Which line is perpendicular to a line that has a slope of 1 half

Answer:

A 95% prediction interval for the drying time for the next trial of the paint is between 3.25 and 4.33 hours.

Step-by-step explanation:

First we have to find the sample mean and the sample standard deviation.

We have 15 measurements. Using a calculator, the mean is [tex]\overline{x} = 3.79[/tex] and the standard deviation is of [tex]s = 0.97[/tex].

Now, we have the standard deviation for the sample, which means that the t-distribution is used to solve this question.

T interval

The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So

df = 15 - 1 = 14

95% confidence interval

Now, we have to find a value of T, which is found looking at the t table, with 14 degrees of freedom(y-axis) and a confidence level of [tex]1 - \frac{1 - 0.95}{2} = 0.975[/tex]. So we have T = 2.1448

The margin of error is:

[tex]M = T\frac{s}{\sqrt{n}} = 2.1448\frac{0.97}{\sqrt{15}} = 0.54[/tex]

In which s is the standard deviation of the sample and n is the size of the sample.

The lower end of the interval is the sample mean subtracted by M. So it is 3.79 - 0.54 = 3.25 hours

The upper end of the interval is the sample mean added to M. So it is 3.79 + 0.54 = 4.33 hours

A 95% prediction interval for the drying time for the next trial of the paint is between 3.25 and 4.33 hours.

Answer:

is that a question?????????????

Answer:

[tex]a) x = k \times \frac{1}{y^2} \ , \ where \ k \ is \ a \ constant\\\\b) x = 3, \ when\ y\ =\ 10\\\\c) y = 10, \ when \ x = 3[/tex]

Step-by-step explanation:

a)

[tex]x \ \alpha \ \frac{1}{y^2}\\\\x = k \times \frac{1}{y^2}\\\\[/tex]                [tex][ \ where \ k \ is \ a \ constant \ ][/tex]

Find k.

Given x = 12, y = 5,

[tex]12 = k \times \frac{1}{5^2}\\\\k = 12 \times 25 = 300[/tex]

b)

Find x.

Given y = 10

We have k = 300

[tex]x = k \times \frac{1}{y^2}\\x = 300 \times \frac{1}{10^2} \\\\x= \frac{300}{100} = 3[/tex]

c)

Find y

Given x = 3

We have k = 300

[tex]x = k \times \frac{1}{y^2}\\\\3 = 300 \times \frac{1}{y^2}\\\\\frac{1}{y^2} = \frac{3}{300}\\\\\frac{1}{y^2} = \frac{1}{100}\\\\y^2 = 100\\\\y = \sqrt{100} = 10[/tex]

Answer:

0.0479 = 4.79% probability that fewer than 11 of them will vote

Step-by-step explanation:

For each voter, there are only two possible outcomes. Either they will vote, or they will not. The probability of a voter voting is independent of any other voter, which means that the binomial probability distribution is used to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

And p is the probability of X happening.

70% of all eligible voters will vote in the next presidential election.

This means that [tex]p = 0.7[/tex]

20 eligible voters were randomly selected from the population of all eligible voters.

This means that [tex]n = 20[/tex]

What is the probability that fewer than 11 of them will vote?

This is:

[tex]P(X < 11) = P(X = 10) + P(X = 9) + P(X = 8) + P(X = 7) + P(X = 6) + P(X = 5) + P(X = 4) + P(X = 3) + P(X = 2) + P(X = 1) + P(X = 0)[/tex]

In which

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 10) = C_{20,10}.(0.7)^{10}.(0.3)^{10} = 0.0308[/tex]

[tex]P(X = 9) = C_{20,9}.(0.7)^{9}.(0.3)^{11} = 0.0120[/tex]

[tex]P(X = 8) = C_{20,8}.(0.7)^{8}.(0.3)^{12} = 0.0039[/tex]

[tex]P(X = 7) = C_{20,7}.(0.7)^{7}.(0.3)^{13} = 0.0010[/tex]

[tex]P(X = 6) = C_{20,10}.(0.7)^{6}.(0.3)^{12} = 0.0002[/tex]

[tex]P(X = 5) = C_{20,5}.(0.7)^{5}.(0.3)^{15} \approx 0[/tex]

The probability of 5 or less voting is very close to 0, so they will not affect the outcome. Then

[tex]P(X < 11) = P(X = 10) + P(X = 9) + P(X = 8) + P(X = 7) + P(X = 6) + P(X = 5) + P(X = 4) + P(X = 3) + P(X = 2) + P(X = 1) + P(X = 0) = 0.0308 + 0.0120 + 0.0039 + 0.0010 + 0.0002 = 0.0479[/tex]

0.0479 = 4.79% probability that fewer than 11 of them will vote

Answer:

Average rate of change = 5

Step-by-step explanation:

Average rate of change of a function is defined by the expression over the interval a ≤ x ≤ b,

Average rate of change = [tex]\frac{f(b)-f(a)}{b-a}[/tex]

Using this rule for the average rate of change of the function (defined by the table) over the interval 4 ≤ x ≤ 5,

Average rate of change = [tex]\frac{f(5)-f(4)}{5-4}[/tex]

From the table,

f(5) = 10

f(4) = 5

Therefore, average rate of change of the function = [tex]\frac{10-5}{5-4}[/tex]

                                                                                    = 5

Answer:

=5

Step-by-step explanation:

9514 1404 393

Answer:

  C.  x -2y = 8

Step-by-step explanation:

One way you can do this is to use the form ...

  (Δy)(x -x1) -(Δx)(y -y1) = 0

where Δx = x2 -x1 = 4 -2 = 2, and Δy = y2 -y1 = -2 -(-3) = 1

This gives ...

  (x -2) -2(y -(-3)) = 0 . . . above form with numbers filled in

  x -2y -8 = 0 . . . . . . . general form

  x -2y = 8 . . . . . . . . .  standard form

_____

Additional comment

You can use any of several other strategies, including finding the slope and y-intercept, then rearranging the equation.

Another strategy that works is to try the answer choices. You might notice that the first given point works in the first equation, so it may make sense to try the second given point in each equation.

The above version of the equation of a line is a variation on one that says the slope of a line is the same everywhere:

  [tex]\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{y-y_1}{x-x_1}\ \Rightarrow\ (y_2-y_1)(x-x_1)=(x_2-x_1)(y-y_1)\\\\(y_2-y_1)(x-x_1)-(x_2-x_1)(y-y_1)=0[/tex]

Answer to your question is B. f(x)= 1/(x+4)^2

The equation of the rational function is f(x) = 1/(x + 4)^2

From the figure, we have the following property:

Vertical asymptote at;

x = -4

Add 4 to both sides

x + 4 = 0

Square both sides

(x + 4)^2 = 0

The above means that the denominator of the equation of the graph is (x + 4)^2

So, we have:

f(x) = 1/(x + 4)^2

Hence, the equation of the rational function is f(x) = 1/(x + 4)^2

Read more about rational function at:

https://brainly.com/question/1851758

#SPJ6

Answer:

$678.83

Step-by-step explanation:

Given :

Principal, P = $600

Rate = 3.09% = 0.0309

Period, t = 4 years

Compounding times per period, n = 12 (monthly)

The compound interest formula :

A = P(1 + r/n)^nt

A = 600(1 + 0.0309/12)^(12*4)

A = 600(1 + 0.002575)^48

A = 600(1.002575)^48

A = 600 * 1.1313834

A = 678.83004

Worth in 4 years = $678.83

Answer:

A term is a single mathematical expression. It may be a single number (positive or negative), a single variable ( a letter ), several variables multiplied but never added or subtracted.

hope this helps

have a good day :)

Step-by-step explanation:

Answer:

600 cm³

Step-by-step explanation:

6000 mm/10 mm = 600 cm

Hope this help!!!

Have a nice day!!!

[tex]\huge\text{Hey there!}[/tex]

[tex]\large\textsf{y = 4x - 1}[/tex]

[tex]\large\text{If x= -3, then substitute it into the given equation}[/tex]

[tex]\large\textsf{y = 4(-3) - 1}[/tex]

[tex]\large\textsf{4(-3) = \boxed{\bf -12}}[/tex]

[tex]\large\textsf{y = -12 - 1}[/tex]

[tex]\large\textsf{-12 - 1 = y}[/tex]

[tex]\large\textsf{-12 - 1 = \boxed{\bf -13}}[/tex]

[tex]\boxed{\boxed{\large\textsf{Answer: \huge \bf y = -13}}}\huge\checkmark[/tex]

[tex]\large\text{Good luck on your assignment and enjoy your day!}[/tex]

~[tex]\frak{Amphitrite1040:)}[/tex]

[tex] \quad \quad \quad \quad\tt{y = 4x - 1}[/tex]

[tex] \quad \quad \quad \quad\tt{y = 4( - 3) - 1}[/tex]

[tex] \quad \quad \quad \quad\tt{y = (- 12)- 1}[/tex]

[tex] \quad \quad \quad \quad\tt{y = - 13}[/tex]

[tex] \quad \quad \quad \quad \boxed{\tt \color{green}{y = - 13}}[/tex]

______

#LetsStudy

Answer:

yes do have in an any job that occurred the an evrey one to know you.

