Rose and Tyler divided their 1.5kg of pizza
dough in the ratio 2:3.
How much did Rose receive?

The volume of the box as a polynomial in the variable x is x(12 - 2x)(7 - 2x)

The complete question is added as an attachment

From the attached image, we have:

Length = 12 - 2x

Width = 7 - 2x

Height = x

The volume is calculated as:

Volume = Length * Width * Height

Substitute the known values in the above equation

Volume = (12 - 2x) * (7 - 2x) * x

This gives

Volume = x(12 - 2x)(7 - 2x)

Hence, the volume of the box as a polynomial in the variable x is x(12 - 2x)(7 - 2x)

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There are 66 ways Kim can put the 10 identical lamps on the 3 identical tables

The given parameters are:

The combination involving identical objects is calculated using:

(n + r - 1)C(r - 1)

So, we have:

n + r - 1 = 10 + 3 - 1

Evaluate the sum

n + r - 1 = 13 - 1

Evaluate the difference

n + r - 1 = 12

Also, we have:

r - 1 = 3 - 1

Evaluate the difference

r - 1 = 2

So, we have:

(n + r - 1)C(r - 1) = 12C2

Apply the following combination formula:

nCr = n!/((n - r)!r!)

So, we have:

12C2 = 12!/((12 - 2)! * 2!)

Evaluate the difference

12C2 = 12!/(10! * 2!)

Expand the numerator

12C2 = 12 * 11 * 10!/(10! * 2!)

Evaluate the quotient

12C2 = 12 * 11/2!

Expand the denominator

12C2 = 12 * 11/2 * 1

Evaluate the product

12C2 = 132/2

Evaluate the quotient

12C2 = 66

Hence, there are 66 ways Kim can put the 10 identical lamps on the 3 identical tables

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The values of trigonometric functions sin(x/2) is [tex]\sqrt{\frac{7+4\sqrt{3}}{14}}[/tex], cos(x/2) is [tex]\frac{1}{\sqrt{14(7+4\sqrt{3})}}[/tex] and tan(x/2) is 7+4√3.

Given that the value of trigonometric function csc(x)=7 for 90°<x<180°.

We are given:

csc(x)=7 Where: 90° < x < 180°

This interval indicates that the angle x in the second quadrant and we know that at that quadrant sin(x) and CSC(x) functions are positive and all other trigonometric functions sign are negative.

Now:

sin(x)=1/csc(x)

sin(x)=1/7

Using the trigonometric identity sin²x+cos²x=1, we get

cosx=±√(1-sin²x)

cosx=±√(1-(1/7)²)

cosx=±√((49-1)/49)

cosx=±(4√3)/7

As x is in second quadrant.

Therefore, cosx=-(4√3)/7

consider the inequality, 90°<x<180°

Divide by 2, we get

45°<x/2<90°

This is the angle x/2 in the first quadrant and in that quadrant all functions sign are positive.

Substitute the value of cosx in half angle formula for sine function,

[tex]\begin{aligned}\cos x&=1-2\sin^2\left(\frac{x}{2}\right)\\ -\frac{4\sqrt{3}}{7}&=1-2\sin^2\left(\frac{x}{2}\right)\\ 2\sin^2 \frac{x}{2}&=1+\frac{4\sqrt{3}}{7}\\\sin \frac{x}{2}&=\pm\sqrt{\frac{7+4\sqrt{3}}{14}}\end[/tex]

As x/2 lies in first quadrant then [tex]\sin \frac{x}{2}=\sqrt{\frac{7+4\sqrt{3}}{14}}[/tex]

Again, Substitute the value of cosx in half angle formula for sine function,[tex]\begin{aligned}\sin x&=2\sin\left(\frac{x}{2}\right)\cos\frac{x}{2}\\ \frac{1}{7}&=2\sqrt{\frac{7+4\sqrt{3}}{14}}\cos\left(\frac{x}{2}\right)\\ \cos \frac{x}{2}&=\frac{1}{14\times\frac{\sqrt{7+4\sqrt{3}}}{\sqrt{14}}}\\\cos \frac{x}{2}&=\frac{1}{\sqrt{14(7+4\sqrt{3})}}\end[/tex]

