Kayla's recipe needs 4 cups of milk and 6 cups of grated cheese. What is the ratio of the number of cups of milk to the number of cups of grated cheese in the recipe?

Answer:

Inequality Form: x > −8

Interval Notation: (−8, ∞)

Step-by-step explanation:

−2 < x/4

Rewrite so x is on the left side of the i nequality.

x/4 > −2

Multiply both sides of the equation by 4.

x > −2 ⋅ 4

Multiply −2 by 4.

x > −8

The result can be shown in multiple forms.

Inequality Form:

x > −8

Interval Notation:

(−8, ∞)

Venn Diagram

Venn diagram is use in answering word problems that involve two sets or three sets. It is the principal way of showing sets diagrammatically. This method consists of entering the elements of a set into a circle or circles.

To represent the given results, let us analyze the problem.

The problem above involves three sets: cats, dogs and birds. - Meaning, we need to make three circles. Then label each with cats, birds and dogs respectively.

10 students liked cats and birds but not dogs - Write 10 in the overlap of cats and birds.

6 students liked cats and dogs but not birds - Write 6 in the overlap of cats and dogs.

2 students liked dogs and birds but not cats - Write 2 in the overlap of birds and dogs.

2 students liked all three pets - Write 2 in the overlap of birds, cats and dogs.

9 students liked dogs only - Write 9 inside the dog part.

10 students liked cats only - Write 10 inside the cat part.

1 student liked birds only - Write 1 in inside the bird part.

I'll attach the venn diagram.

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Answer: 1,2,3,4

Step-by-step explanation:

The domain consists of every x value

The original number was 1.85.

According to the question,

We have the following information:

Alex was thinking of a number. Alex doubles it, then adds 20 to get an answer of 22.7.

Now, in this case, let's take the original number to be x.

So, we have the following expression when something was added to the number after doubling it:

2x+20 = 22.7

Subtracting 20 from both sides of the equation:

2x = 22.7-20

2x = 2.7

Dividing by 2 on both sides of the equation:

x = 2.7/2

x = 1.85

Hence, the original number Alex was thinking of was 1.85.

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Answer:

Total Number of students taking Math and History and not music are 68.

Number of students who took both math and history at the same time is 6.

Step-by-step explanation:

History = 30

Math = 32

Music= 33

Math and Music= 9

History and Music= 13

History and Music and Math = 2

History but not math = 14

We have to find students taking history and math but not music.

Total number of students = 125

From the figure  number of students taking Math and History and not music are

=30+6+32= 68

Number of students who took both math and history at the same time is 6.

The formula for the final velocity,\(v_{f}\) , in terms of initial velocity, vi, acceleration, a, and time, t is given by \(V_{f}=at+V_{i}\)

A =\((V_{f}-V_{i} )/t\)  You can put \(1\) under A and then cross multiply.

\(at =V_{f} -V_{i}\)

Get \(V_{f}\)  by adding  \(V_{i}\) in both sides of the equation.

\(at+V_{i} =V_{f}\)

                                                OR

The final speed \(V_{f}\) in terms of other parameters is given by the relation \(V_{f}\)\(=at+V_{i}\)

How to calculate the acceleration of an object?

Mathematically, acceleration is calculated using this formula:

\(a=(V_{f}-V_{i} )/t\)

Where:

Making \(V_{f}\) the subject of the formula, we have:

\(at =V_{f} -V_{i}\)

\(V_{f} =V_{i} +at\)

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Answer:

8-10 feet

Step-by-step explanation:

If the length of the carpet is two more than the width, the width can be expressed as x and the length can be expressed as x+2. This means that the area(x^2+2x) must be greater than 48 but no less than 80.

Now we can solve for both the maximum and minimum cases:

x^2+2x=48, x^2+2x-48=0, now we can factor, (x+8)(x-6)=0, and now we can use the Zero Product Property to find x=-8;x=6. Since we cant have negative width, x at least has to be equal to 6.

x^2+2x=80,x^2+2x-80=0, now we can factor, (x+10)(x-8), and now using the Zero Product Property to find x=-10;x=8, and since it must be positive, at most x can equal 8.

