n
Which number line represents the solutions to [x - 5] = 1?
-7 -6 -5
-4
-3
--2
-1
0
1
2
3
4
5
6
7
+
--
-7
-5
-4
-3
-2 -1
0
1
2
3
4
6
7
-7 -6
-5
-4
-3
-2 -1
0
1
2
3
4
5
6
7
H
-7 -6 -5
-4 -3 -2 -1 0 1
2
3
4
5
6
7

Answer:

D

Step-by-step explanation:

Answer:

given,

AB= 17

AC= 8

angle BCA =90°

as it is a Right angled triangle ,

taking reference angle BAC

we get,h=AB=17

b=AC=8

p=BC=?

now by the Pythagoras theorem we get,

p=

[tex] \sqrt{h { }^{2} - b {}^{2} } [/tex]

so,p=

[tex] \sqrt{17 {}^{2} - 8 {}^{2} } [/tex]

[tex] = \sqrt{225} [/tex]

=15 is the answer....

hope its wht u r searching for....

Answer:

[tex]\frac{15}{12}[/tex]

Step-by-step explanation:

Use Pythagorean Theorem to find the missing side.

a² + b² = r²

9² + 12² = r²

81 + 144 = r²

225 = r²

r = 15

Use the formula for csc θ.

csc θ = [tex]\frac{r}{y}[/tex] = [tex]\frac{15}{12}[/tex]

csc θ = 15/12

Hope this helps.

Answer:

(a) remainder is -40

(b) The remaining zeroes are (x+3) and (x-3)

Step-by-step explanation:

p(x) = x^4 - 2x^3 -7x^2 + 18x – 18

(a) Remainder of P(x) / (x+1) can be found using the remainder theorem, namely

let x + 1 = 0 => x = -1

remainder

= P(-1)

= (-1)^4 - 2(-1)^3 -7(-1)^2 + 18(-1) – 18

= 1 +2 -7-18-18

= -40

remainder is -40

(b)

If one zero is 1-i, then the conjugate 1+i is another zero.

in other words,

(x-1+i) and (x-1-i) are both factors.

whose product = (x^2-2x+2)

Divide p(x) by (x^2-2x+2) gives

p(x) by (x^2-2x+2)

= (x^4 - 2x^3 -7x^2 + 18x – 18) / (x^2-2x+2)

= x^2 -9

= (x+3) * (x-3)

The remaining zeroes are (x+3) and (x-3)

Answer:

4

Step-by-step explanation:

(segment piece) x (segment piece) =   (segment piece) x (segment piece)

JN* NK = LN * NM

3x = 2*6

3x = 12

Divide by 3

3x/3 =12/3

x =4

Answer:

(A)  (-19,-8)

Step-by-step explanation:

Given that the graph is an inverse variation.

The equation of variation is:

[tex]x=\dfrac{k}{y}[/tex]

Since point (-8, -19) is on the graph

[tex]-8=\dfrac{k}{-19}\\k=152[/tex]

Therefore, the equation connecting x and y is:

[tex]x=\dfrac{152}{y}[/tex]

[tex]\text{When y=-8},x=\dfrac{152}{-8}=-19\\\\\text{When y=19},x=\dfrac{152}{19}=8\\\\\text{When y=8},x=\dfrac{152}{8}=19\\\\\text{When y=-19},x=\dfrac{152}{-19}=-8[/tex]

Therefore, the point that is also on the graph is:

(A)  (-19,-8)

Answer:

The price of one reusable bottle is $8.12

Step-by-steetp explanation:

Ms stone wanted to purchase two reusable bottles but discovered she had only ⅝of the Mone and that ⅝ is equal to $ 10.15.

So the cost of what she wants to purchase will be called x.

Mathematically

⅝ * x = 10.15

X = (10.15*8)/5

X = 81.2/5

X= 16.24

The price of the two bottles is $16.24

So the price if one bottle will be calculated as follows.

2 bottles=$ 16.24

One bottle= $16.24/2

One bottle= $8.12

The price of one reusable bottle is $8.12

Answer:

30 m^3

Step-by-step explanation:

Answer:

B. 20m3

Step-by-step explanation:

i dont know if its correct, hope it is tho

Hey there! :)

Answer:

C. (0, -6).

Step-by-step explanation:

In slope-intercept form ( y = mx + b), the 'b' value represents the y-intercept.

In this instance:

y = 4x - 6

The 'b' value is equal to -6. This means that the y-intercept is at (0, -6).

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

The y-intercept can also be solved for by substituting in 0 for x:

y = 4(0) - 6

y = 0 - 6

y = -6.

Answer:

C. (0, –6)

Step-by-step explanation:

y = 4x - 6

The equation is:

y = mx + b

where b is the y-intercept.

