Add 20 7/12 + 4 2/10

Answer:

0 ≤ t ≤ 5.

Step-by-step explanation:

In the function [tex]f(t)[/tex], [tex]t[/tex] is the independent variable. The domain of [tex]f[/tex] is the set of all values of [tex]t[/tex] that this function can accept.

In this case, [tex]f(t)[/tex] is defined in a real-life context. Hence, consider the real-life constraints on the two variables. Both time and volume should be non-negative. In other words,

The first condition is an inequality about [tex]t[/tex], which is indeed the independent variable.

However, the second condition is about [tex]f[/tex], the dependent variable of this function. It has to be rewritten as a condition about [tex]t[/tex].

[tex]\begin{aligned} f(t) &\ge 0 &&\text{Assumption} \cr 80000 - 16000\, t& \ge 0 && \text{Definition of} ~ f \cr 80000 & \ge 16000\, t && \begin{aligned}&\text{Add $16000\, t$} \\[-0.5em] & \text{to both sides of the inequality}\end{aligned} \cr 5 &\ge t &&\begin{aligned}&\text{Divide both sides of} \\[-0.5em] & \text{the inequality by $16000$}\end{aligned} \cr t &\le 5 && \text{Flip the inequality}\end{aligned}[/tex].

Hence, t ≤ 5.

Combine the two inequalities to obtain the domain:

0 ≤ t ≤ 5.

You can use the fact that 1 quart is equal to 32 ounces.

Next, you can use the division fact, 32 divided by 4 equals 8.

And so, Celia can make 8 smoothies.

Answer:

angle bisector

Step-by-step explanation:

Definitions:

median: line that meets the middle of VX

angle bisector: line that cuts angle Y in half

altitude: line that meets VX at 90°

perpendicular bisector: line that meets VX at 90° and the middle of VX

YW does not meet VX at 90° and does not meet it in the middle. Without measurements or symbols, angle Y seems to be cut in half.

Answer:

The percentage change in volume between cylinder A and cylinder B is 50%

Step-by-step explanation:

The volume of a cylinder is given by the formula

V= πr^2h

For cylinder A, where r=7 and h= 5, π=22/7

V= π * 7^2 * 5

V= π * 49 * 5

V= 769.69 cubic inch

For cylinder B

V= 490π

V= 1539.3804 cubic inch

The percentage change in volume between cylinder A and cylinder B

=[ (VA- VB)/VB] *100

=( 1539.3804 - 769.69) / 1539.3804

= 0.5000 * 100

= 50%

The percentage change in the volume between cylinder A and cylinder B is 50%

A cylinder is a three-dimensional object. It is a prism with a circular base.

volume of a cylinder = πr²h

π=  22/7

r = radius

h = height

Volume of cylinder A = π(7² x 5) = 245π

Percentage change in volume = (245 / 490) - 1 = 50%

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Answer:

You use the Pythagorean theorem.

Step-by-step explanation:

https://math.stackexchange.com/questions/33549/calculating-the-distance-from-top-left-corner-to-bottom-right-corner-on-a-rectan

Answer:

[tex]cos(60^o)=\frac{a}{12}[/tex]

Step-by-step explanation:

The complete question in the attached figure

we know that

In the right triangle of the figure

The cosine of the angle of 60 degrees is equal to divide the adjacent side to the angle of 60 degrees (BC) by the hypotenuse (AB)

so

[tex]cos(60^o)=\frac{BC}{AB}[/tex]

we have

[tex]BC=a\ units\\AB=12\ units[/tex]

substitute the values

[tex]cos(60^o)=\frac{a}{12}[/tex]

The correct equation that represents the side length is Cos 60 = a/12

From the triangle given, we have the following

Using the soh cah toa identity

Cos theta = adj/hyp

Cos 60 = a/12

Hence the correct equation that represents the side length is Cos 60 = a/12

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We are given, [tex]P_1(x_1,y_1)[/tex] and [tex]P_2(x_2,y_2)[/tex] where [tex]P_1(2,2),P_2(0,1)[/tex].

Using slope formula we obtain

[tex]m=\dfrac{\Delta{y}}{\Delta{x}}=\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{1-2}{0-2}=\dfrac{-1}{-2}=\boxed{\dfrac{1}{2}}[/tex]

Hope this helps.