Now since the length is two more than the width, x, you add two to both of these values and get a range of 8-10 feet.

Answer:

the persson who aswered this got it right ( up there or down there )

Step-by-step explanation:

There are 472 more buttons bought by Vance than beads.

For the stated question table is made.

So,

Total number of beads bought by Vance = Number of beads(2 packages of large beads) + Number of beads(1 package of medium beads).

= (2 × 96) + (1 × 64)

= 2 × (90 + 6) + 64

= (2 × 90) + (2 × 6) + 64

= 180 + 12 + 64

= 256 beads

Now,

Total number of buttons bought by Vance = Total number of buttons (2 packages of large buttons) + Number of buttons (2 packages of medium buttons)

= (2 × 56) + (2 × 38)

= 2 × (50 + 6) + 2 × (30 + 8)

= (2 × 50) + (2 × 6) + (2 × 30) + (2 × 8)

= 100 + 12 + 600 + 16

= 728 buttons

Thus,

Difference for the number of buttons and beads

= 728 – 256

= 472 beads

So,

Therefore, there are 472 more buttons bought by Vance than beads.

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The largest open interval where the function f(x) = 1/(x^2+1) is increasing is (-∞, 0) ∪ (0, ∞). On this interval, the function is increasing from negative infinity to zero and from zero to positive infinity.

Explanation:

To find where the function is increasing, we need to find where the first derivative of the function is positive. Taking the derivative of f(x), we get:

f'(x) = (-2x) / (x^2 + 1)^2

The denominator of this expression is always positive, so the sign of f'(x) is determined by the numerator. The numerator is negative for x < 0 and positive for x > 0. Therefore, f(x) is decreasing on (-∞, 0) and increasing on (0, ∞).

We also need to check the endpoints of these intervals to make sure that the function is increasing on the entire interval. As x approaches negative infinity, the function approaches 0, and as x approaches positive infinity, the function approaches 0. Therefore, the function is increasing on (-∞, 0) ∪ (0, ∞).

In summary, the largest open interval where the function f(x) = 1/(x^2+1) is increasing is (-∞, 0) ∪ (0, ∞). On this interval, the function is increasing from negative infinity to zero and from zero to positive infinity.

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Answer:

-3p3+ 5p2- 2p -p3 -8p2-15p

-3p3-p3+5p2-8p2-2p-15p

4p3-3p2-17p

Answer:

Step-by-step explanation:

Measure of an inscribed angle intercepted by an arc is half of the measure of the arc.

From the picture attached,

m(∠A) = \(\frac{1}{2}m(\text{arc BD})\)

           = \(\frac{1}{2}[m(\text{BC})+m(\text{CD}]\)

           = \(\frac{1}{2}[55^{\circ}+145^{\circ}]\)

           = 100°

m(∠C) = \(\frac{1}{2}[(360^{\circ})-m(\text{arc BCD})]\)

           = \(\frac{1}{2}(360^{\circ}-200^{\circ})\)

           = 80°

m(∠B) + m(∠D) = 180° [ABCD is cyclic quadrilateral]

115° + m(∠D) = 180°

m(∠D) = 65°

m(arc AC) = 2[m(∠D)]

m(arc AB) + m(arc BC) = 2(65°) [Since, m(arc AC) = m(arc AB) + m(arc BC)]

m(arc AB) + 55° = 130°

m(arc AB) = 75°

m(arc ADC) = 2(m∠B)

m(arc AD) + m(arc DC) = 2(115°)

m(arc AD) + 145° = 230°

m(arc AD) = 85°

Answer:11.5

Step-by-step explanation:I’ve done this in a test before and that is the correct AnSwEr

\( \: \: \: \: \: \: \)

\( = \frac{1289}{200} \)

see the attachment for explanation

Answer:

top right

Step-by-step explanation:

Answer:

Step-by-step explanation:

The central angle is twice the inscribed angle (same arc).

The inscribed angle forms a supplementary angle with the missing one (opposite angles of the cyclic quadrilateral).

The missing angle is:

To find the probability of a company having both a website and a section in the newspaper, we can use the formula for conditional probability.

