Ryan is trying a low-carbohydrate diet. He would like to keep the amount of carbs consumed in grams between the levels shown in the following compound inequality:

110 < 2x + 10 and 2x + 10 < 310

Solve for x in this inequality, and explain what the answer represents.

x > 50 and x < 150; Ryan needs to consume more than 50 grams of carbohydrates, but less than 150 grams of carbohydrates.
x < 50 and x > 150; Ryan needs to consume less than 50 grams of carbohydrates or more than 150 grams of carbohydrates.
x > 60 and x < 160; Ryan needs to consume more than 60 grams of carbohydrates, but less than 160 grams of carbohydrates.
x < 60 and x > 160; Ryan needs to consume less than 60 grams of carbohydrates or more than 160 grams of carbohydrates.

Answer:

D is the contrapositive.

Step-by-step explanation:

Contrapositive of if A then B is if not B then not A

Answer:

Option D is correct here.

Step-by-step explanation:

A conditional statement is in the form of if p then q.

A contrapositive statement is when we interchange the hypothesis and conclusion of the sentence and negate both of them. It is in the form of - if not q then not p.

Given statement here is - A converse statement is formed by exchanging the hypothesis and conclusion of the conditional.

This is a true statement. It is the definition of converse statement.

Its contrapositive will be : A statement not formed by exchanging the hypothesis and conclusion of the conditional is not a converse statement.

So, here option D is the contrapositive that is also true.

Answer:

Yellow Paint: 0.44736842105%

Red Paint: 0.19736842105%

Water: 0.35526315789%

Step-by-step explanation:

Yelow:

30 x 0.3 = 9

8 + 9 = 17

30 + 8 = 38

17/38 = 0.44736842105%

Red:

30 x 0.25 = 7.5

7.5/38 = 0.19736842105%

Water:

30 x 0.45 = 13.5

13.5/38 = 0.35526315789%

Answer:

The correct answer is option B.  -18

Step-by-step explanation:

It is given an expression : 3 × (50 – 62) ÷ 2

To find the answer we have to use BODMAS principle

BODMAS means that the order of operations

B- Bracket, O - of , D - Division, M - Multiplication, A - Addition and  

S - Subtraction

To find the correct option

Step 1: Do the bracket first

3 × (50 – 62) ÷ 2 =  3 × (-12) ÷ 2

(Multiplication and division are in the order of appearance)

Step 2: Multiplication  

3 × (-12) ÷ 2 = -36  ÷ 2  

Step 3 : Division

-36 ÷ 2 = -18

The correct option is option B.  -18

Answer:

=-18

Step-by-step explanation:

3×(50-62)÷2

Using PEMDAS,  we first evaluate the parentheses. 50-62=-12

The new expression becomes

3×⁻12÷2

We now perform the multiplication in the order in which they occur.

3×-12=-36 and -36÷2= -18

=-18

Answer:

11.15 packs of paper are used in 5 days; therefore, 133.85 are left

Step-by-step explanation:

Set this up as ratio with days on top and packs of paper on the bottom.  Filling in the ratio with the info we have, keeping in mind we are looking for packs of paper left after 5 days:

[tex]\frac{days}{packs}:\frac{65}{145}=\frac{5}{x}[/tex]

Cross multiply to get 65x = 725 and x = 11.15.  This represents the number of packs used.  To get the number of packs remaining, subtract 11.15 from 145 to get 133.85 remaining after 5 days.

Answer:

10x

Step-by-step explanation:

Note the place values of the value 3 in both of the decimals.

The value of the 3 in 46.132 is in the hundredths place.

The value of the 3 in 8.553 is in the thousandths place.

Divide thousands with hundreds: 1000/100 = 10

The value of the 3 in 46.132 is 10x larger than the value of 3 in 8.553

~

Answer:

  100 lbs

Step-by-step explanation:

Let x represent the number pounds of $60 coffee that should be used to create the mix. The total cost of the mix will be ...

  60x + 90·50 = 70(x+50)

  60x +4500 = 70x +3500 . . . . simplify

  1000 = 10x . . . . . . . . . . . . . . . . subtract 3500+60x

  100 = x . . . . . . . . . . . . . . . . . . . divide by 10

The merchant should use 100 pounds of the $60 coffee.

_____

The cost of the mix parts and the total mix is figured from ...

  (dollars/lb)×(lbs) = dollars

Answer:

[tex]\large\boxed{b.\ 15.3}[/tex]

Step-by-step explanation:

[tex]-\dfrac{x}{17}=-0.9\qquad\text{multiply both sides by (-17)}\\\\(-17\!\!\!\!\!\diagup^1)\left(-\dfrac{x}{17\!\!\!\!\!\diagup_1}\right)=(-17)(-0.9)\qquad{/(-)(-)=(+)/}\\\\x=15.3[/tex]

Answer:

  84.8 in³

Step-by-step explanation:

The formula for the volume of a cylinder is ...