Answer:

1/2

Step-by-step explanation:

I took the test :)

Answer:

x =15°

Step-by-step explanation:

Given that the horizontal line is 90° to the vertical line, then both the angles have to necessarily add up to 90° i.e

(5x-10)° + 25° = 90°

5x - 10 + 25 = 90

5x + 15 = 90  (subtract 15 from both sides)

5x = 90 - 15

5x = 75   (divide both sides by 5)

x = 75 / 5 = 15°

Answer:

2000 points

Step-by-step explanation:

Given:

Number of questions in a study guide (Q) = 100

Number of points for 1 question (n) = 20

Now, total number of points is calculated using unitary method by multiplying number of questions and number of points in one question.

Therefore, the total number of points is given as:

Total points = [tex]n\times Q[/tex]

Total points = [tex]20\times 100[/tex]

Total points = [tex]2000[/tex]

Hence, the study guide is worth 2000 points.

Answer:

10

Step-by-step explanation:

Answer:

AB ║ CD. (Proved)

Step-by-step explanation:

See the attached diagram of the triangle.

It is given that Δ ACD is an isosceles triangle.

Therefore, AC = AD and ∠ ACD = ∠ ADC, ⇒ ∠ 3 = ∠ 4 .......... (1)

Again, given that ∠ 1 = ∠ 3 ........... (2)

Now, from equations (1) and (2) we can write, ∠ 1 = ∠ 4

Now, AB and CD are two straight lines and AD is the transverse line and hence, ∠ 1 and ∠ 4 are alternate angles that are equal.

Therefore, AB and CD are parallel straight lines and AB ║ CD. (Proved)

Answer:

No.

Step-by-step explanation:

x+(-2)=-3+(-2)=-3-2=-5, not 5.

Answer:

y=2x-14

Step-by-step explanation:

y=2x+8

y-y1=m(x-x1)

y-(-6)=2(x-4)

y+6=2x-8

y=2x-8-6

y=2x-14

The right answer is Option E.

Step-by-step explanation:

Given,

Total number of students in school = 350

Students who walk to school = [tex]\frac{1}{5}\ of\ total\ students[/tex]

Number of students who walk to school = [tex]\frac{1}{5}*350[/tex]

Number of students who walk to school = 70

70 students walk to the school.

The right answer is Option E.

Keywords: fraction, division

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Final answer:

The calculation shows that 70 students at Riverview Elementary walk to school.

Explanation:

The question is asking us to calculate what fraction of the total number of students at Riverview Elementary walk to school each day.

Since one fifth of the students walk to school, we need to divide the total number of students by 5 to find the number of students who walk to school.

To find one fifth of 350 students, we calculate:

350 ÷ 5 = 70

Therefore, 70 students walk to school each day at Riverview Elementary.

Answer:

48

Step-by-step explanation:

Step #1, Use PEMDAS,(Purple,Eyed,Monster,Drinks,A,Soda

Step #2, Add (3+5)

(8)

Step #3, Multiply 8×6

Step #4, No You

Answer:

48

Step-by-step explanation:

Answer:

a=1 b=5 c=9

Step-by-step explanation:

Answer: answer is A

Step-by-step explanation:

Answer:

Part A) Fisherman's Service will provide a better deal for a three days trip as it will cost $480 compare to the Wild Fishing Inc.'s deal that costs around 550$

Part B) Wild Fishing's Inc. would charge $700 for 6 days for both of them.

Part C) Let w be expression for Wild Fishing Inc. to represent the cost of the trip for both Mr. Martin and his son for n number of days trip.

w = 2(200) + 2n(25) = 400 + 50n

Let f be expression for Fisherman's Service to represent the cost of the trip for both Mr. Martin and his son for n number of days trip.

f = 2(150) + 2n(30) = 300 + 60n

Step-by-step explanation:

Part (A) Which company offers a better deal for a three day trip for Mr. Martin and his son? What will be the cost?

        Round Trip Flight $200 / Daily Rate $25

        Round Trip Flight $150 / Daily Rate $30

Analyzing Wild Fishing Inc. Offer for a three day trip

Expenses cost for Mr. Martin and his son if they chose Wild Fishing Inc

The formula to calculate Mr Martin expenses for 3 day trip:

Round trip Cost +  3 (Daily rate) ⇒ 200 + 3 (25) = $275.......[A]

The formula to calculate Mr Martin's son expenses for 3 day trip:

Round trip Cost +  3 (Daily rate) ⇒ 200 + 3 (25) = $275.......[B]

Adding Equation [A] and [B] will bring the net expense faced by Mr. Martin and his son if they chose to get Wild Fishing Inc. deal:

Net expense faced by Mr. Martin and his son: 275 + 275 = 550$

So, Wild Fishing Inc. will cost 550$ to both Mr. Martin and his son.