Answer:

8 days

Step-by-step explanation:

no of men                                             no of days

4                                                                   6

3                                                                     let be x

there is indirect variation

4/3=6/x

since it is in indirect variation do the reciprocal of any one fraction among these two fractions

4/3=x/6

do cross multiplicatin

3*x=6*4

x=24/3

x=8

therefore it take 8 days to complete the same work by 3 men.

Answer:

5.73 hours

Step-by-step explanation:

70% decay means 30% remains

.3 = (1/2)^(t/3.3)

take the log of both sides

log.3 = t/3.3 * log1/2

Divide both sides by log 1/2

log.3 / log1/2 = t/3.3

use calculator

1.736965594166206 = t/3.3

multiply both sides by 3.3

5.73198646074848 = t

rounded

t = 5.73 hours

Answer:

0.2948 ≅ 0.295

Step-by-step explanation:

According to the Question,

So, the population proportion of students who have previously owned a motorcycle is 115/390 ⇔ 0.2948 ≅ 0.295

Answer: True

Step-by-step explanation:

The subjects of an experiment should be selected at random so that they

represent the population is true.

Once the sample size has been decided, a sample should be taken from the sample size which will represent the population. This gives everyone an equal chance of being selected as there's no bias.

Answer:

6

Step-by-step explanation:

1 qt = 4 cups

1 cup = 8 fl oz

1.125 qt * (4 cups)/(1 qt) * (8 fl oz)/(1 cup) = 36 fl oz

(36 fl oz)/(6 fl oz) = 6

Answer: 6 servings

Answer:

216 square feet

Step-by-step explanation:

The formula for the surface area of a rectangular prism is:

2 (lw + hl + hw)

w= width

h= height

l= length

Use the formula with the given dimensions:

2 (6 • 2 + 12 • 6 + 12 • 2)

= 2 (12 + 72 + 24)

= 2 (108)

= 216

Surface area is measured in square feet

(feet in this case)

Hope this helps

Answer:

zero

Step-by-step explanation:

The optimally fitted straight line via the locations and points on a graph is determined via linear regression. You may use regression equations to see if your data can indeed be fitted into a formula. If you want to create assumptions from your data, either future forecasts or indicators of previous behavior, using the Regression equation is highly beneficial.

The regression line is expressed as:

[tex]Y_i = a +bx_i[/tex]

where;

[tex]Y_i[/tex] = dependent variable

a = intercept

b = slope

[tex]x_i[/tex] = independent variable

So, when [tex]Y_i[/tex] is independent of the variation of [tex]x_i[/tex], it means that [tex]Y_i[/tex] does not linearly depend on [tex]x_i[/tex] . Thus, the slope of the regression will be zero.

Step-by-step explanation:

[(1/6 × 3/4) + (3/4) + 1] n = 51.75 -3

(⅛ + ¾ +1)n = 48.75

15/8 n = 48.75

1.875 n = 48.75

n = 48.75/1.875

n = 26

so, the cost of :

the brush = ⅛×26 = $ 3.25

the sketchbook = ¾×26 = $ 19.5

the pain set = $ 26

Answer

Step-by-step explanation:

9514 1404 393

Answer:

  c  1, 2, 4, 8

Step-by-step explanation:

It can work well to look at the first differences.

  a: 4 -2 = 2; 6 -4 = 2 ⇒ differences are 2, 2, 2

  b: differences are 0, 1, 1

  c: differences are 1, 2, 4

  d: differences are 2, 2, 2

__

Sequences 'a' and 'd' have common differences that are constant. These are arithmetic sequences. Sequence 'b' is of no named type.

Sequence 'c' has first differences that have a common ratio, the same as the sequence itself. This is an indication the sequence is geometric. The ratios of values are 2/1 = 2; 4/2 = 2; 8/4 = 2, so the terms have a common ratio.

Sequence c is a geometric progression.

Answer:

x=28

Step-by-step explanation:

Step 1, comparing triangles:

Let us look at [tex]\triangle ABC[/tex] and [tex]\triangle ADE[/tex].

Therefore, because of AAA (Angle Angle Angle), [tex]\triangle ABC[/tex] and [tex]\triangle ADE[/tex] are similar.

Step 2:

Because the two triangles are similar, their sides should be proportional. Notice that [tex]\overline{AB}[/tex] and [tex]\overline {AD}[/tex] should be proportional.

Therefore, [tex]\overline{AB}[/tex]: [tex]\overline {AD}[/tex] =

[tex]12:30+12=\\12:42=\\2:7[/tex]

(Note, [tex]\overline {AD}[/tex] =  [tex]\overline{AB}[/tex]+ [tex]\overline{BD}[/tex]=12+30)

Step 3:

We figured out that  [tex]\triangle ABC[/tex]  and  [tex]\triangle ADE[/tex] have proportional sides of 2:7. Therefore,  [tex]\overline{BC}[/tex] and [tex]\overline{DE}[/tex] should also have a ratio of 2:7.