  V = πr²h

The volume Mary will be filling will be 3/4 of the 9-inch height of the vase, so is ...

  V = π(2 in)²(3/4·9 in) = 27π in³ ≈ 84.8 in³

_____

Comment on the answer

In more conventional units of measure, that is very nearly 3 pints of water.

Answer: Option D

phase

Step-by-step explanation:

By definition, the cosine function has the following form

[tex]y = cos (x - \phi)[/tex]

Where [tex]\phi[/tex] is known as the phase angle

By definition the sinx function is equal to the cosx function with a phase shift of [tex]\frac{\pi}{2}[/tex]

So if we have the function

[tex]y = cos (x - \phi)[/tex] and we want to transform it into the function [tex]y=sin(x)[/tex] then [tex]\phi = \frac{\pi}{2}[/tex]

Finally

[tex]y = cos(x - \frac{\pi}{2})=sin(x)[/tex]

the answer is the option D

Final answer:

The cosine function aligns with the sine function by introducing a phase shift, typically represented by phi (φ), indicating that D. phase is the correct answer.

Explanation:

The cosine function can be made to have the same values as the sine function for each angle by including a shifted phase in the calculation. This shift is referred to as a phase shift and is typically represented by the Greek letter phi (φ).

In the context of trigonometric functions, a phase shift will slide one function over to match that of another.

Specifically, when the sine function is shifted left by 90 degrees (π/2 radians), it aligns perfectly with the cosine function, indicating that the sine and cosine are out of phase by 90 degrees.

Thus, the correct answer is D. phase.

Answer:

x=5

Knowing that the length of the rectangle is 9, we can simply multiply this by 2 since there are two sides that will equal the same. This gets us 18. If we subtract that from 28, we get 10. There are four sides in a rectangle, meaning we have two sides left. This leaves us to divide 10 by two to get a final answer of the width of the retangle being 5 centimeters.

The value of x, which represents the width of the rectangle, can be found by inserting the given length and perimeter into the perimeter formula of a rectangle, P = 2L + 2W. Then, solve for W to get the value of x.

The first step to solve this problem is to understand the formula for the perimeter of a rectangle. This formula is P = 2L + 2W, where P is the perimeter, L is the length and W is the width. We know that the length (L) is 9 cm and the perimeter (P) is 28 cm based on the problem given. We are looking to find the value for x which represents the width (W).

Let's substitute the given values into the formula:
28 = 2(9) + 2W.

This simplifies to:
28 = 18 + 2W.

Now, let's solve for W by subtracting 18 from both sides of the equation:
10 = 2W.

To isolate W, divide both sides of the equation by 2:
W = 5
So, the value of x, which represents the width of the rectangle, is 5 cm.

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Answer:

Mean = 47.52 degrees

Step-by-step explanation:

We will use the following method to find the mean

Class interval     Frequency(f)     Class Mark(X)     fx

40-44                      3                              42               126

45-49                      4                              47               188

50-54                     10                             52               520

55-59                      6                              57               342

60-64                      2                              62               124

.........................................................................................................

                               25                                                1188

.........................................

The formula for mean is:

Mean = ∑fx / ∑f

= 1188/25

= 47.52 degrees

The computed mean is less than the actual mean of 51.8 degrees ..

For this case we can raise a rule of three:

[tex]\frac {3} {4}[/tex]cup of water ---------> [tex]\frac {1} {8}[/tex] pound of flour

x --------------------------------- > 1 pound of flour

Where:

x: Represents the amount of water that Tamie must use with 1 pound of flour.

[tex]x = \frac {1 * \frac {3} {4}} {\frac {1} {8}}\\x = \frac {\frac {3} {4}} {\frac {1} {8}}\\x = \frac {3 * 8} {4 * 1}\\x = \frac {24} {4}\\x = 6[/tex]

So, Tamie should use 6 cups of water

Answer:

6 cups of water

Answer:

xy = 1.6

Step-by-step explanation:

The equation for inverse variation is

xy = k  where k is the constant of variation

8 * .2 = k

1.6 = k

xy = 1.6

Step-by-step explanation:

59 mi/hr × (5280 ft/mi) × (1 hr / 3600 s) = 86.53 ft/s

Rounded to the nearest whole number, the speed is approximately 87 ft/s.