Analyzing Fisherman's Service Offer for a three day trip

As Mr. Martin and his son are planning a fishing trip to Alaska.

Expenses cost for Mr. Martin and his son if they chose Fisherman's Service

The formula to calculate Mr Martin expenses for 3 day trip:

Round trip Cost +  3 (Daily rate) ⇒ 150 + 3 (30) = $240.......[A]

The formula to calculate Mr Martin's son expenses for 3 day trip:

Round trip Cost +  3 (Daily rate) ⇒ 150 + 3 (30) = $240.......[B]

Adding Equation [A] and [B] will bring the net expense faced by Mr. Martin and his son if they chose to get Fisherman's Service deal:

Net expense faced by Mr. Martin and his son: 240 + 240 = 480$

So, Fisherman's Service will cost 480$ to both Mr. Martin and his son.

Choosing the right company that offers a better 3 days deal:

As we have determined that

Therefore, Fisherman's Service will provide a better deal for a three days trip as it will cost $480 compare to the Wild Fishing Inc.'s deal that costs around 550$.

Part (B) Which company would charge $700 for 6 days for both of them?

Checking Wild Fishing Inc. expenses for 6 days trip:

The formula to calculate Mr Martin expenses for 6 day trip:

Round trip Cost +  6 (Daily rate) ⇒ 200 + 6 (25) = $350.......[A]

The formula to calculate Mr Martin's son expenses for 3 day trip:

Round trip Cost +  6 (Daily rate) ⇒ 200 + 6 (25) = $350.......[B]

Adding Equation [A] and [B] will bring the net expense faced by Mr. Martin and his son if they chose to get Wild Fishing Inc. deal for 6 days:

Net expense faced by Mr. Martin and his son: $350 + $350 = 700$

Checking Fisherman's expenses for 6 days trip:

The formula to calculate Mr Martin expenses for 6 day trip:

Round trip Cost +  6 (Daily rate) ⇒ 150 + 6 (30) = $330.......[A]

The formula to calculate Mr Martin's son expenses for 3 day trip:

Round trip Cost +  6 (Daily rate) ⇒ 150 + 6 (30) = $330.......[B]

Adding Equation [A] and [B] will bring the net expense faced by Mr. Martin and his son if they chose to get Fisherman's Service deal for 6 days:

Net expense faced by Mr. Martin and his son: $330 + $330 = 680$

So, Wild Fishing's Inc. would charge $700 for 6 days for both of them.

Part (C) Write an expression to represent the cost of the trip for Mr. Martin and his son for each company.

Expression for Wild Inc.

Let w be expression for Wild Fishing Inc. to represent the cost of the trip for both Mr. Martin and his son for n number of days trip.

w = 2 (Round trip Cost) +  2n (Daily rate)

As Round trip costs $200 and $25 is the daily rate for Wild Fishing Inc.

So, w can be written as:

w = 2(200) + 2n(25) = 400 + 50n

Expression for Wild Inc.

Let f be expression for Fisherman's Service to represent the cost of the trip for both Mr. Martin and his son for n number of days trip.

f = 2 (Round trip Cost) +  2n (Daily rate)

As Round trip costs $150 and $30 is the daily rate for Fisherma''s Service.

So, w can be written as:

f = 2(150) + 2n(30) = 300 + 60n

Keywords: cost, expenses, deal

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Answer:

b is the correct answer

The placebo effect describes how a person might show improvement simply because they believe a treatment is working, even if it's a dummy treatment. It's an essential aspect considered during clinical studies to distinguish between actual treatment effects and the impact of patients' expectations.

The placebo effect is best described as the phenomenon in which a person experiences a perceived improvement in their condition or symptoms simply due to their belief in the efficacy of the treatment, even if the treatment is inactive or a 'dummy' treatment, such as a sugar pill. This is represented in the provided choices by option B. Subjects may respond to a treatment simply because they believe it is affecting them.

Notably, this effect is considered in the design of clinical trials and studies. This is typically done by using a control group that receives a placebo treatment, which allows researchers to separate the physiological effects of the treatment from psychological effects induced by expectations- a crucial aspect of medical and scientific research.