Now find tan(x/2) as shown below, we get

[tex]\begin{aligned}\tan\frac{x}{2}&=\frac{\sin\frac{x}{2}}{\cos \frac{x}{2}}\\&=\frac{\sqrt{7+4\sqrt{3}}}{\sqrt{14}}\times \frac{\sqrt{14}\sqrt{7+4\sqrt{3}}}{1}\\&=7+4\sqrt{3}\end[/tex]

Hence, when trigonometric function csc(x)=7 for 90°<x<180° then sin(x/2) is [tex]\sqrt{\frac{7+4\sqrt{3}}{14}}[/tex], cos(x/2) is [tex]\frac{1}{\sqrt{14(7+4\sqrt{3})}}[/tex] and tan(x/2) is 7+4√3.

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Answer:

800÷100 = 8

65×8=520

[tex]\frac{520}{800}[/tex]

another way:

100%-65%=35%

35% = 0.35

800×0.35= 280

800-280=520

another way:

65% = 0.65

0.65×800=520

Hope it helped! :)

Answer:

1/2

Step-by-step explanation:

Since 50% is half the number of students it means that half of the students took the first bus which leaves the other half to take the 2nd bus

Answer:

$75

My answer might be a bit off since I'm not really sure what you mean by "Rs 80", which I interpreted as $80, but if my interpretation is wrong, you can still use all the same steps and you should get the correct answer

Step-by-step explanation:

So we can represent the price of each tumbler as the variable "P", since it's some unknown value we're solving for. Let's also just say that "T" is the total price that she paid for all of the tumblers.

Using this equation we can derive the following equation.

1000P = T

Since multiplying the price of each glass tumbler times the price of one glass tumbler should equal the entire price.

Now she only sold 900 of them, since 100 were broken, and she sold them each for 80. So knowing this we can find how much she made in total from selling the remaining 900 glass tumblers

900 * 80 = 72,000

Now if she made a loss of 4%, that means the total money she made back, is only 96% the amount of money she paid for the product. The reason for this is (100-4)% represents a 4% loss.

Remember, how T represents the entire price, well we know that 72,000 represents 96% of it's value. To find what x% is of some number, you generally convert the percentage into a decimal by dividing by 100, so to find x% of some variable "a" you generally use the following equation: [tex]a*\frac{x}{100}[/tex] where the value of this expression will be equal to x% of a.

So let's convert 96% to decimal form: [tex]\frac{96}{100} = 0.96[/tex]. Now if we multiply this decimal 0.96 by T, we should get 72,000 since the 72,000 represents 96% of the original value

[tex]0.96T = 72,000[/tex]

To find the original value of T, we simply divide both sides by 0.96

[tex]T = 75,000[/tex]

So now that we know the original total price, we can use the original equation we derived to solve for P, which represents the price of each individual tumbler.

Original Equation

[tex]1000P = T[/tex]

Substitute 75,000 as T

[tex]1000P = 75,000[/tex]

Divide both sides by 1,000

[tex]75=P[/tex]

This means she sold each for 75

#1

The unit is pounds

#2

So

#3

We shall use cups

#4

We should use pints

Answer:

1. pounds (lb)

2. pints (pt)

3. teaspoon (tsp)

4. cups (c)

Step-by-step explanation:

Liquid

128 fl oz = 16 cups = 8 pints = 4 quarts = 1 gallon

Mass

32000 ounces = 2000 pounds = 1 ton

1.  The best US standard unit in which to measure pumpkin with a mass of 1.2 kg would be pounds (lb).

⇒ 1 kg ≈ 2.205 lb

⇒ 1.2 kg ≈ 1.2 × 2.205 = 2.65 lb

2. The best US standard unit in which to measure stock with a volume of 1.5 L would be pints (pt).

⇒ 1 L ≈ 2.133 pt

⇒ 1.5 L ≈ 1.5 × 2.113 = 3.17 pt

3. The best US standard unit in which to measure sugar of 5 mL would be teaspoon (tsp).

⇒ 5 mL = 5 g ≈ 1 teaspoon

4.  The best US standard unit in which to measure yogurt with a volume of 0.25 L would be cups (c).

⇒ 1 L ≈ 4.167 c

⇒ 0.25 L ≈ 0.25 × 4.167 =  1.04 c

This means that after 0.5 hours, 259.81 milligrams of the medicine remain on the patient's body.

We know that the exponential function defined by:

[tex]m(h) = 300*(3/4)^h[/tex]

Represents the amount of a mediciene, in milligrams, after a number of hours h.

We want to see what does m(0.5) represent. This is the exponential function evaluated in h = 0.5

Then, it just represents the amount of medicine, in miligrams, in a patient's body present 0.5 hours after the medicine was administered.

Replacing h = 0.5 we get:

[tex]m(0.5) = 300*(3/4)^{0.5} = 259.81[/tex]

This means that after 0.5 hours, 259.81 milligrams of the medicine remain on the patient's body.

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Direct variation is modeled by the equation y = kx, where k is a constant and x and y vary based on the other's value.

We'll first need to find k, also known as the constant of variation, using our given values of x and y.

6 = k * -7

k = -6/7

Now that we have k, we can plug it in and substitute other values in for x or y. In this case, we'll plug in 4 for x and solve for y.

y = -6/7x

y = -6/7 * (4)

y = -24/7

y = -24/7

Hope this helps!

Answer:

y = -24/7

Step-by-step explanation:

We can use proportions for this question since y varies directly with x. This means that if x changes, y changes along with the x, and vice versa.

When y = 6, x = -7, so the proportion will be 6 : -7.

We need to find the y when x is 4, so our equation will be:

6 : -7 = y : 4

Since the proportion will be the same.

Next, we multiply the inner two numbers, and the outer two numbers, saying that the values are the same.

-7y = 24

y = 24 / -7

y = - 24/7

So y = -24/7 will be our answer!

+ Since the '-' is already written down, the top box will contain 24, and the bottom box will contain 7.

For triangle DEF,

m∠D = 21°

m∠E = 87°

DF = 16

For triangle RST,

m∠S = 68°

m∠T = 57°

Simple polygons with three sides and three internal angles make up triangles. It is one of the fundamental geometric shapes in which the three vertices are connected to one another.

For ΔDEF, it is given that, m∠F = 72°, DE=15,EF=17.

By the law of cosines,

side DF=(a2+b2﹣2abcosγ)1/2

DF=16

Similarly,

m∠D = 21°

As the sum of angles of triangle is 180,

m∠E = 87°

For ΔRST, it is given that, m∠R = 55°, RS=17,RT=9.

By the law of cosines,

side ST=(a2+b2﹣2abcosγ)1/2

ST=16

Similarly,

m∠S = 68°

As the sum of angles of triangle is 180,

m∠T = 57°

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The correct powers of x are not displayed in several of the goods.

Algebra tiles are mathematical manipulatives that help pupils better comprehend algebraic thinking and its ideas. These tiles have shown to give beginning algebra pupils in elementary, middle, high, and college concrete models.

Blocks called algebra tiles can be used to symbolize constant, linear, and quadratic terms. Small yellow squares stand in for constant blocks, green rectangles for linear blocks, blue squares for quadratic blocks, and red squares for negative sides for all other types of blocks.