Answer:

Step-by-step explanation:

the translation (x,y) --> (x+6,y-4):

(1, 5)--> (1+6,5-4)=(7,1)

(2, 2)--> (2+6,2-4)=(8,- 2)

(6, 3)--> (6+6,3-4)=(12,- 1)

the image of A triangle has vertices of (1, 5), (2, 2), and (6, 3) is :

the triangle has vertices of (7, 1), (8,- 2), and (12, -1)

Answer:

see explanation

Step-by-step explanation:

Find equivalent routes for the directed lines, that is

(a)

FE = FA + AB + BE = b + a - 3b = a - 2b

(b)

BC = BE + ED + DC = - 3b + a + 2b = a - b

(c)

FC = FA + AB + BE + ED + DC

     = b + a - 3b + a + 2b = 2a

ANSWER

(0,2)

EXPLANATION

The mapping point A has coordinate (0,2).

We want to find the coordinates of this point after a rotation of -90° about the origin.

In other words, we want to find the image of this point after a rotation of 90° anticlockwise.

The rule is

[tex](x,y) \to( - y,x)[/tex]

This implies that

[tex](2,0) \to(0,2)[/tex]

Answer:

  A.  8, 10, 14

Step-by-step explanation:

As a rough cut, a triangle will be obtuse if the longest side is about 1.4 or more times the length of the second-longest side. This derives from the relationship in an isosceles right triangle, where the hypotenuse is √2 ≈ 1.414 times the length of the two equal-length sides. If one side is shorter than the other, and the hypotenuse is still 1.414 times the length of the second-longest side, then the triangle is no longer a right triangle, but is an obtuse triangle.

Here, the first selection has a middle-length side of 10 and a longest side of 14, about 1.4 times 10. It is an obtuse triangle.

_____

More rigorously, you can see if the sum of the squares of the short sides is less than the square of the longest side. If so, the triangle is obtuse. (The Law of Cosines will tell you the angle opposite the longest side must have a negative cosine, so must be greater than 90°.)

Our answer choices are ...

  A. 8^2 + 10^2 = 164 < 14^2 = 196 . . . . . obtuse

  B. 9^2 + 12^2 = 225 = 15^2 . . . . . . . . . . right

  C. 10^2 +14^2 = 296 > 17^2 = 289 . . . . . acute

  D. 12^2 +15^2 = 369 > 19^2 = 361 . . . . . acute

Answer:

A) 8, 10 and 14

correct on edg2020 :)

Answer:

The exact volume of an oblique cylinder is [tex]V=2,000\pi\ cm^{3}[/tex]

Step-by-step explanation:

we know that

The Cavalieri's principle states that if two or more figures have the same cross-sectional area at every level and the same height, then the figures have the same volume

so

The volume of the oblique cylinder is equal to

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

we have

[tex]h=20\ cm[/tex]

[tex]r=10\ cm[/tex]

substitute

[tex]V=\pi (10)^{2} (20)[/tex]

[tex]V=2,000\pi\ cm^{3}[/tex]

Answer:

the volume of an oblique cylinder is V=2,000\pi\ cm^{3}

Answer:

a 16

Step-by-step explanation:

16 x 12 = 192 plates

496 total plates - 192 = 304

304 packages of 8 plates

304 / 8 = 38 sets of 8 plates

38 + 16 = 54 packs of plates

Answer:

5.5% per year

Step-by-step explanation:

Using Formula A = P (1 + rt)

Where

A = Final amount = $10,000 + $6,600  = $16,600

P = Principal = Beginning Amount = $10,000

t = time = 12 years

r = rate in $/year (which we need to find)

Assembling the formula

A = P (1 + rt)

16,600 = 10,000 (1 + 12r)

[tex]\frac{16,600}{10,000}[/tex] = 1 + 12r

1.66 = 1 + 12r

1.66 - 1 = 12r

0.66 = 12 r

r = 0.055 = 5.5%

Answer:

Option A.Exponential decay, 55% decrease

Step-by-step explanation:

we have

[tex]f(x)=54(0.45)^{x}[/tex]

This is a exponential function of the form

[tex]f(x)=a(b)^{x}[/tex]

where

a is the initial value

b is the base

b=(1+r)

r is the rate of change

In this problem

a=54

b=0.45

so

0.45=1+r

r=0.45-1

r=-0.55

Convert to percentage

r=-55% ------> is negative because is a exponential decay

Answer:

Exponential decay, 55% decrease

Step-by-step explanation:

[tex]f(x) = 54(0.45)^x[/tex]

General exponential growth function is [tex]y=a(1+r)^x[/tex]

exponential growth function is [tex]y=a(1-r)^x[/tex]

The value of 1-r is less than 1 then it is exponential decay

In the given f(x) , the 1-r is 0.45 that is less than 1

So it is exponential decay.