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Answer:

Option 3) (0.38, -2.85) and (2.62,3.85)

Step-by-step explanation:

we have

[tex]y=x^{2}-3[/tex] ----> equation A

[tex]y=3x-4[/tex] ----> equation B

Solve the system by graphing

Remember that the solution of the system of equations is the intersection point both graphs

using a graphing tool

The intersection points are (0.38,-2.85) and (2.62,3.85)

see the attached figure

therefore

The graphs intersect approximately at (0.38,-2.85) and (2.62,3.85)

Answer:

61 miles.

Step-by-step explanation:

Given: driving north for 11 miles and drive east for another 60 miles.

As given in the question, the travelling pattern show a right angle triangle, where hypotenuse line is the way to return back directly to starting point. As shown in picture attached.

∴ we can say, adjacent (a) is 11 miles and opposite (b) is 60 miles

Now, using Pythagoras theorem to get distance to return.

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

⇒ [tex]h^{2} = 11^{2} +60^{2}[/tex]

⇒ [tex]h^{2} = 121+3600= 3721[/tex]

⇒ [tex]h= \sqrt{3721}[/tex]

∴[tex]h= 61[/tex]

∴ 61 miles need to be travel to return back directly to starting point.

Answer:

Step-by-step explanation:

The formula for simple interest is

I = Prt,

where I is the interest earned,

P is the initial investment amount,

r is the interest rate in decimal form, and

t is the time in years.  For us,

I = 75,

P = ?

r = .05

t = 1

Filling in what we were given:

75 = P(.05)(1) and

.05P = 75 so

P = 1500

Answer:

17.25%.

Step-by-step explanation:

We have been given that last ear 225 students attended the annual school dance at CCMS. This year 211 students attended the dance. We are asked to find the percent of decrease.

We will use percent decrease formula to solve our given problem as:

[tex]\text{Percent decrease}=\frac{|\text{Final - Original}|}{\text{Original}}\times 100\%[/tex]

[tex]\text{Percent decrease}=\frac{|211-255|}{255}\times 100\%[/tex]

[tex]\text{Percent decrease}=\frac{|-44|}{255}\times 100\%[/tex]

[tex]\text{Percent decrease}=\frac{44}{255}\times 100\%[/tex]

[tex]\text{Percent decrease}=0.1725490\times 100\%[/tex]

[tex]\text{Percent decrease}=17.25490\%[/tex]

[tex]\text{Percent decrease}\approx 17.25\%[/tex]

Therefore, percent decrease is approximately 17.25%.

Answer:

1) angle bisector

2) w = 72°

3) t = 44°

4) t = 51°

5) FG = 16 units

Step-by-step explanation:

1) Given that, ∠VYW ≅ ∠WYV

The line which cuts any angle into equal halves is angular bisector of the angle

⇒ YW is angle bisector

2) In a triangle, sum of two interior angle is equal to exterior angle of other side.

⇒ w-41° + w-31° = w.

⇒ w = 72°

3) Sum of interior angles in a pentagon is 540°

(For a n sided it is (n-2)180° )

⇒ 149° + 139° + t+32° + 3t +t = 540°

⇒ t = 44°

4) sum of all exterior angles taken one at each vertex = 360°

⇒ 2t-50° + 46° + 2t + 34° + 2t-50° + 34° + 40° = 360°

⇒ t = 51°

5) Here, by comparing ΔHGF and ΔHIF

   ∠GHF = ∠IHF

  ∠HGF = ∠HIF

 and HF is common side for both triangles

⇒  ΔHGF ≡ ΔHIF ;  i.e) ΔHGF , ΔHIF are congruent triangles

⇒ FG = FI = 16 units

Answer:

The value of A =  [tex]\dfrac{1}{16}[/tex]

The value of B = [tex]\dfrac{1}{16}[/tex]

The value of C =  [tex]\dfrac{25}{16}[/tex]

The value of D =  [tex]\dfrac{5}{4}[/tex]

Step-by-step explanation:

Given as :

The following relations are as

[tex]\dfrac{d}{5}[/tex] =4 A           ...........1

d = 20 B                                       ...........2

d = [tex]\dfrac{4}{5}[/tex] C           ...........3

And d = [tex]\dfrac{5}{4}[/tex]

Now, From the above relations

Put the value of d in eq 1

∵ 4 A = [tex]\dfrac{d}{5}[/tex]

