Question
The sum of three consecutive even integers is -312. Find the Integers.

Answer:

1) a)  accepting the new drug is better based on its effectiveness when in reality the drug ain't better than the drug in current use because of its side effects

b) Accepting and using the current drug in use when it is not as effective as the new drug

c) Type 1 error

2) a) rejecting the vitamin supplement based on not knowing the harmful side effects

b) Accepting the Vitamin supplement based on just health benefits it portrays without comparison with other supplement.

c) Type II error

3) Increase the significance level  ( A )

Step-by-step explanation:

1)

a) To make a type 1 error in this situation is accepting the new drug is better and prescribing it to the millions of people based only on its effectiveness when in reality the drug ain't better than the drug in current use because of its side effects

b) A type II error in context is :Accepting and using the current drug in use when it is not as effective as the new drug

c)  Type I error

2)

a) Type 1 error is rejecting the vitamin supplement based on not knowing the harmful side effects

b) Accepting the Vitamin supplement based on just health benefits it portrays without comparison with other supplement.

c) Type II error

3) If committing a type 1 error is much worse

Increase the significance level

Answer:

the value of x is 29°

hope it helps

have a nice day

Answer:

C, D, D.

Step-by-step explanation:

Problem 6)

We want to determine the equation of the graphed inequality.

First, let's determine the equation of the line for the inequality. We can see that it passes through the points (-2, 0) and (0, 2). Find the slope:

[tex]\displaystyle m=\frac{\Delta y}{\Delta x}=\frac{2-0}{0-(-2)}=\frac{2}{2}=1[/tex]

So, the slope of the line is one.

And since it passes through the point (0, 2), our y-intercept is two. Therefore, the equation of the line is:

[tex]y=x+2[/tex]

Next, notice that the shaded region is below the line. Also, the line itself is also shaded.

Since the shaded region is below the line, y is less than the graph of the line and since the line itself is shaded, our sign is less than or equal to.

Hence:

[tex]y \leq x + 2[/tex]

Our answer is C.

Problem 7)

We have the inequality:

[tex]-2x+8+5x>2x+1[/tex]

First, solve the inequality. Combine like terms:

[tex]3x+8>2x+1[/tex]

Subtract x from both sides:

[tex]x+8>1[/tex]

And subtract 8 from both sides:

[tex]x>-7[/tex]

Therefore, any value greater than -7 will satisfy the inequality.

Out of the choices, the only choice greater than -7 is -5.

So, our answer is D.

Problem 8)

We have the inequality:

[tex]5x+7\leq 8x-3+2x[/tex]

Again, solve the inequality. Combine like terms:

[tex]5x+7\leq 10x-3[/tex]

Subtract 5x from both sides:

[tex]7\leq 5x-3[/tex]

And add three to both sides:

[tex]10\leq 5x[/tex]

Divide both sides by five:

[tex]2\leq x[/tex]

Flip:

[tex]x\geq 2[/tex]

Therfore, any value greater than or equal to 2 will satisfy the inequality.

Out of the choices, the only choice greater than or equal to 2 is 2.

So, our answer is D.

9514 1404 393

Answer:

   (s, t) = (2, 4)

Step-by-step explanation:

We can eliminate the t variable by subtracting the first equation from half the second.

  (1/2)(8s +8t) -(3s +4t) = (1/2)(48) -(22)

  s = 2

  3(2) +4t = 22

  4t = 16

  t = 4

The solution is (s, t) = (2, 4).

Answer:

9.2

Step-by-step explanation:

You can do this calculation with a calculator by taking the square root of 85.

Hi there!  

»»————-　★　————-««

I believe your answer is:  

9.2

»»————-　★　————-««  

Here’s why:

Assuming that you mean "the square root of 85 rounded to the nearest tenth..."  

⸻⸻⸻⸻

[tex]\boxed{\text{Calculating the Answer...}}\\\\\rightarrow \sqrt{85} = 9.21954445729....[/tex]

⸻⸻⸻⸻

Since the digit to the right of the tenth (the 1) is less than or equal to four, we round down.

⸻⸻⸻⸻

[tex]9.21954445729...\approx\boxed{9.2}[/tex]

⸻⸻⸻⸻  

»»————-　★　————-««  

Hope this helps you. I apologize if it’s incorrect.

Answer:

? = 130

Step-by-step explanation:

I'm letting ? be x

Since the triangles are similar, larger outer and smaller inner, then the ratios of corresponding sides are equal.

If x is the length of side of larger then x - 70 is corresponding length of smaller.