In this case, - 6 is the vertical intercept.

Do not confuse from (-6, 0) because that represents an x-intercept.

Answer:

[tex]f = \frac{1}{\frac{1}{u}+ \frac{1}{v} }\\[/tex]

Step-by-step explanation:

[tex]1/u=1/f-1/v\\\frac{1}{f} = \frac{1}{u} +\frac{1}{v}\\Divide- both- sides- by; 1\\\frac{1}{f} \div \frac{1}{1} = ( \frac{1}{u} +\frac{1}{v}) \div \frac{1}{1}\\\\f = \frac{1}{\frac{1}{u}+ \frac{1}{v} }[/tex]

The 55th term of the 7, 10, 13, 16, ... arithmetic sequence is a(55) = 169.

This is an arithmetic sequence since there is a common difference between each term. In this case , adding 3 to the previous term in the sequence gives the next term.

a(n) = a(1) + d( n- 1)

d = 3

This is the formula of an arithmetic sequence.

an = a(1) + d( n- 1)

Substitute in the values of

a(1) = 7 and

d = 3

a(n) = 7 + 3 ( n- 1)

Simplify each term.

a(n) = 7 + 3n- 3

Subtract 3 from 7.

a(n) =  3n + 4

The nth term = 3n + 4. The formula for the nth term of an arithmetic progression is a(n) = dn + a(1) - d. Therefore in your sequence, the difference d = 3, and the first term a(1) = 7.

Substitute in the value of n to find the nth term.

a(55) = 3 (55) + 4

Multiply 3 by 55 .

a(55) = 165 + 4

Add 165 and 4.

a(55) = 169

Thus , The 55th term in the arithmetic progression of 7, 10, 13, 16,... is a(55) = 169.

To learn more about Aritmetic sequence

https://brainly.com/question/6561461

#SPJ1

Answer:

3.16% probability that the sample proportion of surgeons will differ from the population proportion by greater than 5%

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal probability distribution

When the distribution is normal, we use the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]

In this question:

[tex]p = 0.47, n = 460, \mu = 0.47, s = \sqrt{\frac{0.47*0.53}{460}} = 0.0233[/tex]

What is the probability that the sample proportion of surgeons will differ from the population proportion by greater than 5%

Sample proportion lower than 0.47 - 0.05 = 0.42 or higher than 0.47 + 0.05 = 0.52.

Since they are equidistant from the mean of 0.47 they are equal. So we find one of them, and multiply by two.

Lower than 0.42:

pvalue of Z when X = 0.42. So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

By the Central Limit Theorem

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{0.42 - 0.47}{0.0233}[/tex]

[tex]Z = -2.15[/tex]

[tex]Z = -2.15[/tex] has a pvalue of 0.0158

2*0.0158 = 0.0316

3.16% probability that the sample proportion of surgeons will differ from the population proportion by greater than 5%

Answer:

15

Step-by-step explanation:

You can go from Andy to Billy by 3 roads.

For each of those 3 roads, you can go from Billy to Willie by 5 roads.

3 * 5 = 15

Answer: 15

Answer:

B. 0.220

Step-by-step explanation:

The table is presented properly below:

[tex]\left|\begin{array}{c|cccc|c}$toppings&$Freshman&$Sophomore&$Junior&$Senior&$Total\\---&---&---&---&---&---\\$Cheese&11&15&24&28&78\\$Meat&23&28&15&11&77\\$Veggie&15&11&23&28&77\\---&---&---&---&---&---\\$Total&&&&&232\end{array}\right|[/tex]

Number of junior students who prefers veggies =23

Number of senior students who prefers veggies =28

Total =23+28=51

Therefore, the probability that a randomly selected student who is a junior or senior prefers veggie

=51/232

=0.220 (to the nearest thousandth)

The correct option is B.

Answer:

Q(x) = 4

R(x) = 0

Step-by-step explanation:

Q(x) = 2x + 2 ----- (1)

R(x) = x² - 1 -------- (2)

i) For (R * Q)(5)  and [(Q * R)], we have as follow:

[(x² - 1)(2x + 2)] (5)

= (2x³ + 2x² - 2x - 2)(5)

= x³ + x² - x - 1

When x = -1

x³ + x² - x - 1 = 0

∴ (x³ + x² - x - 1) ÷ (x + 1) = x² - 1

If x + 1 = 0

x = -1

and x² - 1 = 0

x = 1

From (1), when x= 1: Q(x) = 4

From (2), when x= 1 or -1: R(x) = 0

Answer:

  35 inches

Step-by-step explanation:

The right angle and the given measures in the ratio 3:4 tell you this is a 3:4:5 right triangle. k = 7·5 = 35 inches.