So, d = 5 × 4 A

Or, [tex]\dfrac{5}{4}[/tex] = 20 A

∴ A = [tex]\frac{\frac{5}{4}}{20}[/tex] = [tex]\dfrac{1}{16}[/tex]

I.e The value of A =  [tex]\dfrac{1}{16}[/tex]

Again

From eq 2

∵ d = 20 B

Put the value of d

So, [tex]\dfrac{5}{4}[/tex]  = 20 B

Or, B = [tex]\frac{\frac{5}{4}}{20}[/tex]

∴ B = [tex]\dfrac{1}{16}[/tex]

I.e The value of B = [tex]\dfrac{1}{16}[/tex]

Similarly

From eq 3

d = [tex]\dfrac{4}{5}[/tex] C  

Put the value of d

So, [tex]\dfrac{5}{4}[/tex] =  [tex]\dfrac{4}{5}[/tex] C    

Or, C = [tex]\frac{5\times 5}{4\times 4}[/tex]

∴ C = [tex]\dfrac{25}{16}[/tex]

I.e The value of C =  [tex]\dfrac{25}{16}[/tex]

Hence The value are

The value of A =  [tex]\dfrac{1}{16}[/tex]

The value of B = [tex]\dfrac{1}{16}[/tex]

The value of C =  [tex]\dfrac{25}{16}[/tex]

The value of D =  [tex]\dfrac{5}{4}[/tex]

Answer

The answer is 1 mile an hour

Answer:

Step-by-step explanation:

1 1/4 (or 1.25) cups to 20 servings = 1 gallon (16 cups) to x servings

 1.25        16

--------- = --------  cross multiply

 20           x

(1.25)(x) = (20)(16)

1.25x = 320

x = 320/1.25

x = 256 servings <===

Answer:

[tex]f^{-1}[/tex](x) = x - 5

Step-by-step explanation:

Let y = f(x) and make x the subject

y = x + 5 ( subtract 5 from both sides )

y - 5 = x

Change y back into terms of x, thus

[tex]f^{-1}[/tex](x) = x - 5

Answer:

25

Step-by-step explanation:

Do multiplication first 6*3 is 18 18+4 is 22 22+3 is 25

The volume of the square pyramid is: 3072 ft³

What is the volume of the square pyramid?

The volume (V) of a square pyramid can be calculated using the formula:

V = ⅓ × base area × height

The base area of a square pyramid is given by the formula:

base area = base edge²

Given that the base edges (a) is 24 ft and the slant height (s) is 20 ft, we can calculate the height (h) of the pyramid using the Pythagorean theorem.

h = √(20² - (24/2)²)

h = √256

h = 16 ft

Thus:

Volume = ⅓ * 256 * 16

Volume = 3072 ft³

The inequalities that require flipping the sign are:

-5x - 10 > 5

[tex]\frac{x}{-7} + 3 \leq 4[/tex]

Solution:

Let us the inequalities one by one

You can perform on operations on both sides of inequality, and have its truth value unchanged

But if we multiply or divide by a negative number , we must flip the sign

-5x - 10 > 5

Move -10 from L.H.S to R.H.S

-5x > 5 + 10

-5x > 15

Divide the above expression by 5

[tex]-x > 3[/tex]

Divide the above inequality by -1, so we must flip the sign

x < -3

[tex]7x - 5 \leq 16[/tex]

Move the constant term from L.H.S to R.H.S

[tex]7x \leq 16 + 5\\\\7x \leq 21\\\\[/tex]

Divide the above inequality by 7

[tex]x \leq 3[/tex]

This does not required flipping the symbol

[tex]\frac{x}{5} - 6 > -11[/tex]

Move the constant term from L.H.S to R.H.S

[tex]\frac{x}{5} > -11 + 6\\\\\frac{x}{5} > -5[/tex]

Multiply both the sides by 5

[tex]x > -25[/tex]

This does not required flipping the symbol

[tex]x + 12 \leq 29[/tex]

Move the constant term from L.H.S to R.H.S

[tex]x \leq 29 - 12\\\\x \leq 17[/tex]

This does not required flipping the symbol

[tex]\frac{x}{-7} + 3 \leq 4[/tex]

Move the constant term from L.H.S to R.H.S

[tex]\frac{x}{-7} \leq 4-3\\\\\frac{x}{-7} \leq 1\\\\[/tex]

Multiply both the sides by -7, so we must flip the sign

[tex]x \geq -7[/tex]

Thus this requires flipping the sign

Answer: -5x - 10 > 5

Step-by-step explanation: