Mia is designing a cake for a birthday party. She plans for a total of 15 guests, each of whom may eat a piece of cake that has a volume of 8 cubic inches. Which of the following cakes would provide enough cake for each guest to have one piece of cake, with the least amount left over? (1 point) Square cake: side = 7 in., height = 3 in. Round cake: diameter = 7 in., height = 3 in. Round cake: diameter = 9 in., height = 2 in. Rectangular cake: length = 7 in., width = 10 in., height = 2 in

Answer:

A.) -2

Step-by-step explanation:

I took a test and got it right

The equation of the line in slope-intercept form that passes through the point (-6, -5) with a slope of 6 is y = 6x + 31. The correct answer is option (D).

Given that the line passes through the point (-6, -5) with a slope of 6, we can plug these values into the equation to find the y-intercept (b).

Using the point-slope form of the equation:

y - y₁ = m(x - x₁)

Substitute (-6, -5) and the given slope (m = 6):

y - (-5) = 6(x - (-6))

y + 5 = 6(x + 6)

Now, let's simplify the equation:

y + 5 = 6x + 36

To get the equation in slope-intercept form (y = mx + b), isolate y:

y = 6x + 36 - 5

y = 6x + 31

Thus, the correct answer is option (D).

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Step-by-step explanation:

8. As the name implies, a box-and-whisker plot looks like a box with two whiskers.  The box is the middle 50%.  The whiskers are the bottom 25% and the top 25%.

First, we need to sort the numbers from smallest to largest.  Starting with Set A:

Set A = {56, 57, 62, 68, 71, 82, 84, 92, 97, 101, 103, 106}

Now we find the median of the set, or the middle number.  Set A has 12 data points.  Since 12 is an even number, the median will be the average of the 6th and 7th numbers.

M = (82 + 84) / 2 = 83

Next, we find the median of the lower half.  There are 6 numbers in the lower half, so the median is the average of the 3rd and 4th numbers.

Ml = (62 + 68) / 2 = 65

Now we find the median of the upper half.  Again, there are 6 numbers in the upper half, so the median will be the average of the 3rd and 4th numbers.

Mu = (97 + 101) / 2 = 99

So the left whisker is from 56 to 65.

The box is from 65 to 99.

The right whisker is from 99 to 106.

Don't forget to mark the median, 83.

Repeat for Set B.

Set B = {36, 37, 42, 46, 48, 56, 58, 63, 69, 72, 75, 78}

M = (56 + 58) / 2 = 57

Ml = (42 + 46) / 2 = 44

Mu = (69 + 72) / 2 = 70.5

So the left whisker is from 36 to 44.

The box is from 44 to 70.5.

The right whisker is from 70.5 to 78.

The median is 57.

By graphing both on the same number line, we can easily compare them.

9. To make a dot plot, draw a number line starting from the smallest number and ending at the largest number.  For each number, draw a dot every time the number appears in the set.  For example, the number 3 appears twice in Set A, so draw two dots on 3.  You may find it helpful to sort the data first.

10. Draw a dot plot of the set to determine the shape.

Answer:

Age

Step-by-step explanation:

it is about them.

If it were how many siblings they have it, then would not be just about them.

If it were there sport it would not be about them it would also be about sports

4.2 x 10^8 is  2*10^6  times the value of 2.1 x 10^2 when division is performed.

The concept that will be used to solve the question is division operation.

We were given 4.2 x 10^8 which is greater than  2.1 x 10^2

The operation can be expressed as :

4.2 x 10^8 =( n *2.1 x 10^2)

where n = the number of times that 4.2 x 10^8  is greater than 2.1 x 10^2

Then make n the subject of the formular which is

n = 4.2 x 10^8/2.1 x 10^2

n = 2*10^6

Therefore, the values of 4.2 x 10^8 is greater than 2.1 x 10^2 in 2*10^6 times.

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Answer:

Step-by-step explanation:

If the diameter is 4 meters, then the radius has to be 2 because the radius is half of the diameter.

Answer:

Chloe is making a mural. She spends 6 hours designing it.

She paints it during 3 sessions. Each session is the same

number of hours long. In all, Chole spends 24 hours making

the mural.

Step-by-step explanation:

Answer:

Each painting session is 6 hours long

Step-by-step explanation:

You can represent the situation with an equation.

3h+6=24

3h+6/3=24/3

h+2=8

h+2-2=8-2

h=6

Certainly! The problem can be solved using the Pythagorean theorem,

which states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

In this case, the ladder acts as the hypotenuse, and we need to find the length of the vertical side (height) it reaches up the wall.

The ladder forms the hypotenuse, and its length is given as 12 meters. The distance from the foot of the ladder to the base of the wall represents one side of the triangle, which is 4.5 meters.

By substituting the given values into the Pythagorean theorem equation: (12m)^2 = h^2 + (4.5m)^2, we can solve for the unknown height 'h'.

Squaring 12m gives us 144m^2, and squaring 4.5m yields 20.25m^2. By subtracting 20.25m^2 from both sides of the equation, we isolate 'h^2'.

We then take the square root of both sides to find 'h'. The square root of 123.75m^2 is approximately 11.12m.

Therefore, the ladder reaches a height of approximately 11.12 meters up the wall.

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Answer:

14/5 cm3 ??

Step-by-step explanation:

Answer:

Volume V = 18.735 m3

Step-by-step explanation:

hope this helps

Answer:

No

solution

Step-by-step explanation:

Step one:

given the expression

\((v + 7)^2 +3 = 43\)

opening the bracket we have

\((v+7)(v+7)+3= 43\\\\v^2+7v+7v+49=43\\\\\)

collect like terms

\(v^2+14v+49=43\\\\v^2+14v+49-43=0\\\\V^2+14v-6=0\)

Given statement solution is :- It  would cost $680 to install tile in the dining room and $315 to install carpet in the bedroom.

To find the cost of installing tile in the dining room and carpet in the bedroom, we need to calculate the areas of both rooms first.

Given:

Every 2 centimeters on the floor plan represents 1 meter of the house.

Dining Room:

On the floor plan, the dining room is 8 cm by 10 cm.

Converting this to meters, the dimensions of the dining room are 8 cm / 2 = 4 meters by 10 cm / 2 = 5 meters.

The area of the dining room is 4 meters * 5 meters = 20 square meters.

Bedroom:

On the floor plan, the bedroom is 6 cm by 10 cm.

Converting this to meters, the dimensions of the bedroom are 6 cm / 2 = 3 meters by 10 cm / 2 = 5 meters.

The area of the bedroom is 3 meters * 5 meters = 15 square meters.

Now, let's calculate the costs.

Cost of Tile:

The cost of installing tile is $34 per square meter.

The area of the dining room is 20 square meters.

Therefore, the cost of installing tile in the dining room is 20 square meters * $34/square meter = $680.

Cost of Carpet:

The cost of installing carpet is $21 per square meter.

The area of the bedroom is 15 square meters.

Therefore, the cost of installing carpet in the bedroom is 15 square meters * $21/square meter = $315.

Therefore, it would cost $680 to install tile in the dining room and $315 to install carpet in the bedroom.

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Answer:

its 9

Step-by-step explanation:

Hope this answer helps.

Answer:

true

Step-by-step explanation:

trust me

Answer:

\(128\pi\)

Step-by-step explanation:

Formula of cylinder: \(\pi r^{2} h\)

\((\pi )(4^{2}) (8)\)=128pi

Step-by-step explanation:

law of sine :

a/sin(A) = b/sin(B) = c/sin(C)

a, b, c are the sides, A, B, C are the corresponding opposite angles.

so,

16/sin(90) = x/sin(30)

16/1 = x/0.5

0.5 × 16 = x

x = 8 units

Pythagoras now gets us half the baseline (and therefore the full baseline) :

16² = x² + (baseline/2)² = 8² + (baseline/2)²

256 = 64 + baseline²/4

192 = baseline²/4

768 = baseline²

baseline = sqrt(768) = sqrt(256×3) = 16×sqrt(3) units

the area of a triangle is

baseline × height / 2

in our case

16×sqrt(3) × 8 / 2 = 16×sqrt(3) × 4 = 64×sqrt(3) units² =

= 110.8512517... units²

Answer:

A

Algebra For what values of the variables must ABCD be a parallelogram?

B

23. A 2y + 2 B 24. B

(3x + 10)

(8x + 5)º

3x + 6

54°

D

С

D

A

Зу - 9 с

ly+4

Hi there!

~

Let's solve your equation step-by-step.

\(x^{2} =\ 255\)

Step 1: Take square root.

\(x =\) ± \(\sqrt{255}\)

\(x = \sqrt{255}\) or \(= - \sqrt{255}\)

Hope this helped you!

9514 1404 393

Answer:

Step-by-step explanation:

The slope of a line in the form ...

  ax +by = c

is ...

  m = -a/b

So, the slope of the given line is ...

  -4/(-3) = 4/3

The slope of the perpendicular line is the opposite reciprocal of this,

  m' = -1/(4/3) = -3/4

__

The point-slope equation of a line is ...

  y -k = m(x -h) . . . . . . . . line with slope m through point (h, k)

Then your perpendicular line with slope -3/4 through point (-8, 7) is ...

  y -7 = -3/4(x +8)

Rearranging to slope-intercept form, we get ...

  y = -3/4x -3/4(8) +7

  y = -3/4x +1

Answer:

0.3 reoccurring = 1/3

0.125=1/8

0.6 reoccurring =1/6

0.2=1/5

0.75=3/4

The value of integral is 3.

Let's evaluate the integral over the positive half of the interval:

∫[0 to π] (cos(x) / √(4 + 3sin(x))) dx

Let u = 4 + 3sin(x), then du = 3cos(x) dx.

Substituting these expressions into the integral, we have:

∫[0 to π] (cos(x) / sqrt(4 + 3sin(x))) dx = ∫[0 to π] (1 / (3√u)) du

Using the power rule of integration, the integral becomes:

∫[0 to π] (1 / (3√u)) du = (2/3) . 2√u ∣[0 to π]

Evaluating the definite integral at the limits of integration:

(2/3)2√u ∣[0 to π] = (2/3) 2(√(4 + 3sin(π)) - √(4 + 3sin(0)))

(2/3) x 2(√(4) - √(4)) = (2/3) x 2(2 - 2) = (2/3) x 2(0) = 0

So, the value of integral is

= 3-0

= 3

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Answer:

\(3-\displaystyle \int^{\pi}_{-\pi} \dfrac{\cos x}{\sqrt{4+3 \sin x}}\; \text{d}x\approx 0.806\; \sf (3\;d.p.)\)

Step-by-step explanation:

First, compute the indefinite integral:

\(\displaystyle \int \dfrac{\cos x}{\sqrt{4+3\sin x}}\; \text{d}x\)

To evaluate the indefinite integral, use the method of substitution.

\(\textsf{Let} \;\;u = 4 + 3 \sin x\)

Find du/dx and rewrite it so that dx is on its own:

\(\dfrac{\text{d}u}{\text{d}x}=3 \cos x \implies \text{d}x=\dfrac{1}{3 \cos x}\; \text{d}u\)

Rewrite the original integral in terms of u and du, and evaluate:

\(\begin{aligned}\displaystyle \int \dfrac{\cos x}{\sqrt{4+3\sin x}}\; \text{d}x&=\int \dfrac{\cos x}{\sqrt{u}}\cdot \dfrac{1}{3 \cos x}\; \text{d}u\\\\&=\int \dfrac{1}{3\sqrt{u}}\; \text{d}u\\\\&=\int\dfrac{1}{3}u^{-\frac{1}{2}}\; \text{d}u\\\\&=\dfrac{1}{-\frac{1}{2}+1} \cdot \dfrac{1}{3}u^{-\frac{1}{2}+1}+C\\\\&=\dfrac{2}{3}\sqrt{u}+C\end{aligned}\)

Substitute back u = 4 + 3 sin x:

                            \(= \dfrac{2}{3}\sqrt{4+3\sin x}+C\)

Therefore:

\(\displaystyle \int \dfrac{\cos x}{\sqrt{4+3\sin x}}\; \text{d}x= \dfrac{2}{3}\sqrt{4+3\sin x}+C\)

To evaluate the definite integral, we must first determine any intervals within the given interval -π ≤ x ≤ π where the curve lies below the x-axis. This is because when we integrate a function that lies below the x-axis, it will give a negative area value.

Find the x-intercepts by setting the function to zero and solving for x in the given interval -π ≤ x ≤ π.

\(\begin{aligned}\dfrac{\cos x}{\sqrt{4+3\sin x}}&=0\\\\\cos x&=0\\\\x&=\arccos0\\\\\implies x&=-\dfrac{\pi }{2}, \dfrac{\pi }{2}\end{aligned}\)

Therefore, the curve of the function is:

So to calculate the total area, we need to calculate the positive and negative areas separately and then add them together, remembering that if you integrate a function to find an area that lies below the x-axis, it will give a negative value.

Integrate the function between -π and -π/2.

As the area is below the x-axis, we need to negate the integral so that the resulting area is positive:

\(\begin{aligned}A_1=-\displaystyle \int^{-\frac{\pi}{2}}_{-\pi} \dfrac{\cos x}{\sqrt{4+3\sin x}}\; \text{d}x&=- \left[\dfrac{2}{3}\sqrt{4+3\sin x}\right]^{-\frac{\pi}{2}}_{-\pi}\\\\&=-\dfrac{2}{3}\sqrt{4+3 \sin \left(-\frac{\pi}{2}\right)}+\dfrac{2}{3}\sqrt{4+3 \sin \left(-\pi\right)}\\\\&=-\dfrac{2}{3}\sqrt{4+3 (-1)}+\dfrac{2}{3}\sqrt{4+3 (0)}\\\\&=-\dfrac{2}{3}+\dfrac{4}{3}\\\\&=\dfrac{2}{3}\end{aligned}\)

Integrate the function between -π/2 and π/2:

\(\begin{aligned}A_2=\displaystyle \int^{\frac{\pi}{2}}_{-\frac{\pi}{2}} \dfrac{\cos x}{\sqrt{4+3\sin x}}\; \text{d}x&= \left[\dfrac{2}{3}\sqrt{4+3\sin x}\right]^{\frac{\pi}{2}}_{-\frac{\pi}{2}}\\\\&=\dfrac{2}{3}\sqrt{4+3 \sin \left(\frac{\pi}{2}\right)}-\dfrac{2}{3}\sqrt{4+3 \sin \left(-\frac{\pi}{2}\right)}\\\\&=\dfrac{2}{3}\sqrt{4+3 (1)}-\dfrac{2}{3}\sqrt{4+3 (-1)}\\\\&=\dfrac{2\sqrt{7}}{3}-\dfrac{2}{3}\\\\&=\dfrac{2\sqrt{7}-2}{3}\end{aligned}\)

Integrate the function between π/2 and π.

As the area is below the x-axis, we need to negate the integral so that the resulting area is positive:

\(\begin{aligned}A_3=-\displaystyle \int^{\pi}_{\frac{\pi}{2}} \dfrac{\cos x}{\sqrt{4+3\sin x}}\; \text{d}x&= -\left[\dfrac{2}{3}\sqrt{4+3\sin x}\right]^{\pi}_{\frac{\pi}{2}}\\\\&=-\dfrac{2}{3}\sqrt{4+3 \sin \left(\pi\right)}+\dfrac{2}{3}\sqrt{4+3 \sin \left(\frac{\pi}{2}\right)}\\\\&=-\dfrac{2}{3}\sqrt{4+3 (0)}+\dfrac{2}{3}\sqrt{4+3 (1)}\\\\&=-\dfrac{4}{3}+\dfrac{2\sqrt{7}}{3}\\\\&=\dfrac{2\sqrt{7}-4}{3}\end{aligned}\)

To evaluate the definite integral, sum A₁, A₂ and A₃:

\(\begin{aligned}\displaystyle \int^{\pi}_{-\pi} \dfrac{\cos x}{\sqrt{4+3\sin x}}\; \text{d}x&=\dfrac{2}{3}+\dfrac{2\sqrt{7}-2}{3}+\dfrac{2\sqrt{7}-4}{3}\\\\&=\dfrac{2+2\sqrt{7}-2+2\sqrt{7}-4}{3}\\\\&=\dfrac{4\sqrt{7}-4}{3}\\\\ &\approx2.194\; \sf (3\;d.p.)\end{aligned}\)

Now we have evaluated the definite integral, we can subtract it from 3 to evaluate the given expression:

\(\begin{aligned}3-\displaystyle \int^{\pi}_{-\pi} \dfrac{\cos x}{\sqrt{4+3 \sin x}}\; \text{d}x&=3-\dfrac{4\sqrt{7}-4}{3}\\\\&=\dfrac{9}{3}-\dfrac{4\sqrt{7}-4}{3}\\\\&=\dfrac{9-(4\sqrt{7}-4)}{3}\\\\&=\dfrac{13-4\sqrt{7}}{3}\\\\&\approx 0.806\; \sf (3\;d.p.)\end{aligned}\)

Therefore, the given expression cannot be zero.

The ratio of rainy days to total days written as a percent will be 75%.

Ratio demonstrates how many times one number can fit into another number. Ratios contrast two numbers by ordinarily dividing them. A/B will be the formula if one is comparing one data point (A) to another data point (B).

Ratio is used to compare two or more numbers. It is also used to indicate how big or small a quantity is when it is compared to another. It should be noted that in a ratio, two quantities are compared using division.

Since in the last 24 days, it rained 18 days.

Number of rainy days = 18.

Number of total days = 24

The ratio of rainy days to total days written as a percent will be:

= Number of rainy days / Total days × 100

= 18/24 × 100

= 3/4 × 100

= 75%

Therefore, the ratio is 3:4 which is 75%.

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Answer: If angle A is congruent to angle E

Answer:

C

Step-by-step explanation:

32/sqrt(2) = 32sqrt(2)/2 = 16sqrt2

Answer:

C.

Step-by-step explanation:

It is a right triangle with hypotenuse c = 12, also for having two equal angles is an isosceles triangle, the missing sides (catethus) are equal (a and b)
a = b = the legs

Apply the Pythagorean theorem

\(c^{2}=a^{2} +b^{2} \\c^{2} =2a^{2}\)

\(a^{2} =\frac{c^{2} }{2}=\frac{(32)^{2} }{2} =512\)

\(a=\sqrt{512} =\sqrt{256(2)} =16\sqrt{2}\)

Hope this helps

Answer:

D) 56

Step-by-step explanation:

\(\displaystyle \frac{8!}{(8-2)!}=\frac{8!}{6!}=\frac{8*7*6*5*4*3*2*1}{6*5*4*3*2*1}=8*7=56\)

Answer:

  (a)  twenty-eight ninths, square root of nineteen, cube root of eighty-eight

Step-by-step explanation:

When ordering a list of numbers by hand, it is convenient to convert them to the same form. Decimal equivalents are easily found using a calculator.

The attachment shows the ordering, least to greatest, to be ...

  \(\dfrac{28}{9}.\ \sqrt{19},\ \sqrt[3]{88}\)

__

Additional comment

We know that √19 > √16 = 4, and ∛88 > ∛64 = 4, so the fraction 28/9 will be the smallest. That leaves us to compare √19 and ∛88, both of which are near the same value between 4 and 5.

One way to do the comparison is to convert these to values that need to have the same root:

  √19 = 19^(1/2) = 19^(3/6) = sixthroot(19³)

  ∛88 = 88^(1/3) = 88^(2/6) = sixthroot(88²)

The roots will have the same ordering as 19³ and 88².

Of course, these values can be found easily using a calculator, as can the original roots. By hand, we might compute them as ...

  19³ = (20 -1)³ = 20³ -3(20²) +3(20) -1 = 8000 -1200 +60 -1 = 6859

  88² = (90 -2)² = 90² -2(2)(90) +2² = 8100 -360 +4 = 7744

Then the ordering is ...

  28/9 < 19³ < 88²   ⇒   28/9 < √19 < ∛88

Answer:

the ordering is

28/9 < 19³ < 88²   ⇒   28/9 < √19 < ∛88

Step-by-step explanation:

Answer:

We want to calculate the volume of the spherical shell of chocolate.

The chocolate shell is spherical with a thickness of 0.5cm

Volumes of spherical shells can be calculated with the formula;

The outer diameter is 8cm. The outer radius is therefore 4cm

The inner diameter is 8-2(0.5)=7cm. The inner radius is therefore 3.5cm

Therefore, we can find the volume of the chocolate shell as;

Therefore,