Then

[tex]\frac{x}{x-70}[/tex] = [tex]\frac{78}{36}[/tex] ( cross- multiply )

78(x - 70) = 36x ← distribute left side

78x - 5460 = 36x ( subtract 36x from both sides )

42x - 5460 = 0 ( add 5460 to both sides )

42x = 5460 ( divide both sides by 42 )

x = 130

Answer:

The volume is decreasing at a rate of about 118.8 cubic feet per minute.

Step-by-step explanation:

Recall that the volume of a cylinder is given by:

[tex]\displaystyle V=\pi r^2h[/tex]

Take the derivative of the equation with respect to t. V, r, and h are all functions of t:

[tex]\displaystyle \frac{dV}{dt}=\pi\frac{d}{dt}\left[r^2h\right][/tex]

Use the product rule and implicitly differentiate. Hence:

[tex]\displaystyle \frac{dV}{dt}=\pi\left(2rh\frac{dr}{dt}+r^2\frac{dh}{dt}\right)[/tex]

We want to find the rate at which the volume of the cylinder is changing when the radius if 4 feet and the volume is 32 cubic feet given that the radius is growing at a rate of 2ft/min and the height is shrinking at a rate of 3ft/min.

In other words, we want to find dV/dt when r = 4, V = 32, dr/dt = 2, and dh/dt = -3.

Since V = 32 and r = 4, solve for the height:

[tex]\displaystyle \begin{aligned} V&=\pi r^2h \\32&=\pi(4)^2h\\32&=16\pi h \\h&=\frac{2}{\pi}\end{aligned}[/tex]

Substitute:

[tex]\displaystyle\begin{aligned} \frac{dV}{dt}&=\pi\left(2rh\frac{dr}{dt}+r^2\frac{dh}{dt}\right)\\ \\ &=\pi\left(2(4)\left(\frac{2}{\pi}\right)\left(2\right)+(4)^2\left(-3\right)\right)\\\\&=\pi\left(\frac{32}{\pi}-48\right)\\&=32-48\pi\approx -118.80\frac{\text{ ft}^3}{\text{min}}\end{aligned}[/tex]

Therefore, the volume is decreasing at a rate of about 118.8 cubic feet per minute.

9514 1404 393

Answer:

  LCD = 18

Step-by-step explanation:

6 and 9 have a common factor of 3, so the LCD is ...

  (6×9)/3 = 18

Then the fractions can be written as ...

  3/6 = 9/18

  2/9 = 4/18

Answer:

I think the choose (B)

5x/x + 3/x

Answer:

I thinkchoose no.3

5x+3

5x+3x

Answer:

(a) [tex]PQ \sim ST[/tex]

Step-by-step explanation:

Given

See attachment

Required

Which must be true

[tex]\triangle PQR \simeq \triangle STU[/tex] implies that:

The following sides are corresponding

[tex]PQ \sim ST[/tex]

[tex]PR \sim SU[/tex]

[tex]QR \sim TU[/tex]

The following angles are corresponding

[tex]\angle P \sim \angle S[/tex]

[tex]\angle Q \sim \angle T[/tex]

[tex]\angle R \sim \angle U[/tex]

From the given options, only option (a) is true because:

[tex]PQ \sim ST[/tex]

Answer:the answer is 9

Step-by-step explanation:

Answer:

[tex]\frac{x+6}{2x^2-9x+5}=-\sum_{n=0}^{\infty} [(-2)^{n}x^{n} + \frac{x^{n}}{5^{n+1}}][/tex]

when:

[tex]|x|<\frac{1}{2}[/tex]

Step-by-step explanation:

In order to solve this problem, we must begin by splitting the function into its partial fractions, so we must first factor the denominator.

[tex]\frac{x+6}{2x^2-9x+5}=\frac{x+6}{(2x+1)(x-5)}[/tex]

Next, we can build our partial fractions, like this:

[tex]\frac{x+6}{(2x+1)(x-5)}=\frac{A}{2x+1}+\frac{B}{x-5}[/tex]

we can then add the two fraction on the right to get:

[tex]\frac{x+6}{(2x+1)(x-5)}=\frac{A(x-5)+B(2x+1)}{(2x+1)(x-5)}[/tex]

Since we need this equation to be equivalent, we can get rid of the denominators and set the numerators equal to each other, so we get:

[tex]x+6=A(x-5)+B(2x+1)[/tex]

and expand:

[tex]x+6=Ax-5A+2Bx+B[/tex]

we can now group the terms so we get:

[tex]x+6=Ax+2Bx-5A+B[/tex]

[tex]x+6=(Ax+2Bx)+(-5A+B)[/tex]

and factor:

[tex]x+6=(A+2B)x+(-5A+B)[/tex]

so we can now build a system of equations:

A+2B=1

-5A+B=6

and solve simultaneously, this one can be solved by substitution, so we get>

A=1-2B

-5(1-2B)+B=6

-5+10B+B=6

11B=11

B=1

A=1-2(1)

A=-1

So we can use these values to build our partial fractions:

[tex]\frac{x+6}{(2x+1)(x-5)}=\frac{A}{2x+1}+\frac{B}{x-5}[/tex]

[tex]\frac{x+6}{(2x+1)(x-5)}=-\frac{1}{2x+1}+\frac{1}{x-5}[/tex]

and we can now use the partial fractions to build our series. Let's start with the first fraction:

[tex]-\frac{1}{2x+1}[/tex]

We can rewrite this fraction as:

[tex]-\frac{1}{1-(-2x)}[/tex]

We can now use the following rule to build our power fraction:

[tex]\sum_{n=0}^{\infty} ar^{n} = \frac{a}{1-r}[/tex]

when |r|<1

in this case a=1 and r=-2x so:

[tex]-\frac{1}{1-(-2x)}=-\sum_{n=0}^{\infty} (-2x)^n[/tex]

or

[tex]-\frac{1}{1-(-2x)}=-\sum_{n=0}^{\infty} (-2)^{n} x^{n}[/tex]

for: |-2x|<1

or: [tex] |x|<\frac{1}{2} [/tex]

Next, we can work with the second fraction:

[tex]\frac{1}{x-5}[/tex]

On which we can factor a -5 out so we get:

[tex]-\frac{1}{5(1-\frac{x}{5})}[/tex]

In this case: a=-1/5 and r=x/5

so our series will look like this:

[tex]-\frac{1}{5(1-\frac{x}{5})}=-\frac{1}{5}\sum_{n=0}^{\infty} (\frac{x}{5})^n[/tex]

Which can be simplified to:

[tex]-\frac{1}{5(1-\frac{x}{5})}=-\sum_{n=0}^{\infty} \frac{x^n}{5^(n+1)}[/tex]

when:

[tex]|\frac{x}{5}|<1[/tex]

or

|x|<5

So we can now put all the series together to get:

[tex]\frac{x+6}{2x^2-9x+5}=-\sum_{n=0}^{\infty} [(-2)^{n}x^{n} + \frac{x^{n}}{5^{n+1}}}[/tex]

when:

[tex]|x|<\frac{1}{2}[/tex]

We use the smallest interval of convergence for x since that's the one the whole series will be defined for.

Hi there!

[tex]\large\boxed{12/5}}[/tex]

tan (angle) = Opposite side / Adjacent side, so:

Tan (A) = opposite side / adjacent side

= 24 / 10

Simplify:

= 12 / 5

The equation of the hyperbola is,

(x/12)² - 4y²/(527) = 1

The standard equation of the hyperbola is

(x/a)² - (y/b)² = 1

Here (a, 0) and (-a, 0) are vertices and asymptotes y = ± √(b/a)x

Foci are (c, 0) & (-c, 0)

Then a² + b² = c²

Here we have to give that.,

2a = 24

a = 12

And 2c = 7

c = 7/2

Therefore a = 12 and c = 3.5

Substituting a and c in Pythagorean identity;

b² = 527/4

Then, the equation of the hyperbola is

(x/12)² - 4y²/(527) = 1

For further information regarding hyperbolas, kindly refer

brainly.com/question/28989785

#SPJ4

We have b = 0, which implies that the foci coincide with the vertices, making the hyperbola a degenerate case. In this scenario, the equation of the border would be a vertical line passing through the vertices/foci, given by the equation x = ±a.

To find the equation of the hyperbolic border created by the shadow on the wall, we can start by understanding the properties of a hyperbola. A hyperbola is defined as the set of all points such that the difference of the distances from any point on the hyperbola to two fixed points, called the foci, is constant.

Let's label the vertices of the hyperbola as A and B, and the foci as F1 and F2. The distance between the vertices is given as 2a inches, and the foci are located at a distance c inches from the vertices.

Using the given information, we can find the value of a and c. Since the center of the hyperbola is at the origin, the coordinates of the vertices are (±a, 0), and the coordinates of the foci are (±c, 0).

The distance between the foci is given by the equation:

c = √(a^2 + b^2)

We know that the distance between the foci is given as 2c inches, so:

2c = 2√(a^2 + b^2)

Since c is given as a distance from the vertices, we can substitute c = a - b to simplify the equation:

2(a - b) = 2√(a^2 + b^2)

Squaring both sides to eliminate the square root:

4(a - b)^2 = 4(a^2 + b^2)

Expanding the equation:

4(a^2 - 2ab + b^2) = 4a^2 + 4b^2

Simplifying the equation:

4a^2 - 8ab + 4b^2 = 4a^2 + 4b^2

Canceling out the common terms:

-8ab = 0

Dividing by -8:

ab = 0

This implies that either a = 0 or b = 0. However, since a represents the distance between the vertices and b represents the distance between the foci and vertices, we can rule out a = 0 as it would result in a degenerate hyperbola.

for such more question on hyperbola

https://brainly.com/question/16454195

#SPJ8

Answer:

[tex]\frac{ 5 \sqrt3 \ + \ 5 \sqrt2 \ - \ \sqrt6 \ - \ 2}{23}[/tex]

Step-by-step explanation:

[tex]\frac{\sqrt3 \ + \ \sqrt2 }{5 \ + \ \sqrt2 } \\\\=\frac{\sqrt3 \ + \ \sqrt2 }{5 \ + \ \sqrt2 } \times \frac{5 \ - \ \sqrt2 }{5 \ - \ \sqrt2 } \\\\=\frac{( \sqrt3 \ + \ \sqrt2)(5 \ - \ \sqrt2)}{(5 \ + \ \sqrt2)( 5 \ - \ \sqrt 2 )}\\\\=\frac{( \sqrt3 \ + \ \sqrt2)(5 \ - \ \sqrt2)}{(5 \ + \ \sqrt2)( 5 \ - \ \sqrt 2 )}\\\\=\frac{5 \sqrt3 \ + \ 5\sqrt 2 \ - \ \sqrt{ 3\times 2 } \ - \ \sqrt{2 \times 2}}{(5)^2 \ - \ (\sqrt2)^2}\\\\= \frac{ 5 \sqrt3 \ + \ 5 \sqrt2 \ - \ \sqrt6 \ - \ 2}{25 - 2}\\\\[/tex]

[tex]= \frac{ 5 \sqrt3 \ + \ 5 \sqrt2 \ - \ \sqrt6 \ - \ 2}{23}[/tex]

Answer:

1. subtracting 5

2. adding 20

3. dividing by 1/2

4. multiplying by 10

Answer:

third one

Step-by-step explanation:

Answer:

3(m-4)=33

3m-12=33

3m=45

m=15

Check:

3(15-4)=33

3(11)=33

33=33

Hope This Helps!!!

Answer:

m = 15

Step-by-step explanation:

3 ( m - 4 ) = 33

Solve for m

3 ( m - 4 ) = 33

Divide both side by 3

[tex]\small \sf \frac{3(m-4)}{3} = \frac{33}{3} \\ [/tex]

m - 4 = 11

Add 4 to both side

m - 4 + 4 = 11 + 4

m = 15

Answer:

The lowest cost of the tiles for George, for coring the considered triangular floor with the tiles of rate £39.95 per meter sq. is £226.3 approximately.

Remember that volume, area, length etc all are measured relatively.

If you are 1.7 meters tall, then you're height is measured relative to meters. This is called unit of the measurement. It means that if we collect 1 meter and 0.7 meters too,they together will be equally tall as you.

Similarly, if we say that a triangle has area of 40 square inches, then it means that its area is equal to 40 squares of 1 inch sides.

In the same way, volume is measured usually relative to unit cubes. Like how many unit cubes (cubes with 1 unit length of their sides) can be fitted (without any overlap or gap, but can be sliced to make them fit inside) inside the considered shape.

For this case, the tiles we will use will have the same area as the area of the triangular floor.

The triangular floor is of height and base of size 305 cm and 371.5 cm

Since the price rate of tiles is in meter sq, so it would be better if we convert the legths specified in meters.

100 cm = 1 m

1 cm = 1/100 m

305 cm = 305/100 = 3.05 m

371.5 cm = 3.715 m

The area of a triangle is half of the product of its base and height.

Thus, we get:

Area of tiles that will be used = area of the considered triangular floor =

[tex]\dfrac{3.05 \times 3.715}{2} \approx 5.665 \: \rm m^2[/tex]

Since 1 sq. m cost £39.95, therefore, 5.665 sq. meters will cost [tex]5.665 \times 39.95 \approx 226.3 \: \rm euros[/tex]

Thus, the lowest cost of the tiles for George, for coring the considered triangular floor with the tiles of rate £39.95 per meter sq. is £226.3 approximately.

Learn more about interpretation of measurement here: https://brainly.com/question/3424879

Answer: 103 degrees

Step-by-step explanation:

51 + 26 = 77

A triangle adds up to 180 degrees

180 - 77 = 103

= 103 degrees

Answer:

12

Step-by-step explanation:

Answer:

50% chance

Step-by-step explanation:

lol math go brrr

Answer:

100 psia

Step-by-step explanation:

Applying,

Pressure law,

P/T = P'/T'................. Equation 1

Where P = initial pressure, P' = Final pressure, T = initial temperature, P' = Final temperature.

make P' the subject of the equation

P' = PT'/T............ Equation 2

From the question,

Given: P = 50 psia, T = 300°R = (300×5/9)K = 166.66 K, T' = 600°R = (600×5/9)K = 333.33 K

Substitute these values into equation 2

P' = (50×333.33)/166.66

P' ≈ 100 psia

P ≈ 100 psia

Answer:

1716 ways

Step-by-step explanation:

Given that :

Number of entrants = 13

The number of ways of attaining first, second and third position :

The number of ways of attaining first ; only 1 person can be first ;

Using permutation :

nPr = n! ÷(n-r)!

13P1 = 13! ÷ 12! = 13

Second position :

We have 12 entrants left :

nPr = n! ÷(n-r)!

12P1 = 12! ÷ 11! = 12

Third position :

We have 11 entrants left :

nPr = n! ÷(n-r)!

11P1 = 11! ÷ 10! = 11

Hence, Number of ways = (13 * 12 * 11) = 1716 ways

Answer:

Answer is 6.

Step-by-step explanation:

The product is

[tex]15\times \frac{2}{5}[/tex]

Now, it does not means that the product of two quantities is always more than the individual quantities.

here, 2/5 is a part of whole.

So,

The product is

[tex]15\times \frac{2}{5}\\\\=3\times 2\\\\= 6[/tex]

The answer is 6 which is less than 15.

Here, it is the 2/5 part of whole 15.

Hi there!

[tex]\large\boxed{(-\infty, 9)}[/tex]

We can find the range using completing the square:

y = -x² - 2x + 8

Factor out a -1:

y = -(x² + 2x) + 8

Use the first two terms. Take the second term's coefficient, divide by 2, and square:

y = -(x² + 2x + 1) + 8  

Remember to add by 1 because we cannot randomly add an additional number into the equation:

y = -(x² + 2x + 1) + 8 + 1

Simplify:

y = -(x + 1)² + 9

Since the graph opens downward (negative coefficient), the range is (-∞, 9)

Answer:

The ocean surface is at 0 ft elevation. A diver is underwater at a depth of 138 ft. In this area, the ocean floor has a depth of 247 ft.

Step-by-step explanation:

Answer:

1. log3 81 = 4

2. 4 3/2=8

Step-by-step explanation:

1. Convert the exponential equation to a logarithmic equation using the logarithm base (3)(3) of the right side (81)(81) equals the exponent (4)(4).

log3(81)=4

or

you can remember this

loga Y= X

so, a^x =y

2. Use the definition of a logarithm,

log

b

(

x

)

=

y

⟹

b

y

=

x

, to convert from the logarithmic form to the exponential form.

Answer: D. 38x + 1,450 > 4,000

Step-by-step explanation:

It has to be greater than 4,000 so A makes no sense

The parentheses are in the wrong place completely changing the meaning for B

C disregards the info we have about how she's already typed 1,450 words

The answer has to be D

Answer:

≤ y ≤ 70 and 0 ≤ x ≤ 500

Step-by-step explanation:

In this relation we have two things to analyze, the number of gallons of water in the heater, that is 500 gallons, and the time that it took to empty the heater.

Let's count the time.

First, there are 20 minutes in wich 100 gallons are drained.

then, another drain valve is opened, so in 20 minutes they drain 200 gallons of water.

now, the wait for 10 minutes.

Now there are 200 gallons remaining, so the workers must wait for the other 20 minutes to drain the 200 gallons remaining.

The total amount of time is 70 minutes.

So if we have a relationship of water in the heater vs time, where X is the water remaining and Y is the time, the correct domains are:

Y from 0 minutes to 70 minutes

X from 0 gallons to 500 gallons  

So the correct options are C and E.

0 ≤ y ≤ 70 and 0 ≤ x ≤ 500