Future:

The image shows,

3x(2x - 1) = 6x² - 3x

This should be the appropriate representation on the tile:

_____+x _____ +x _____ +x

+x _ +x² ______+x² ______+x²

|

+x__ +x² _____ +x² ______+x²

|

- __ -x ______ -x _______-x

+6x² - 3x

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If I discovered two numerical values that were twice as big as the next highest value, I would expunge them because they can affect the final results.

A numerical data is also referred to as a quantitative data and it can be defined as a data set that is primarily expressed in numbers only.

This ultimately implies that, a numerical data is a data set consisting of numbers rather than words.

An outlier can be defined as a numerical value that is either unusually too small or large (big) in comparison with the overall pattern of the numerical values contained in a data set.

Assuming I am counting the number of expert tutors on Brainly and I discovered two numerical values that were twice as big as the next highest value, I would expunge them because they can affect the final results.

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Step-by-step explanation:

abx^2-aby^2+xya^2-xyb^2

abx^2+xya^2-aby^2-xyb^2

ax(bx+ya)-yb(ay+xb)

ax(bx+ya)-yb(xb+ay)

(ax-yb) (bx+ya)

Answer:

0.1 cases

Step-by-step explanation:

100(1-0.90)^3

100(0.10)^3

100(0.001)

0.1

For a sample of size 300 from a population with the population proportion, the μphat and σphat are 0.0287.

A share is an equation in which ratios are set equal to each other. for example, if there may be 1 boy and three women you can write the ratio as 1 : 3 (for each boy there are 3 women) 1 / 4 are boys and three / 4 are girls.

The formula for proportion is components /complete = percent/100. This system can be used to locate the percentage of a given ratio and to locate the lacking value of an element or an entire.

A proportion is generally written as equal fractions. for example: note that the equation has a ratio on each facet of the same signal. Every ratio compares the equal units, inches, and feet, and the ratios are equivalent due to the fact the devices are regular and equal.

Given 300 2   and p 0.45

p = 0.45 Up

and Õp-sqrt(p(1-p)/n) sqrt(0.45 * 0.55/300) sqrt(0.000825) =0.0287

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Answer:

B

Step-by-step explanation:

for the lines to be parallel , then

8x - 14 and 2x + 54 are same- side interior angles and sum to 180°, that is

8x - 14 + 2x + 54 = 180

10x + 40 = 180 ( subtract 40 from both sides )

10x = 140 ( divide both sides by 10 )

x = 14

The domain of the exponential function shown in the graph is -oo < x < oo

The function on the graph is an exponential function.

The domain is the set of x values the function can take

From the graph, we have the following x values

This means that the domain of x in the graph is -oo < x < oo

Hence, the domain of the exponential function shown in the graph is -oo < x < oo

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Answer:

[tex]y = \sqrt{x+25} + 5[/tex]

Step-by-step explanation:

Swap x and y

x = y² – 10y

Add 25 to each side to complete the square

x + 25 = y² – 10y + 25

Factor

x + 25 = (y – 5)²

Take the square root of each side

[tex]\sqrt{x+25}[/tex] = y – 5

Add 5 to both sides

[tex]\sqrt{x+25}[/tex] + 5 = y

Answer:

8

Step-by-step explanation:

Kari has 2 choices for jackets and 4 choices for jumpsuits. We'll multiply those together to find the number of options she has.

Since the numbers are very small, we can grind out this same number (but be organized):

Jean/white

Jean/tan

Jean/green

Jean/black

Leather/white

Leather/tan

Leather/green

Leather/black

These are the eight choices.

The distance the bird has flown by the time Alice and Bob meet is 40 feet.

Distance is a measurement of time and speed.

The distance equals speed multiplied by time.

Distance between Alice and Bob = 1,000 feet

Distance between the bird and Bob = 1,000 feet

Speed of Alice and Bob = 10 feet per second, respectively

The combined speed of Alice and Bob = 20 feet per second

Since the two are running directly toward each other, the distance each will cover at the meeting point is 50 feet (1,000/20)

The time covered at the meeting point = 20 seconds (1,000/50)

Speed of the bird = 20 feet per second

The distance covered by the bird towards Bob at their meeting point is 40 feet (20 feet x 20 seconds)

Thus, the total distance covered by the bird at the meeting point is 40 feet.