[tex]1-r= 0.45[/tex]

Subtract 1 on both sides

[tex]r=0.55[/tex]

Multiply by 100 to get %

r= 55%

Exponential decay, 55% decrease

Answer:

8x^2+3x

Step-by-step explanation:

What I read is 2x+8x^2-4x+5x

combining like terms means putting the terms that have the same variable part together

8x^2 is the only one that doesn't have any terms like it as far as the variable part

so 8x^2+2x-4x+5x

We just need to figure out 2-4+5 which is -2+5=3

So the answer is 8x^2+3x

Answer:

h = 2 and k = 6

Step-by-step explanation:

Since the lines intersect at (- 3, 1) then this is the solution to the system of equations.

That is x = - 3 and y = 1

Substitute these values into the equations and solve for h and k

hx - 4y = - 10

- 3h - 4 = - 10 ( add 4 to both sides )

- 3h = - 6 ( divide both sides by - 3 )

h = 2

Similarly

kx + 3y = - 15

- 3k + 3 = - 15 ( subtract 3 from both sides )

- 3k = - 18 ( divide both sides by - 3 )

k = 6

Answer:

  A.  4

Step-by-step explanation:

The common ratio will be the ratio of any adjacent pair of y-values:

  32/8 = 128/32 = 512/128 = 2048/512 = 4

Answer:

x=7 satisfy the equation, so it is the solution.

x=4 doesn't satisfy the equation so it is extraneous solution.

Step-by-step explanation:

The equation given is:

[tex]\sqrt{x-3}+5=x[/tex]

Adding -5 on both sides

[tex]\sqrt{x-3}=x-5[/tex]

Taking square on both sides

[tex](\sqrt{x-3})^2=(x-5)^2[/tex]

Now solving

[tex]x-3 = x^2 -10x+25\\Arranging\\x^2-10x-x+3+25=0\\x^2-11x+28=0\\Factorizingx^2-7x-4x+28=0\\\\x(x-7)-4(x-7)=0\\(x-4)(x-7)=0\\x-4=0 \,\,and\,\, x-7=0\\x=4 \,\,and\,\, x=7[/tex]

Verifying solutions:

Putting x=4 in the equation

[tex]\sqrt{x-3}+5=x[/tex]

[tex]\sqrt{4-3}+5=4[/tex]

[tex]\sqrt{1}+5=4[/tex]

[tex]1+5=4[/tex]

[tex]6\neq 4[/tex]

So, x=4 doesn't satisfy the equation so it is extraneous solution.

Now Putting x=7 and verifying

[tex]\sqrt{x-3}+5=x[/tex]

[tex]\sqrt{7-3}+5=7[/tex]

[tex]\sqrt{4}+5=7[/tex]

[tex]2+5=7[/tex]

[tex]7=7[/tex]

x=7 satisfy the equation, so it is the solution.

Answer:

= 7

Step-by-step explanation:

Answer:

x³ - 6x² + 18x - 10

Step-by-step explanation:

(f - g)(x) = f(x) - g(x)

= x³ - 2x² + 12x - 6 - (4x² - 6x + 4)

= x³ - 2x² + 12x - 6 - 4x² + 6x - 4 ← collect like terms

= x³ - 6x² + 18x - 10

Hello There!

-The Numbers Ordered From Least To Greatest-

-59   -41   -23   -11

The closer the number is to zero, it is going to be a bigger number than a number far away from zero.

Answer:

The vertex of the parabola is (2 , 2) ⇒ answer B

Step-by-step explanation:

* Lets revise the equation of a parabola

- The equation is in the form (x − h)² = 4p (y − k), where h and k are the

 vertex of the parabola

- If  p > 0, the parabola opens up  

- If p < 0, the parabola opens down

* Lets solve the problem

∵ The equation of the parabola is (x - h)² = 4p (y - k)

∵ The equation of the parabola is (x - 2)² = -12 (y - 2)

- By comparing the two equations

∴ 4p = -12 ⇒ divide both sides by 4

∴ p = -3 ⇒ -3 < 0

∵ p < 0

∴ The parabola opens down

- From the two equations

∴ h = 2 ⇒ the x-coordinate of the vertex

∴ k = 2 ⇒ the y-coordinate of the vertex

∴ The vertex of the parabola is (2 , 2)

The vertex of the given parabola (x - 2)^2 = -12(y - 2) is at the point (2, 2), which corresponds to Option B.

The vertex of the parabola defined by the equation (x - 2)^2 = -12(y - 2) can be found by identifying the point (h, k), where the equation fits the general form (x \\- h)^2 = 4p(y \\- k). Here, h and k represent the coordinates of the vertex, and p indicates the distance from the vertex to the focus or directrix. The given equation can be rearranged to match the general form with h = 2 and k = 2, making the vertex (2, 2). Hence, the correct answer is Option B.

Answer:

There is a 1 and 6 chance (16.666...%)