__

Using the Law of Cosines, ...

  k² = m² +j² -2mj·cos(K)

  k² = 21² +28² -2·21·28·cos(90°) = 441 +784 -0 = 1225

  k = √1225 = 35

The length of k is 35 inches.

Answer:

35 Inches

Step-by-step explanation:

Instead of using the Law of Cosines, you can use the Pythagorean Theorem; or A^2 + B^2 = C^2 because angle K is 90 degrees. The equation would look like:

21^2 + 28^2 = C^2

441 + 784 = C^2            Square Each Term

1,225 = C^2                   Simplify

35 = C                            Find Square Root

k = 35                             In This Situation, k is C

Answer:

2

Step-by-step explanation:

5÷2 1/5 = 2

Answer:

2 3/11

Step-by-step explanation:

To find the original number, we need to divide 5 by 2 1/5.

5/ 2 1/5

Convert 2 1/5 to an improper fraction:

11/5

5/ 11/5

When dividing fractions, we can multiply the first number by the reciprocal of the second one to get the answer.

5*5/11

25/11

2 3/11

Answer:

C. 44 °

Step-by-step explanation:

Angles on a straight line add up to 180 degrees.

180 - 88 = 92

Angles in a triangle add up to 180 degrees.

y + y + 92 = 180

y + y = 88

2y = 88

y = 88/2

y = 44

Answer:

The answer is 46"

Step-by-step explanation:

A triangle is 180 degrees

so u already know one side

180"-88" is 92

then divide 92 by 2 which is 46

Answer: 46"

Answer:

Area = 40×20

=800Step-by-step explanation:

Answer:

62 [tex]cm^{2}[/tex]

Step-by-step explanation:

A 1 centimetre cube implies that its length = width = height = 1 cm.

Thus, the area of a surface of the cube = length × length

                                                                 = 1 × 1

                                                                 = 1 [tex]cm^{2}[/tex]

Considering the views or parts of the given solid;

Surface area of its left side = Surface area of its right side = 1 × 10

                                             = 10 [tex]cm^{2}[/tex]

Surface area of the front elevation = Surface area of its back = 1 × 9

                                              = 9 [tex]cm^{2}[/tex]

Surface area of its plan = Surface area of its bottom = 1 × 12

                                               = 12 [tex]cm^{2}[/tex]

Total surface area of the solid = 10 + 10 + 9 + 9 + 12 + 12

                                                 = 62 [tex]cm^{2}[/tex]

The total surface area of the solid is 62 [tex]cm^{2}[/tex].

Answer:

The value will decrease.

Step-by-step explanation:

Answer:

  8 : 1

Step-by-step explanation:

The graph shows a point at the location corresponding to 8 cups of raspberry juice and 1 cup of lemon-lime soda. So the ratio is ...

  raspberry juice : lemon-lime soda = 8 : 1

Answer:

D

Step-by-step explanation:

raspberry : lemon lime soda::8:1

Answer:

198.5

Step-by-step explanation:

() = 200 - 1.5

() = 198.5

im not sure if this is what you are asking, but i hope it helps

Answer:

S=p(200-1.5)  

Answer:

A pair of vertical angles are ADE and BDC. Vertical angles are located across from each other.

Answer:

D. Angle ADE and angle BDC

Step-by-step explanation:

Vertically opposite angles are equal.

Angle ADE and angle BDC are a pair of vertical angles.

Answer: Volume = [tex]\frac{20\pi }{3}[/tex]

Step-by-step explanation: The washer method is a method to determine volume of a solid formed by revolving a region created by any 2 functions about an axis. The general formula for the method will be

V = [tex]\pi \int\limits^a_b {(R(x))^{2} - (r(x))^{2}} \, dx[/tex]

For this case, the region generated by the conditions proposed above is shown in the attachment.

Because it is revolting around the y-axis, the formula will be:

[tex]V=\pi \int\limits^a_b {(R(y))^{2} - (r(y))^{2}} \, dy[/tex]

Since it is given points, first find the function for points (3,2) and (1,0):

m = [tex]\frac{2-0}{3-1}[/tex] = 1

[tex]y-y_{0} = m(x-x_{0})[/tex]

y - 0 = 1(x-1)

y = x - 1

As it is rotating around y:

x = y + 1

This is R(y).

r(y) = 1, the lower limit of the region.

The volume will be calculated as:

[tex]V = \pi \int\limits^2_0 {[(y+1)^{2} - 1^{2}]} \, dy[/tex]

[tex]V = \pi \int\limits^2_0 {y^{2}+2y+1 - 1} \, dy[/tex]

[tex]V=\pi \int\limits^2_0 {y^{2}+2y} \, dy[/tex]

[tex]V=\pi(\frac{y^{3}}{3}+y^{2} )[/tex]

[tex]V=\pi (\frac{2^{3}}{3}+2^{2} - 0)[/tex]

[tex]V=\frac{20\pi }{3}[/tex]

The volume of the region bounded by the points is [tex]\frac{20\pi }{3}[/tex].