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Lakisha's total job benefits per year are (D) $58,196.

To find  Lakisha's total job benefits:

If Lakisha's employer pays $2,150 in health insurance and $86 in life insurance per year, and she also gets $3,520 in paid time off per year, then Lakisha's total job benefits per year are equal to:

Total Benefits = Health Insurance + Life Insurance + Paid Time Off + Annual Gross Pay

Therefore,  Lakisha's total job benefits per year are (D) $58,196.

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Answer The answer is D

Step-by-step explanation:

I got it correct on edg

Juan's home is about 12 kilometers from Adam's.

In the study of mathematics and science, measurement is the fundamental idea. By quantifying an object's or event's qualities, we can compare them to those of other objects or occurrences. When discussing the division of a quantity, the phrase "measurement" is most frequently employed.

The distance between Adam's and Juan's residences on the map in centimeters is simply multiplied by the number of kilometers that each centimeter on the map represents, which in this case is 6, to determine how far Adam's house is from Juan's.

2 * 6 = 12

Which is our response.

Juan's home is about 12 kilometers from Adam's.

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Check the picture below.

so the lateral area of the pyramid is really just the area of four triangles whose base is 10 and height is also 10, now, we're excluding the bottom because that's not lateral area.

[tex]\stackrel{\textit{area of four triangles}}{4\left[\cfrac{1}{2}(\stackrel{b}{10})(\stackrel{h}{10}) \right]}\implies 2(100)\implies \text{\LARGE 200}~ft^2[/tex]

Answer:

 [tex]h(x)=7(1.3)^x[/tex]

Step-by-step explanation:

Since this is an exponential equation we will use

[tex]h(x)=a(b)^x[/tex]

[tex]a[/tex] Is your starting value, 7

[tex]b[/tex] Is your percentage of change, remember its not 0.3, as that would hint the population is decreasing by thirds exponentially, instead we will use 1.3 as our percent of change, as the 1 maintains the original value and the 0.3 adds 30%, now all we have to do is put it all together!

[tex]h(x)=7(1.3)^x[/tex]

Answer:

84

Step-by-step explanation:

Multiply 35 by 2.5

Answer:

75 windows

Step-by-step explanation:

35 ---- 7

x ----- 15

[tex]x=\frac{(35)(15)}{7} =75[/tex]

Hope this helps

The arc length of the circle exists 846.65922 cm.

A unit circle by definition contains a radius of 1 unit.

We have to estimate the length of the arc subtended by an angle of [tex]7\pi/2[/tex] radians.

arc length = radius [tex]*[/tex] angle

s = r[tex]$ * \theta[/tex]

Where s be the arc length

r be the radius of the circle

[tex]\theta[/tex] be the angle measured in radians

arc length = 77cm[tex]$*7\pi/2[/tex]

arc length = 77 [tex]*[/tex] 7(3.14) / 2

arc length = 846.65922 cm

Therefore, the arc length of the circle exists 846.65922 cm.

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Answer:

1. ∠1 ≅ 6 : Given

2. ∠3 ≅ ∠ 4 : Vertical Angles Congruence Property

3. ∠2 ≅ ∠5 : Corollary III of Theorem 19 : If two angles of two triangles are congruent, then the third angle of both triangles are congruent.

Step-by-step explanation: For ∠3 ≅ ∠4, the angles are in a diagonal placement, meaning they are vertical angles. Vertical angles are always congruent.

Lookimg at one of the problems you posted earlier, the Corollary III of Theorem 19 given, states that if two angles are congruent in both triangles, then the third angle is congruent in both triangles. Since we have 2 angles already congruent to 2 other angles, ∠2 and ∠5 must be congruent.

Hope this helped!