Let's denote the events as follows:
A: A company has a section in the newspaper
B: A company has a website

We are given the following probabilities:
P(A) = 0.43 (Probability of a company having a section in the newspaper)
P(B|A) = 0.84 (Probability of a company having a website given that it has a section in the newspaper)

The probability of both events A and B occurring can be calculated as:
P(A and B) = P(A) * P(B|A)

Substituting in the values we have:
P(A and B) = 0.43 * 0.84
P(A and B) = 0.3612

Therefore, the probability of a company having both a website and a section in the newspaper is 0.3612 or 36.12%.

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Answer:

306

Step-by-step explanation:

101+102+103=306

Answer:

71,400

Step-by-step explanation:

1) Given, the crops and their weight:

apples = 40 lbs

sweet potatoes = 60 lbs

tangerines = 40 lbs

summer squash = 65 lbs

2) The Truck is carrying:

10² bushels of sweet potatoes = 60 x 100 = 6,000 lbs

10¹ bushels of tangerines = 40 x 10 = 400 lbs

10³ bushels of summer squash = 65 x 1000 = 65,000 lbs  

3) All together, the total weight of the crops are:

6,000 lbs + 400 lbs + 65,000 lbs = 71,400 lbs.

The total weight of the crops is 71,400 lbs.

Answer:

$48

Step-by-step explanation:

given

1 ticket -----> costs $8

therefore,

6 tickets ----> costs $8 x 6 = $48

hope this helps

edit: spelling correction

Answer:

This would be $48.

Step-by-step explanation:

1 ticket costs $8.

6 tickets costs 6 * 8 = $48.

The cost for 6 movie tickets would be $48 dollars.

hope this helps.

Answer:

Subtracting a negative number from a negative number – a minus sign followed by a negative sign, turns the two signs into a plus sign. So, instead of subtracting a negative, you are adding a positive. Basically, - (-4) becomes +4, and then you add the numbers.

Step-by-step explanation:

- 4 ( - - ) 2 =

this turns in a positive number.

The shape of the cross section of a right rectangular pyramid sliced vertically (down) by a plane not passing through the vertex of the pyramid m is a trapezoid. (A)

This is because when a pyramid is sliced vertically, the resulting cross section is always a two-dimensional representation of the pyramid's base.

Since the base of a right rectangular pyramid is a rectangle, slicing it vertically will result in a trapezoid-shaped cross section. The top and bottom sides of the trapezoid will be parallel, and the other two sides will be slanted.

In a right rectangular pyramid, the vertex m is located directly above the center of the rectangle base. When a plane is passed through this vertex, it will result in a triangular cross section. However, when a plane is passed through a different point, as described in the question, it will result in a trapezoidal cross section.(A)

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It saves time, doesn't need to be changed if a row or column is added to the range, and adjusts the range when the function is copied to another cell.

Based on the values in another column, we'll discover how to add up a column of numerical data. We are attempting, for instance, to assess product sales based on the typical customer rating. Thus, each of our products has an average rating of 9.8, 7.2, 6.1, and so on because customers score our products on a scale of 1 to 10. The sales totals for goods with ratings of 9 to 10, 7 to 8, and so forth should be calculated.

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Triangle RST is rotated 180° about the origin, and then translated up 3 units.  Then , ΔRST ≅ ΔBAC

We know that  To rotate a figure 180 degrees, you will need to apply the rule (x, y) → (-x, -y).

Thus, The coordinates of triangle RST becomes

R (1,1) → R'(-1,-1)

S (3,4) → S'(-3,-4)

T(-5,0) → T'(5,0)

Also ΔRST after rotation is translated up 3 units. , so we apply the rule (x,y)→(x,y+3)

R'(-1,-1)→R"(-1,-1+3)=R"(-1,2)→ B

S'(-3,-4) → S"(-3,-4+3) = R"(-3,-1) → A

C'(-5,0) → C"(-5,0+3) → C"(-5,3) → C

As rotation and translation both are rigid transformation that maps only congruent figures.

