38. Express these rates in the lowest terms.

a. $56: 16 kg
b. There are six teachers for every 108 students

39. Change to unit rates.

a. $20 for five T-shirts
b. 45 miles in half an hour
​

ANSWER

See sample space below

EXPLANATION

The sample space refers to the set of all the possible outcomes.

When two fair dice are rolled, the possible by outcomes are:

{(1,1),(1,2),(1,3),(1,4),(1,5),(1,6),(2,1),(2,2),(2,3),(2,4),(2,5),(2,6),(3,1),(3,2),(3,3),(3,4),(3,5),(3,6),(4,1),(4,2),(4,3),(4,4),(4,5),(4,6),(5,1),(5,2),(5,3),(5,4),(5,5),(5,6),(6,1),(6,2),(6,3),(6,4),(6,5),(6,6)}

The total number of outcomes is 36.

Answer:

Liberty Hill

Step-by-step explanation:

It rises the most over the same horizontal distance

Answer:

Liberty Hill. For every 4 feet at a horizontal distance, it rises 3 ft at the vertical rise of the street.

Step-by-step explanation:

Looking at the data, we can trace a parallel to the Cartesian Plane. As the Horizontal Distance would be the x-axis and the Vertical Axis, y-axis. So to determine the steepest hill we need to check the slope.

Like this:

Reference point (0,0)

Dixie Hill

[tex]m=\frac{40-0}{80-0}=\frac{1}{2}[/tex]

Bell Hill

[tex]m=\frac{20-0}{80-0} =\frac{20}{80}=\frac{1}{8}[/tex]

Liberty Hill

[tex]m=\frac{60-0}{80-0} =\frac{60}{80}=\frac{3}{4}[/tex]

The base Liberty Hill makes the largest angle, therefore the steepest hill.

For every 4 feet at a horizontal distance, it rises 3 ft at the vertical rise of the street.

Answer:

1:4

Step-by-step explanation:

24 divided by 6 is 4. and 6 divided by 6 is 1

Answer:

1:4

Step-by-step explanation:

24÷6=4 and 6÷6=1 this is all you need

Answer:

14.93

Step-by-step explanation:

For this problem you need to know distance formula, which is

d=√(x2-x1)²+(y2-y1)². You'll want to plug in (0,3) and (-2, 9) and go on to plug in all of them at some point. You'll get 6.32 as the distance between (0,3) and (-2, 9), 3.61 as the distance between (-2, 9) and (-4, 6), and 5 as the distance between (-4, 6) and (0, 3). You add them up and get your answer.

Leo needs 6 red roses and 9 pink daisies for 3 bouquets, calculated by dividing the number of flowers needed for 5 bouquets by 5 and then multiplying by 3.

To calculate the amount of red roses and pink daisies Leo needs for 3 bouquets, we first determine the number needed for one bouquet. Since Leo needs 10 red roses and 15 pink daisies for every 5 bouquets, we divide each amount by 5 to find the number per single bouquet:

Now, we multiply the number of flowers needed per bouquet by 3 to find the total number for 3 bouquets:

Therefore, for 3 bouquets, Leo needs 6 red roses and 9 pink daisies.

Company C and Company D both manufacture batteries having the greatest variation in lifespan, which is an 8 month variation. This was determined by calculating the range of each data set.

The variation in lifespan for each company's laptop battery can be determined by looking at the range of the data, which is found by subtracting the smallest value (minimum) from the largest value (maximum). So we have:

As we can see, Company C and Company D both have the greatest variation in lifespan of their laptop batteries, with a range of 8 months.

https://brainly.com/question/12591498

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Answer:

[tex]300,000.04\ people[/tex]

Step-by-step explanation:

we know that

To find how many people live in that city multiply the population density by the area of the city

so

[tex](46\ \frac{people}{mi^{2}})(6,521.74\ mi^{2})=300,000.04\ people[/tex]

okay so you should know that the formula for a triangle is:

A=1/2×b×h

where b is breadth and h is height

A is area

so they already gave the area which is 16.2 and they already gave a side ( doesn't matter if it's b or h in this question)

so we put these into the equation of the area of a triangle

A=1/2×b×h

16.2=1/2 × 6 × h

then you will solve algebraically to get 5.4cm which is you answer

to check if correct you can always put in all numbers in equation and you should get 16.2cm

In this case it's correct ✌

Answer:

AC = 5.4 cm

Step-by-step explanation:

The area (A) of a triangle is calculated using the formula

A = [tex]\frac{1}{2}[/tex] bh ( b is the base and h the perpendicular height )

here AC is the base (b) and AB the height (h), thus

[tex]\frac{1}{2}[/tex] × AC × 6 = 16.2

3AC = 16.2 ( divide both sides by 3 )

AC = 5.4 cm

3 terms. Just count the terms (which are separated by the +/- signs)

The answer is:

The polynomial have 3 terms. (it's a trinomial).

