{-4s}}s[/tex]

Solve for Y(s), then take the inverse transform to solve for y(t):

[tex](s+1)Y(s)=\dfrac{1-e^{-4s}}s[/tex]

[tex]Y(s)=\dfrac{1-e^{-4s}}{s(s+1)}[/tex]

[tex]Y(s)=(1-e^{-4s})\left(\dfrac1s-\dfrac1{s+1}\right)[/tex]

[tex]Y(s)=\dfrac1s-\dfrac{e^{-4s}}s-\dfrac1{s+1}+\dfrac{e^{-4s}}{s+1}[/tex]

[tex]\implies y(t)=1-h(t-4)-e^{-t}+e^{-(t-4)}h(t-4)[/tex]

[tex]\boxed{y(t)=1-e^{-t}-h(t-4)(1-e^{-(t-4)})}[/tex]

Answer:

For 0,90 of Confidence we reject H₀

For  0,95 CI we reject H₀

Step-by-step explanation:

To evaluate a difference between two proportion with big sample sizes we proceed as follows

1.-Proportion 1

n = 2160

243 had rear license  p₁ = 243/2160     p₁ = 0,1125

2.Proportion 2

n = 358

55   had rear license   p₂ = 55/ 358     p₂ = 0,1536

Test Hypothesis

Null Hypothesis                            H₀      ⇒   p₂   =  p₁

Alternative Hypothesis                Hₐ     ⇒    p₂  >  p₁

With signficance level  of  0,05  means  z(c) = 1,64

T calculate   z(s)

z(s) =  ( p₂ - p₁ ) / √ p*q ( 1/n₁  +  1/n₂ )

p = ( x₁  +  x₂ ) / n₁  +  n₂

p = 243  +  55 / 2160 + 358

p = 0,1183     and then    q = 1 -  p     q =  0,8817

z(s) =  ( 0,1536 - 0,1125 ) / √ 0,1043 ( 1/ 2160   +  1 / 358)

z(s) =  0,0411 /√ 0,1043*0,003256

z(s) = 0,0411 / 0,01843

z(s) =  2,23

Then  z(s) > z(c)      2,23  >  1,64

z(s) is in the rejection region we reject H₀

If we construct a CI for  0,95   α = 0,05   α/2  =  0,025

z (score ) is  from z- table    z = 1,96

CI = ( p ±  z(0,025*SE)

CI = ( 0,1536 ± 1,96*√ 0,1043*0,003256 )

CI = ( 0,1536 ± 1.96*0,01843)

CI = ( 0,1536 ± 0,03612 )

CI = ( 0,11748  ;  0,18972 )

In the new CI we don´t find  0 value so we have enough evidence to reject H₀

Answer:

Step-by-step explanation:

Can you please include a image?

Thanks!!!

Answer:

the linear system has two valid solution.

Answer:one solution

Step-by-step explanation:

Answer:

Step-by-step explanation:

First , let us rewrite the given equation into y= mx+b format

.y= -x +7

Slope is -1

Slope of the line perpendicular to the given equation is -(-1) ie., 1

Let us find the y-intercept by plugging in the values of x,y and slope into the equation y= Mx +b

1 = -1 +b

2 = b

Equation of the line perpendicular to the given equation and passing through (-1,1) is

y=x +2