Therefore, ΔRST ≅ Δ BAC

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\(\frac{1}{4}\)  fraction cups of flour will go into each of the new crusts .

let x be the total amount of flour used to makes 30 pie crusts each day

and it is given that each crusts requires  \(\frac{1}{6}\) cup of flour .

so total flour required = \(\frac{1}{6} * 30\) = 5 cups

so we need 5 cups of flour to bake 30 pie crusts

so, x=5 cups

now using this total amount of flour we have to find how cups of flour each pie crusts requires

let each pie crusts requires  \(\frac{1}{y}\) cups of flour .

total flour used in this case = \(\frac{1}{y} * 20\)

and \(\frac{1}{y} *20\) must be equal to 5

so \(\frac{1}{y} *20 = 5\)   => y = 20 /5 =4

so y = 4

so we need  \(\frac{1}{4}\) fraction cups of flour in 2nd case .

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The real numbers with decimal representations consisting of all 1s are non-existent.

To determine if a real number with a decimal representation consisting of all 1s exists, we can examine the nature of such a number. Let's assume there is a number "x" that fits this criteria. Its decimal representation would be 1.1111..., where the digit 1 repeats indefinitely.

We can attempt to find the value of this number by performing a calculation:

x = 1.1111...

10x = 11.1111...

Now, if we subtract the equation for x from 10x, we can eliminate the repeating decimal:

10x - x = 11.1111... - 1.1111...

9x = 10

x = 10/9

Thus, we find that the value of x is 10/9. However, the number 10/9 does not have a decimal representation consisting of all 1s. Its decimal representation is a repeating decimal, where the digit 1 repeats indefinitely: 1.1111....

After careful examination and calculation, we can conclude that there are no real numbers with decimal representations consisting solely of 1s. The closest representation to a repeating decimal of all 1s is the fraction 10/9, which has a repeating decimal representation of 1.1111....

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Answer:

M<2= 95° M<3=85° M<4=95°

Step-by-step explanation:

Remember that the angles could be either supplementary or congruent angles so since angle 2 and 1 are supplemental take 85 and subtract it from 180. So 2 =95 Now the congruent angle for angle 2 is 4 so 4=95. Applying the same property angle 1 is congruent to 3 so 3=85

Hope this helps!

Answer:

∠2 = 95°

∠3 = 85°

∠4 = 95°

Step-by-step explanation:

∠85° and ∠3 are vertical angles therefore they are equal to each so we know that ∠3 = 85°.

In order to find ∠2, we need to notice that ∠85° and ∠2 are supplementary angles (this means that they add up to 180°). So now we can make an equation...

∠2 = 180° - 85°

∠2 = 95°

To find ∠4 we use the same logic as for ∠2 and we get that ∠4 = 95°

The measure of angles are

The length of the hypotenuse of the right triangle = 11 inches

The length of the one leg = 10 inches

Then the length of the other leg is the square root of the sum of the hypotenuse square and one leg square

Then the equation will be

The length of the other leg = \(\sqrt{11^2-10^2}\)

= \(\sqrt{121-100}\)

= 4.58 inches

Therefore AC = 11 inches

AB = 10 inches

BC = 4.58 inches

The angle B = 90 degrees

Consider the angle A

cos θ = Adjacent side / hypotenuse

cos θ = 10 /11

θ = 24.61 degrees

Consider the angle C

cos θ = Adjacent side / Hypotenuse

cos θ = 4.58 / 11

θ = 65.39 degrees

Hence, the measure of angles are

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The length of the midsegment of trapezoid ABCD is 6.23 units.

In this question, we have been given a trapezoid ABCD with vertices A(0,0), B(2, 5), C(3, 5) and D(8, 0)

We need to find the length of the midsegment of trapezoid.

We know that the length of the midsegment is one-half the sum of the lengths of the bases.

The length of base AB,

AB = √(2 - 0)² + (5 - 0)²

AB = √4 + 25

AB = √29

AB = 5.38

The length of base CD would be,

CD = √(8 - 3)² + (0 - 5)²

CD = √5² + (-5)²

CD = √25 + 25

CD = 5√2

So, the length of the midsegment would be,

l = 1/2[(5.38 + 5√2)]

l = 6.23

Therefore, the length of the midsegment of trapezoid ABCD is 6.23 units.

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