A polynomial is an expression which consists of one or more terms (numbers or variables) being added or subtracted.

So, we are given the polynomial:

[tex]x^{2} +xy-y^{2}[/tex]

We have that there are three terms separated by differents being added and subtracted, so, the polynomial has 3 terms, and it's a trinomial.

Have a nice day!

Answer:

false

Step-by-step explanation:

One milliliter of water has one gram of mass, and weighs one gram in typical situations

One milliliter of water does not have a mass of 2.00 grams.

Water has a density of 1g/mL, so one milliliter of water has a mass of 1 gram.

Find the length of a side of a square with an area of 169 in^2.

Answer:

D. 13 in

Step-by-step explanation:

A square has sides of equal length.

A = L^2 where:  A = area  and  L = side

L^2 = 169

L=√169

L=13 in^2.    

The length of a side of a square with an area of 169 in2 is calculated by taking the square root of the area, which is 13 inches. The correct answer is D. 13 in.

The student is asking to find the length of a side of a square given that the area of the square is 169 square inches. The formula to calculate the area of a square is side length squared, which can be written as:

Area = side × side

To find the side length, we need to take the square root of the area:

Side = √169

Upon calculation, the side length is:

Side = 13 {in}

Therefore, the correct answer is D. 13 in.

Answer:

Step-by-step explanation:

[tex](a+b)^2=a^2+2ab+b^2\qquad(*)\\\\\\2x^2+12x-14=0\qquad\text{divide both sides by 2}\\\\x^2+6x-7=0\qquad\text{add 7 to both sides}\\\\x^2+2(x)(3)=7\qquad\text{add}\ 3^2=9\ \text{to both sides}\\\\\underbrace{x^2+2(x)(3)+3^2}_{(*)}=7+9\\\\(x+3)^2=16\Rightarrow x+3=\pm\sqrt{16}\\\\x+3=-4\ or\ x+3=4\qquad\text{subtract 3 from both sides}\\\\x=-7\ or\ x=1[/tex]

Answer:

No.

Step-by-step explanation:

To be prime, it has to be a number more than 1.

Answer:

No

Step-by-step explanation:

The number 1 is only divisible by itself, so it is neither prime nor composite.

Answer: (4y - 3)(3x - 2)

Step-by-step explanation: Factor the polynomial.

Hope this helps! :) ~Zane

For this case we must factor the following expression:

[tex]12xy-9x-8y + 6[/tex]

So:

We group the first two and two last terms:

[tex](12xy-9x) + (- 8y + 6) =[/tex]

we factor the maximum common denominator of each group:

[tex]3x (4y-3) -2 (4y-3) =[/tex]

We factor the polynomial by factoring the highest common denominator:

[tex](3x-2) (4y-3)[/tex]

ANswer:

[tex](3x-2) (4y-3)[/tex]

Answer:

[tex]\frac{1}{3}(base area)(height)[/tex]

Step-by-step explanation:

Hi!

For the Pyramid´s volume equation is referred to one third of the area base multiply for the height of the pyramid. Take into account that the base area just going to change for the kind of base you will have into the pyramid, for example if the base is rectangular you have to use the equation a for it while for a triangular base you have to use equation b

Equation a

base X height

Equation b    

base X (height)/2

B 22

11+11=22

AC is the chord

Answer:

B. 22 units.

Step-by-step explanation:

A perpendicular dropped from center to a chord bisects the chord.

In the given figure O is the center of the circle .OB is a perpendicular dropped from center of circle to the chord AC and hence it bisects the chord .

AB=BC= 11 units .

By addition of line segments :

Length of chord AC =  AB+BC =11+11 = 22 units.