[tex]8: \overline{DE}=2:7\\8:\overline{DE}=8:28\\\overline{DE}=\fbox{28}[/tex]

x=28

I hope this helps! Let me know if you have any questions :)

Answer:

x = 20

Step-by-step explanation:

If we look at the given diagram, we will see that ΔABC and ΔADE are similar. Because they a similar we know that corresponding sides are in proportion. In order to solve this question, we need to know what the coefficient of similarity is.

AB and AD are corresponding sides, in order to get from 12 to 30 we need to multiple 12 by 2.5. That means that the coefficient of similarity between the two triangles is 2.5. To get x (length of DE) we need to multiply the length of BC by the coefficient of similarity. And so we get...

x = 2.5(BC)

x = 2.5(8)

x = 20

Answer:

Step-by-step explanation:

37

Answer:

[tex] \orange{ \bold{\frac{dy}{dx} =\frac{ 5{x}^{2} + 3 }{3\sqrt[3]{(1 + {x}^{2})^{2} } }}}[/tex]

Step-by-step explanation:

[tex]y = x \sqrt[3]{1 + {x}^{2} } \\ assuming \: log \: both \: sides \\log y = log(x \sqrt[3]{1 + {x}^{2} } ) \\ \therefore log y = logx + log(\sqrt[3]{1 + {x}^{2} } ) \\ \therefore log y = logx + \frac{1}{3} log({1 + {x}^{2} } ) \\ differentiating \: both \: sides \: w.r.t.x \\ \frac{1}{y} \frac{dy}{dx} = \frac{1}{x} + \frac{1}{3} . \frac{1}{(1 + {x}^{2}) } (0 + 2x) \\ \frac{1}{y} \frac{dy}{dx} = \frac{1}{x} + \frac{2x}{3(1 + {x}^{2}) }\\ \frac{1}{y} \frac{dy}{dx} =\frac{3(1 + {x}^{2}) + 2 {x}^{2} }{3x(1 + {x}^{2}) }\\ \frac{1}{y} \frac{dy}{dx} =\frac{3 + 3{x}^{2} + 2 {x}^{2} }{3x(1 + {x}^{2}) }\\ \frac{1}{y} \frac{dy}{dx} =\frac{3 + 5{x}^{2} }{3x(1 + {x}^{2}) }\\ \frac{dy}{dx} =\frac{y(3 + 5{x}^{2} )}{3x(1 + {x}^{2}) } \\ \\ \frac{dy}{dx} =\frac{x \sqrt[3]{1 + {x}^{2} } (3 + 5{x}^{2} )}{3x(1 + {x}^{2}) }\\ \\ \frac{dy}{dx} =\frac{(3 + 5{x}^{2} )\sqrt[3]{1 + {x}^{2} } }{3(1 + {x}^{2}) }\\ \\ \purple{ \bold{\frac{dy}{dx} =\frac{ 5{x}^{2} + 3 }{3\sqrt[3]{(1 + {x}^{2})^{2} } }}}[/tex]

Answer:

A = 30 inches^2

Step-by-step explanation:

The area of a trapezoid is given by

A = 1/2 (b1+b2)h  where b1 and b2 are the lengths of the bases

A = 1/2 ( 10+5) * 4

A = 1/2 (15)*4

A = 30 inches^2

Answer:

Area of trapezoid is 30 inches ².

Step-by-step explanation:

A trapezoid having length of Base ¹ and Base ² are 10 in. and 5 in. and it's height is 4 in. Find the area of trapezoid.

Area of trapezoid is given by

= 1/2 × ( B¹ + B² ) × h

Where, B¹ = 10 in.

B ² = 5 in.

h = 4 in.

substitute the values

Area = 1 / 2 × ( 10 in × 5 in ) × 4 in

multiplying the values

Area = 1 / 2 × 15 in. × 4 in

Area = 1 / 2 × 60 in ².

Area = 30 in².

Hence, Area of trapezoid is 30 inches ².

Answer:

Step-by-step explanation:

Answer:

Step-by-step explanation:

★1. The farmers' crops are destroyed when there are heavy rains which

result to flooding.

★2. Loss of lives and damage to properties happen due to fiooding and

landslides

★3. Thousands of families become homeless.

•4. Fishermen can go fishing and abundant catch awaits them.

★5. The power supply is cut off for several days as falling trees destroy the

electric posts and power lines.

★6. People lose their homes and means of livelihood.

•7. The prices of basic commodities become cheaper.

•8. People visit malls for shopping.

•9. A few houses of first-class materials are partially damaged,

•10. Children play on the playground.