Consider the phrase "the sum of 3 times a number and the quotient of the number and 4." Let’s break it down. You want the sum of two values. The first value is 3 times a number. What expression represents 3 times a number?

9514 1404 393

Answer:

  (a) -- the correct choice is highlighted

Step-by-step explanation:

The units of specific heat tell you what quantities make up the ratio.

  [tex]\dfrac{390\text{ J}}{1\text{ kg$\cdot^\circ$C}}=\dfrac{-12.0\text{ J}}{0.012\text{ kg}\cdot\Delta T}\\\\\Delta T=\dfrac{-12.0}{0.012\cdot390}\ ^\circ\text{C}\approx-2.56\text{ $^\circ$C}[/tex]

The temperature will decrease by 2.56 C.

Answer:

[tex]{ \tt{ \frac{y}{x} = - \frac{6}{7} }} \\ { \tt{y = - \frac{6}{7}x }} \\ { \boxed{ \bf{constant = - \frac{6}{7} }}}[/tex]

Answer:

Move triangle ABC over 2 and up 1

Step-by-step explanation:

A transformation in geometry is to essentially move a shape. To move ABC onto A1B1C1 you would move triangle ABC over 2 and up 1.

Answer:

Following are the solution to the given points:

Step-by-step explanation:

Normal Distribution:

[tex]\mu=50\\\\\sigma= 6\\\\Z=\frac{X-\mu}{\sigma} \sim N(O,l)[/tex]

For point a:

[tex]P(X< 56)=\frac{(56-50)}{6}= \frac{6}{6}=1\\\\[/tex]

[tex]=P(Z<1)\ From\ \sigma \ Table=0.8413\\\\P(X>= 56)=(1-P(X< 56))=1-0.8413=0.1587\\\\[/tex]

For point b:

[tex]P(X< 49)=\frac{(49-50)}{6}=-\frac{1}{6} =-0.1667\\\\=P(Z<-0.1667)\ From\ \sigma \ Table\\\\=0.4338[/tex]

For point c:

To Find [tex]P(a\leq Z\leq b)= F(b) - F(a)\\\\[/tex]

[tex]P(X< 45)=\frac{(45-50)}{6}=\frac{-5}{6} =-0.8333\\\\P (Z<-0.8333) \ From \ \sigma \ Table\\\\=0.20233\\\\P(X< 55)=\frac{(55-50)}{6} =\frac{5}{6}=0.8333\\\\P ( Z< 0.8333) \ From \ \sigma\ Table\\\\=0.79767\\\\P(45 < X < 55) =0.79767-0.20233 =0.5953[/tex]

Answer:

the last one

Step-by-step explanation:

this is because it is an equalactral triangle meaning that the line at the side is the only one which its degrees is 90 so if u add 45 and 45 its 90(hope this helps)

Answer:

Two sides have the same length, which iS less than

the length of the third side.

Step-by-step explanation:

Hypotenuce is a sode opposite to right angle, which is always bigger then any side of right triangle. since both angles are the same, Adjacent and Opposite are similar size as well.

Answer: B. X It passes the vertical line test :)

Step-by-step explanation:

Answer:

FnH = {Meagan}

Step-by-step explanation:

Given the following sets and events:

S = {Albert, Betty, Abel, Jack, Patty, Meagan}

F = {Betty, Patty, Meagan},

H = {Abel, Meagan}

P = {Betty, Abel}.

In order to get FnH

The intersection of F and H is the element that is common to both sets. Hence for the set given, we can see that Meagan is common to both sets, therefore:

FnH = {Meagan}

Answer:

11, 18, 25, 32, .....

Option D

Step-by-step explanation:

The formula for the nth term of an AP is a+(n-1)d

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

a+nd-d=a+nd-2d+7

d=7

As the common difference is 7.