[tex]\bf v(x)=32500(0.92)^x\qquad \qquad \stackrel{\textit{2 years later, x = 2}}{v(2)=32500(0.92)^2} \\\\\\ v(2)=32500(0.8464)\implies v(2)=27508[/tex]

Answer:

$27508.

Step-by-step explanation:

We have been given that the value of certain truck after x years is represented by equation [tex]v(x)=32500(0.92)^x[/tex]. We are asked to find the value of truck after 2 years.

To find truck's value after 2 years, we need to substitute [tex]x=2[/tex] in our given equation.

[tex]v(2)=32500(0.92)^2[/tex]

[tex]v(2)=32500*0.8464[/tex]

[tex]v(2)=27508[/tex]

Therefore, the truck is worth $27508 after 2 years.

Answer:

600 blue spruce trees

Step-by-step explanation:

Let

x-----> the total number of blue spruce trees in the forest

using proportion

36/3=x/50

x=50*36/3

x=600 blue spruce trees

ANSWER: THE SOLUTION OF GIVEN INEQUALITIES IS ALL REAL NUMBER EXCEPT [1.167,3.5].

Answer:

Sample Response: When solving the first inequality, you get x > 3.5. When solving the second inequality, you get x < 3.5. The solution of an "or” compound in equality is everything in both solution sets, so the solution set is all of the numbers less than 3.5 and greater than 3.5. Since neither of the inequalities includes 3.5, the compound inequality has a solution of all real numbers except 3.5.

Step-by-step explanation:

Answer:

Part 1) The inscribed angle is the angle ∠TRS and the intercept arc is the arc LST

Part 2) The inscribed angle is the angle ∠YWX and the intercept arc is the minor arc XY

Part 3) The inscribed angle is the angle ∠YXZ and the intercept arc is the arc YBZ

Part 4) The figure does not show an inscribed angle

Step-by-step explanation:

Part 1) The figure shown a inscribed angle

The inscribed angle is the angle ∠TRS

The intercept arc is the arc LST

Remember that

The inscribed angle measures half that of the arc comprising

so

∠TRS=(1/2)[arc LST]

Part 2) The figure shown a inscribed angle

The inscribed angle is the angle ∠YWX

The intercept arc is the minor arc XY

Remember that

The inscribed angle measures half that of the arc comprising

so

∠YWX=(1/2)[minor arc XY]

Part 3) The figure shown a inscribed angle

The inscribed angle is the angle ∠YXZ

The intercept arc is the arc YBZ

Remember that

The inscribed angle measures half that of the arc comprising

so

∠YXZ=(1/2)[arc YBZ]

Part 4) The figure does not show an inscribed angle

The figure shown a interior angle ∠BAC

Answer:

C 13,7,1

Step-by-step explanation:

The given expression is [tex]y=-3x+7[/tex].

To find the corresponding y-values, we need to plug in the x-values.

When x=-2, [tex]y=-3(-2)+7[/tex],  [tex]\implies y=6+7=13[/tex]

When x=0, [tex]y=-3(0)+7[/tex],  [tex]\implies y=0+7=7[/tex]

When x=2, [tex]y=-3(2)+7[/tex],  [tex]\implies y=-6+7=1[/tex]

Therefore the numbers that completes the table are: 13,7,1

The correct answer is C

Answer: The answer is 94

Step-by-step explanation: First you should pay attention to the main numbers and since more and many are addition word than you should add 7 + 4 which equals 11 then add 83 + 11 which would equal 94. Tell me if the answer is wrong and I would find another way to answer it.  

Final answer:

Linda sent 8 text messages, Jim sent 15 messages, and Dale sent 60 messages during the weekend.

Explanation:

The question asks to solve a word problem to find out how many text messages Linda, Dale, and Jim sent over the weekend.

Let's denote the number of messages Linda sent as L, Jim as J, and Dale as D.

The problem states that Jim sent 7 more messages than Linda, so J = L + 7.

Dale sent 4 times as many messages as Jim, so D = 4J.

Together they sent 83 messages, which gives us the equation L + J + D = 83.

Substituting the expressions for J and D in terms of L into the equation, we get L + (L + 7) + 4(L + 7) = 83.

This simplifies to 6L + 35 = 83. Solving for L gives us L = 8.