Answer:

Step-by-step explanation:

Given the initial value of X0 = -1, we can determine the solution of the equation x³ + 5x +2 = 0 using the Newton's method. According to newton's approximation formula;

[tex]y = f(x_0) + f'(x_0)(x-x_0)[/tex]

[tex]x_n = x_n_-_1 - \frac{f(x_n_-_1 )}{f'(x_n_-_1 )}[/tex]

If [tex]x_0 = 1\\[/tex]

We will iterate using the formula;

[tex]x_1 = x_0 - \frac{f(x_0 )}{f'(x_0 )}[/tex]

Given f(x) = x³ + 5x +2

f(x0) = f(-1) = (-1)³ + 5(-1) +2

f(-1) = -1 -5 +2

f(-1) = -4

f'(x) = 3x²+5

f'(-1) = 3(-1)²+5

f'(-1) = 8

[tex]x_1 = -1+4/8\\x_1 = -1+0.5\\x_1 = -0.5\\\\x_2 = x_1 - \frac{f(x_1)}{f'(x_1)}\\x_2 = -0.5 - \frac{f(-0.5)}{f'(-0.5)}[/tex]

f(-0.5) = (-0.5)³ + 5(-0.5) +2

f(-0.5) = -0.125-2.5+2

f(-0.5) = -0.625

f'(-0.5) = 3(-0.5)²+5

f'(-0.5) = 3(0.25)+5

f'(-0.5) = 0.75+5

f'(-0.5) = 5.75

[tex]x_2 = -0.5 - \frac{(-0.625)}{5.75}\\x_2 = -0.5 + \frac{(0.625)}{5.75}\\x_2 = -0.5 + 0.1086957\\x_2 = -0.3913[/tex]

The estimated solution is -0.3913 (to 4dp)

Answer:

173.20 ft

Step-by-step explanation:

[tex] \tan \: 30 \degree = \frac{length \: of \: tunnel}{depth \: of \: tunnel} \\ \\ \frac{1}{ \sqrt{3} } = \frac{length \: of \: tunnel}{300} \\ \\ length \: of \: tunnel \\ \\ = \frac{300}{ \sqrt{3} } \\ \\ = \frac{300 \sqrt{3} }{3} \\ \\ = 100 \sqrt{3} \\ \\ = 100 \times 1.7320 \\ \\ = 173.20 \: ft[/tex]

Answer:

Vertical Line

Step-by-step explanation:

A vertical line is x = [a number]

A horizontal line is y = [a number]

Answer:

vertical line

Step-by-step explanation:

A vertical line is of the form

x =

All the x values are the same and the y value changes

x = -4 is a vertical line

Answer:

$41,330

Step-by-step explanation:

To find the cost to asphalt a circular path, first, calculate the area of the circular path:

Area of circular path = area of big circle (A1) - Area of small circle (A2)

Area of circle = πr²

Radius of big circle (R) = 145 ft

Area of big circle (A1) = 3.14*145²

= 3.14*21,025

A1 = 66,018.5 ft²

Radius of small circle (r) = 80ft

Area of small circle (A2) = 3.14*80²

= 3.14*6,400

A2 = 20,096 ft²

=>Area of path =  66,018.5 - 20,096 = 45,922.5 ft²

If 100ft = $90

45,922.5 ft = x

Cross multiply and find x (cost to asphalt the circular path)

100*x = 45,922.5*90

100x = 4,133,025

Divide both sides by 100

x = 4,133,025/100

x = $41,330.25

To the nearest dollar, $41,330 is needed to asphalt the circular path

Answer:

Hey there! Your answer would be:  [tex]3x^2+4=x[/tex]

The quadratic formula is (-b±√(b²-4ac))/(2a), and helps us find roots to a quadratic equation.

All quadratic equations can be written in the [tex]ax^2+bx+c[/tex] form, and a, b, and c, are numbers we need for the quadratic equation.

Our given quadratic equation is 1±√(-1)²-4(3)(4)/2(3)

We can see that b is -1, as -b is positive 1.

That gives us  [tex]ax^2+-1x+c[/tex], which can be simplified to [tex]ax^2-x+c[/tex].

We can see that a is 3, because 2a=6, so a has to be 3.

That gives us [tex]3x^2-x+c[/tex]

Finally, we see that 4 is equal to b, clearly shown in the numerator of this fraction.

Which gives us a final answer of [tex]3x^2-x+4[/tex], or [tex]3x^2+4=x[/tex]