The only option given which is in an AP is the 4th option

Answer:

Option (C)

Step-by-step explanation:

Surface area of a right prism = 2(Area of the triangular base) + Ph

Here, P = Perimeter of the base

h = Height of the prism

Area of the triangular base = [tex]\frac{1}{2}(\text{Height})(\text{Base})[/tex]

                                             = [tex]\frac{1}{2}(5)(12)[/tex]

                                             = 30 cm²

Height of the prism = 15 cm

Perimeter of the base = (5 + 12 + 13)

                                     = 30 cm

Surface area of the right prism = 2(30) + 30(15)

                                                   = 60 + 450

                                                   = 510 cm²

Therefore, Option (C) will be the correct option.

Answer:

47.1

Step-by-step explanation:

We know side LM corresponds with side OP with a factor of some number. The value of side LM is 8, and the value of side OP is 29. If we divide the two numbers, we will find the scale factor of which triangle NOP is larger than KLM. 29/8 simplifies to 3.625. Now, to find the value of side PN, we must find the side it corresponds to on triangle KLM. Because K corresponds with N, and M corresponds with P, we know the side that PN corresponds with on triangle KLM is side KM. Side KM has a value of 13, so side PN must be 3.625 times larger than 13.

13 times 3.625 = 47.125. The question says to round to the nearest tenth, so the answer would be 47.1

Answer:

B

Step-by-step explanation:

Answer:

x = 14.4

Step-by-step explanation:

x is sin(angle 24/30)×24

how do we get the angle at 24/30 ?

by using the extended Pythagoras for baselines opposite other than 90 degrees.

c² = a² + b² - 2ab×cos(angle opposite of c)

in our example the angle 24/30 is opposite of the side 18.

so,

18² = 24² + 30² - 2×24×30×cos(angle 24/30)

324 = 576 + 900 - 1440×cos(angle 24/30)

324 = 1476 - 1440×cos(angle 24/30)

1440×cos(angle 24/30) = 1152

cos(angle 24/30) = 1152/1440 = 576/720 = 288/360 = 144/180 = 72/90 = 36/45 = 12/15 = 4/5

angle 24/30 = 36.9 degrees

x = sin(36.9) × 24 = 14.4

First, we find the point estimate, given by the sample mean. Then, with this, and the standard deviation of the population given, we can find the margin of error, and then, we can find the confidence interval and the minimum sample size necessary.

Doing this, we get that:

a) The point estimate for the population mean cost of fast food bills at this restaurant is $18.21.

b) The 95% margin of error is $1.64.

c) The 95% confidence interval for the population mean cost of fast food bills at this restaurant is: $16.57 ≤ µ ≤ $19.85.

d) The sample size needed is 135.

Question a:

The point estimate for the population mean is the sample mean, which is of $18.21.

The point estimate for the population mean cost of fast food bills at this restaurant is $18.21.

Question b:

We have to find our  level, that is the subtraction of 1 by the confidence interval divided by 2. So:

[tex]\alpha = \frac{1 - 0.95}{2} = 0.025[/tex]

Now, we have to find z in the Z-table as such z has a p-value of .

That is z with a p-value of , so Z = 1.96.

Now, find the margin of error M as such

[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]

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

[tex]M = 1.96\frac{5.92}{\sqrt{50}} = 1.64[/tex]

The 95% margin of error is $1.64.

(c) State the 95% confidence interval for the population mean cost of fast food bills at this restaurant.

The lower end of the interval is the sample mean subtracted by M. So it is 18.21 - 1.64 = 16.57

The upper end of the interval is the sample mean added to M. So it is 18.21 + 1.64 = 19.85

The 95% confidence interval for the population mean cost of fast food bills at this restaurant is: $16.57 ≤ µ ≤ $19.85.

(d) What sample size is needed if the error must not exceed $1.00?

This is n for which M = 1. So

[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]

[tex]1 = 1.96\frac{5.92}{\sqrt{n}}[/tex]

[tex]\sqrt{n} = 1.96*5.92[/tex]

[tex](\sqrt{n})^2 = (1.96*5.92)^2[/tex]

[tex]n = 134.6[/tex]

Rounding up:

The sample size needed is 135.

For a question in which you find a confidence interval using the z-distribution, you can check https://brainly.com/question/24175328

To find the minimum sample size for a confidence interval, you can check https://brainly.com/question/22667000

Answer:

Answer:

Solution given:

f(x)=5x-3

let

y=f(x)

y=5x-3

interchanging role of x and y

x=5y-3

x+3=5y

y=[tex]\frac{x+3}{5}[/tex]

$o,

f-¹(x)=[tex]\frac{x+3}{5}[/tex]

we conclude that

f-¹(x)≠g(x)

Each pair of function are not inverses.

g(x)=x/5+3

let g(x)=y

y=x/5+3

interchanging role of x and y

x=y/5+3

x-3=y/5

doing crisscrossed multiplication

5(x-3)=y

y=5x-15

g-¹(x)=5x-15

So

g-¹(x)≠f-¹(x)

Each pair of function are not inverses.

Answer:

51°

Step-by-step explanation:

Reference angle (θ) = ?

Opposite side length = 31

Hypotenuse length = 40

Apply SOH, which is;

Sin θ = Opp/Hyp

Plug in the values

Sin θ = 31/40

θ = sin^{-1}(31/40)

θ = 51° (neatest whole degree)

9514 1404 393

Answer:

Step-by-step explanation:

Let x and y represent the cost of a hot dog and a hamburger, respectively. The the two purchases can be described by ...

  3x +2y -9.75 = 0

  2x +3y -10.25 = 0

We can list the coefficients of these general-form equations in 2 rows, listing the first one again at the end:

  3, 2, -9.75, 3

  2, 3, -10.25, 2

Now, we can form differences of cross-products in adjacent pairs of columns:

  d1 = (3)(3) -(2)(2) = 9 -4 = 5

  d2 = (2)(-10.25) -(3)(-9.75) = -20.50 +29.25 = 8.75

  d3 = (-9.75)(2) -(-10.25)(3) = -19.50 +30.75 = 11.25

Then the solutions are found from ...

  1/d1 = x/d2 = y/d3

  x = d2/d1 = 8.75/5 = 1.75

  y = d3/d1 = 11.25/5 = 2.25

The cost of one hot dog is $1.75; the cost of one hamburger is $2.25.

_____

Additional comment

This is my simplification of the "cross-multiplication method" of solving a pair of linear equations. That method can be found described on web sites and in videos. This version, and the versions described elsewhere, are variations on Cramer's Rule and on the Vedic Maths method of solving equations. Each of those do similar differences of cross products, perhaps in less-easily-remembered fashion.

For a given pair of columns with coefficients ...

  a b

  c d

The cross-product we form is ad -cb.

Answer:

277 cm

Step-by-step explanation:

[tex]A=l*w\\3,878=l*14\\l=\frac{3,878}{14} \\l=277[/tex]

Step-by-step explanation:

One easy way to find a number that has all of these numbers as factors is to multiply them all together, so 2 * 5 * 7 = 10 * 7 = 70, which is one number.

To find the other number, we can multiply the number we already have by any integer greater than 1, e.g. 2, to get 70* 2= 140 as our other number, making our numbers 70 and 140

Answer:

Seth would need 10 hours to paint the room.

Step-by-step explanation:

Let's define:

S = rate at which Seth works

T = rate at which Ted works

When they work together, the rate is S + T

And we know that when they work together they can pint one room in 5 hours, then we can write:

(S + T)*5 h = 1 room.

We also know that Ted alone would need one hour more than Seth alone.

Then if Seth can paint the room in a time t, we have:

S*t = 1room

and

T¨*(t + 1h) = 1room

Then we have 3 equations:

(S + T)*5 h = 1

S*t = 1

T¨*(t + 1h) = 1

(I removed the "room" part so it is easier to read)

We want to find the value of S.

First, let's isolate one variable (not S) in one of the equations.

We can isolate t in the second one, to get:

t = 1/S

Now we can replace it on the third equation:

T¨*(t + 1h) = 1

T¨*( 1/S + 1h) = 1

Now we need to isolate T in this equation, we will get:

T = 1/( 1/S + 1h)

Now we can replace this in the first equation:

(S + T)*5h = 1

(S + 1/( 1/S + 1h) )*5h = 1

Now we can solve this for S

(S + 1/( 1/S + 1h) )= 1/5h

S + 1/(1/S + 1h) = 1/5h

Now we can multiply both sides by (1/S + 1h)

(1/S + 1h)*S + 1 = (1/5h)*(1/S + 1h)

1 + S*1h + 1 = 1/(S*5h) + 1/5

S*1h + 2 = (1/5h*S) + (1/5)

Now we can multiply both sides by S, to get:

(1h)*S^2 + 2*S = (1/5h) + (1/5)*S

Now we have a quadratic equation:

(1h)*S^2 + 2*S  - (1/5)*S -  (1/5h) = 0

(1h)*S^2 + (9/5)*S - (1/5h) = 0

The solutions are given by the Bhaskara's formula:

[tex]S = \frac{-(9/5) \pm \sqrt{(9/5)^2 - 4*(1h)*(-1/5h)} }{2*1h} = \frac{-9/5 \pm 2}{2h}[/tex]

Then the solution (we only take te positive one) is:

S = (-9/5 + 2)/2h

S = (-9/5 + 10/5)/2h = (1/5)/2h = 1/10h

Then Seth needs a time t to paint one room:

(1/10h)*t = 1

t = 1/(1/10h) = 10h

So Seth would need 10 hours to paint the room.

Answer:

16

Step-by-step explanation:

Answer:

C    

If x = o then f(0) = 4(2) * 0 = 0

If f(x) = 4(2) 0 - 13

then f(x) = -13 at x = 0

Answer:

it will indeed be c

Step-by-step explanation:

deesnuts

Answer:

A. It was decreasing by -138,629.44 barrels

B. 26 years of time

Step-by-step explanation:

Due to the length of this question solution, I was unable to type it. The answer is contained in the attachment.

A. At 1200000

Bt = 1200000

-1/6ln2 x 1200000

Solve this using a calculator

= -138,629.4361

So the amount of oil is decreasing by -138,629.44 barrels

it isn't possible to just give extra points in a simple and reliableway. anyways, let's starts.

a. is simple, just put the terms in order

r² +6r -5

because:

[tex] {r}^{2} + {6r}^{1} + {5r}^{0} [/tex]

anything to the power of 0 equals 1,

because it's the same as r/r, and 5 * r/r = 5*1

b. same logic as above

a²b² -5ab +33

c.

-c³ +ab +d +9

d.

-9y^5 - 2x³y²z +4x² +10x +1

^5 = to the power of five, it's the fastest way to type it without the special math input tool.

hope it helps you

Answer:

I agree with the above one.

Answer: B. f(x - 3) = 6x - 16

Concept:

When encountering a question that gives you a function and the evaluation value, then basically plug the given value into the function.

Solve:

Given function and value

f(x) = 6x + 2

f(x - 3)

Substitute the value into the given expression

f(x - 3) = 6 (x - 3) + 2

f(x - 3) = 6x - 18 + 2

f(x - 3) = 6x - 16

Hope this helps!! :)

Please let me know if you have any questions

Step-by-step explanation:

there are two answers for a

Answer:

The ANSWER IS 1/6

Step-by-step explanation:

Answer:

t=55+6w

Hope This Helps!!!

Answer:  [tex]-\infty < y < \infty[/tex] which is choice A

This is the set of all real numbers.

===========================================================

Explanation:

If you were to graph this function, then it spans infinitely upward and infinitely downward as well. That means that we can land on any y value we want, and that's why the range is the set of all real numbers.

Another approach we could take is to swap x and y to get [tex]x = \sqrt[3]{y+8}[/tex] which solves to [tex]y = x^3-8[/tex] . This is the inverse of the original function your teacher gave you. Recall that the domain and range swap roles when going from the original function to the inverse. What this means is that because the domain of

Domain of inverse = set of all reals

Range of original = set of all reals

Answer:

17d/20

Step-by-step explanation:

100-25=85

85/100×d

=17/20×d

=17d/20

Answer:

4 + 42s

Step-by-step explanation:

When y = 6 and x = 4,

measure horizontally

measure vertically

measure depth..