This means Linda sent 8 messages, Jim sent 15 messages (8 + 7), and Dale sent 60 messages (4 times 15).

Answer:

A. 30cm

Step-by-step explanation:

You would need to use the Pythagorean Theorem to find the answer. The theorem is a^2+b^2=c^2.

A and B represent the legs and C represents the hypotenuse.

Now substitute the values: 18^2+24^2=c^2

Calculate the exponents: 324+576=c^2

Now add: 900=c^2

Find the square root of 900: 30

So, the length of the hypotenuse is 30cm.

33 hours is the answe

Answer:

so appx, 33 and a half hours per week

Step-by-step explanation:

366/11= 33.27

Answer:

3(x-2)÷(x-2)=3.....

Answer:

Step-by-step explanation:

[tex]3x-6\qquad\text{distributive}\\\\=(3)(x)-(3)(2)=(3)(x-2)=3(x-2)\\\\\dfrac{3x-6}{x-2}=\dfrac{3(x-2)}{x-2}\qquad\text{cancel}\ (x-2)\\\\=\dfrac{3(1)}{1}=3[/tex]

Answer: Third option.

Step-by-step explanation:

We know that the sine function is:

[tex]f(x)=Asin(bx)[/tex]

Where "A" is the amplitude of the function( This is half the vertical distance between minimum value and maximum value of the function) and [tex]\frac{2\pi }{b}[/tex] is the period.

Observe in the graph that the amplitude is:

[tex]A=1[/tex]

And the period is 1, then "b" is:

[tex]1=\frac{2\pi }{b}\\\\b=\frac{2\pi }{1}\\\\b=2\pi[/tex]

Then the function shown in the graph is:

[tex]f(x)=sin(2\pi x)[/tex]

By definition in the transformation of the function:

When [tex]kf(x)[/tex] and [tex]k>1[/tex] then the function is stretched vertically by a factor of "k".

In this case we know that the function shown in the graph is vertically stretched by a factor of 2 to produce a new graph. Then:

[tex]k=2[/tex]

Therefore,the function that represents the new graph is:

[tex]f(x)=2sin(2\pi x)[/tex]

Answer:

Nikolaus Otto was  responsible for inventing the first working four-stroke engine.

​

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

Using the rule of logarithms

• [tex]log_{b}[/tex] x = n ⇔ x = [tex]b^{n}[/tex]

Given

[tex]log_{x}[/tex] ([tex]\frac{1}{8}[/tex] ) = - [tex]\frac{3}{2}[/tex], then

[tex]\frac{1}{8}[/tex] = [tex]x^{-\frac{3}{2} }[/tex]

Square both sides

[tex]\frac{1}{64}[/tex] = [tex]x^{-3}[/tex]

[tex]4^{-3}[/tex] = [tex]x^{-3}[/tex] ⇒ x = 4 → B

[tex]\bf \textit{Pythagorean Identities} \\\\ sin^2(\theta)+cos^2(\theta)=1\implies cos^2(\theta )=1-sin^2(\theta ) \\\\[-0.35em] ~\dotfill\\\\ \cfrac{sin^2(\theta )}{1-sin^2(\theta )}\implies \cfrac{sin^2(\theta )}{cos^2(\theta )}\implies \left[ \cfrac{sin(\theta )}{cos(\theta )} \right]^2\implies tan^2(\theta )[/tex]

Answer:

61 second I would say but what is the weight of the rock?

Answer:

Option B. 7.8 seconds

Step-by-step explanation:

Shyanne drops a rock from a hill at initial height of 975 feet above the ground level.

We have to calculate the time taken by rock to hit the ground.

As we know the formula of motion under gravity is

h = ut + [tex]\frac{1}{2}gt^{2}[/tex]

Here h = initial height = 975 feet

u = initial velocity = 0

t = time taken by the rock to hit the ground

g = 32.174 [tex]\frac{\text{Feet}}{\text{Second}^{2}}[/tex]

Now we plug in these values in the formula

975 = 0 + [tex]\frac{1}{2}(32.174)(t)^{2}[/tex]

975 = 16.087t²

t² = [tex]\frac{975}{16.087}[/tex]

t = [tex]\sqrt{60.60}[/tex]

t = 7.78 ≈ 7.8 seconds

Option B. 7.8 seconds is the answer.