Gerald has a punch bowl in the shape of a hemisphere as shown below.

One cup is equivalent to approximately 15 cubic inches. Which of the following is closest to the maximum number of cups the punch bowl can hold?

A. 60 cups
B. 45 cups
C. 30 cups
D. 18 cups

Answer:

[tex]f^{-1}(x)=\dfrac{1}{3}(\ln x +1)[/tex]

Step-by-step explanation:

Given function:

[tex]f(x)=e^{3x-1}[/tex]

Replace f(x) with y:

[tex]\implies y=e^{3x-1}[/tex]

Take natural logs of both sides:

[tex]\implies \ln y = \ln e^{3x-1}[/tex]

Apply the Power Log Law   [tex]\ln x^n=n\ln x[/tex] :

[tex]\implies \ln y = (3x-1)\ln e[/tex]

As [tex]\ln e=1[/tex] then:

[tex]\implies \ln y = 3x-1[/tex]

Rearrange to make x the subject:

[tex]\implies 3x=\ln y +1[/tex]

[tex]\implies x=\dfrac{1}{3}(\ln y +1)[/tex]

Swap x for [tex]f^{-1}(x)[/tex]  and y for x:

[tex]\implies f^{-1}(x)=\dfrac{1}{3}(\ln x +1)[/tex]

Answer:

1 - 135

2 - 45

3 - 45

4 - 135

5 - 135

6 - 45

7 - 45

8 - 135

3(5x+7)-6(4-2x) - given

15x+21-24+12x - distributive property

27x-3 - combine like terms

Answer:A

Step-by-step explanation:

-23/6 - 7/3 =-6.16666666667

-37/6 = -6.16666666667

Answer:

[tex] \frac{ - 37}{6} [/tex]

Step-by-step explanation:

[tex] \frac{23}{6} - \frac{7}{3} \\ lcm = 6 \\ \frac{ - 23 - 14} {6} = - \frac{ - 37}{6} \\ final \: answer \\ = \frac{ - 37}{6} [/tex]

[tex]\text{The base and height have to be factors of 60, since}\\\\~~~~~~~~\text{Area}= \dfrac{1}{2} \times \text{Base} \times \text{Height}\\\\\implies 30 = \dfrac 12 \times \text{Base} \times \text{Height}\\\\\implies \text{Base} \times \text{Height}= 60[/tex]

[tex]\textbf{Example 1:}\\\\\text{Height} = 6~ cm \\\\\text{Base} = 10~ cm\\\\\text{Area} = \dfrac 12 \times 6 \times 10 = 30~ cm^2\\\\\textbf{Example 2:}\\\\\text{Height} = 5~ cm\\\\\text{Base} = 12~ cm\\\\\text{Area} = \dfrac 12 \times 12 \times 5 = 30~ cm^2\\\\\textbf{Example 3:}\\\\\text{Height} =4~ cm\\\\\text{Base} = ~15 ~cm\\\\\text{Area} = \dfrac 12 \times 15 \times 4 = 30~ cm^2[/tex]

Let's see

Base be B

Height be H

So

The ppossible values are

The area of the figure is 51.4 unit²

Figure ABCDEF is shown. A is located at 5, negative 8. B is located at 11, negative 8. C is located at 11, 0. D is located at 6

See attachment for the figure

The figure can be divided into the following shapes:

The area of the trapezoid is:

Area = 0.5 * (Sum of opposite sides) * height

So, we have:

Trapezoid 1 = 0.5 * (8 + 5) * 5 = 32.5

Trapezoid 2 = 0.5 * (5 + 4.8) * 2 = 9.8

The area of the triangle is:

Area = 0.5 * Base * Height

This gives

Triangle = 0.5 * 4.8 * 4 = 9.6

Add the individual areas

Area = 32 + 9.8 + 9.6

Evaluate the sum

Area = 51.4

Hence, the area of the figure is 51.4 unit²

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Based on the calculations, the equation of this parabola is equal to (x - 6)² = 16(y + 4).

Mathematically, the standard equation with the vertex for a parabola is given by:

(y - k)² = 4a(x - h) for horizontal parabola.

(x - h)² = 4a(y - k) for vertical parabola.

where:

By critically observing the points, we can deduce that both the focus and vertex lie on the same vertical line x = 6.

Given the following data:

Focus with points = (6, 2).

Vertex (h, k) = (6, –4).

Note: a = 2 - (-4) = 2 + 4 = 6.

Substituting the given parameters into the formula, we have;

(x - 6)² = 4 × 4(y - (-4))

(x - 6)² = 16(y + 4).

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Answer:

80 000

Step-by-step explanation:

1 cm : 20 000 (The question does not state the unit of the other half)

So

4 cm : 4×20 000

4 cm : 80 000

I'm not sure about units but hope this helped and brainliest please

Answer:

80 000 meters

Step-by-step explanation:

In the map:

1 cm = 20000 m

4 cm = 4(20000) = 80 000 meters

4 cm on the map represents 80 km in reality.

Hope this helps

A second-degree polynomial takes the form

[tex]f(x) = ax^2 + bx + c[/tex]

for some constants a, b, and c. Such a function is continuous and differentiable everywhere in its domain.

Differentiating f(x) with respect to x gives

[tex]\dfrac{df}{dx} = 2ax + b[/tex]

We're told that

• f(x) is increasing on [0, 8]

• f(x) is decreasing on ]-10, 0]

and since df/dx is continuous, this tells us that df/dx = 0 when x = 0. It follows that b = 0, and we can write

[tex]f(x) = ax^2 + c[/tex]

We're also given that the curve passes through the point (-8, 4), which gives rise to the constraint

[tex]f(-8) = 64a - 8b + c = 4 \implies 64a + c = 4[/tex]

Since f(x) is decreasing on ]-10, 0], we have df/dx < 0 when x = -8, so

[tex]2ax+b < 0 \implies -16a < 0 \implies a > 0[/tex]

This means f(x) is minimized when x = 0, with min{f(x)} = c, so the co-domain of f(x) is the set {f(x) ∈ ℝ : f(x) ≥ c}.

Without another condition, that's all we can say about the co-domain. There are infinitely many choices for the constants a and c that satisfy the given conditions. For example,

a = 1, c = -60   ⇒   f(x) = x² - 60   ⇒   f(-8) = 4

⇒   co-domain = {f(x) ∈ ℝ : f(x) ≥ -60}

a = 2, c = -124   ⇒   f(x) = 2x² - 124   ⇒   f(-8) = 4

⇒   co-domain = {f(x) ∈ ℝ : f(x) ≥ -124}

etc.

Answer:

i think 6 years because i always used it

Step-by-step explanation:

make me my brainliest answer

AnswEr :

Let's assume , three Consecutive integers be x , ( x +1 ) & ( x+2 ) , such that , x < ( x +1 ) < ( x +2 ) .

⠀⠀⠀⠀⠀⠀[tex]\underline {\boldsymbol{\star\: According \: to \: the \: Given \: Question \::}}\\[/tex]

⠀⠀⠀⠀⠀— The product of three consecutive integers is 30 times the smallest of the three integers.

[tex] \sf \dashrightarrow \:30\: \bigg\{ \: Smallest_{(\:integer\:)}\:\bigg\}\:\:=\: \:\bigg\{ \: I^{st} \:Integer\:\bigg\}\: \:\bigg\{\: II^{nd}\:Integer\:\bigg\}\: \:\bigg\{ \: III^{rd} \:Integer\:\bigg\}\:\:\: \\\\\sf \dashrightarrow \:30\: \bigg\{ \:x\:\bigg\}\:\:=\: \:\bigg\{ \: x\:\bigg\}\: \:\bigg\{ \: x + 1\:\bigg\}\: \:\bigg\{ \: x +2 \:\bigg\}\:\:\: \\\\ \sf \dashrightarrow \:30\: \:\:=\: \:\bigg\{ \: x + 1\:\bigg\}\: \:\bigg\{ \: x +2 \:\bigg\}\:\:\: \\\\ \sf \dashrightarrow \:30\: \:\:=\: \:x^2 + 3x + 2 \:\:\: \\\\ \sf \dashrightarrow \:x^2 + 3x - 28 \:= \:0\: \\\\ \sf \dashrightarrow \:\:\bigg\{ \: x - 2 \:\bigg\}\:\:\bigg\{ \: x + 7 \:\bigg\}\: \:= \:0\: \\\\ \pmb {\underline {\boxed {\purple {\:\frak{ \:x\:\:=\:-7\: \&\:2\:}}}}}\:\bigstar \: \\\\\\[/tex]

Therefore ,

When , x = 2 ,

When , x = –7 ,

Answer:

Hi,

Step-by-step explanation:

If the "is" means is equal to

Let's say a-1, a, a+1 the 3 consecutive integers.

[tex](a-1)*a*(a+1)=30*(a-1)\\\\(a-1)*(a*(a+1)-30)=0\\\\(a-1)(a^2+a-30)=0\\\\(a-1)(a^2+6a-5a-30)=0\\\\(a-1)(a(a+6)-5(a+6))=0\\\\(a-1)(a+6)(a-5)=0\\\\a=1\ or\ a=-6\ or\ a=5\\[/tex]

[tex]\begin{array}{|c|c|c|c|c|}a&a-1&a+1&Prod&30*(a-1)\\---&----&----&----&--------\\1&0&2&0&30*0=0\\5&4&6&120&4*30=120\\-6&-7&-5&-210&30*(-6)=-180\end{array}\\[/tex]

The two sets are : (0,1,2) and (4,5,6).

Step-by-step explanation:

an open (empty) point means the point itself is not included.

a closed (filled) point means the point itself is included.

the x values going from -3 (not included) to -1 (included) means

-3 < x <= -1

so, the second answer is correct.

Answer: Both plans cost the same when 50 texts are sent.

Step-by-step explanation:

When x=50 (meaning 50 texts are sent), the y coordinate (which represents the cost) is the same.

Answer:

Yes

Step-by-step explanation:

The sum must be greater than 8 it can't be 7 anyway. Sums can be 9, 10 or 12. P = (4+3+1)/36 = 3/36

Answer:

4,186.67 in³

Step-by-step explanation:

V = (4/3)πr³

V = (4/3)(3.14)(10 in)³

V = (4/3)(3.14)(1,000 in³)

V = 4,186.666667 in³

The volume of 10 ounces of lemonade in litres is 0.295735 litres.

He needs 10 ounces of lemonade.

To know the volume in litres, we have to convert from ounces to litres.

Therefore,

1 ounces = 0.0295735 litres

10 ounces = ?

cross multiply

volume in litres = 0.0295735 × 10

volume in litres = 0.295735

Therefore, the volume of the lemonade in litres is 0.295735 litres.

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Answer:

When -3v = -18 is solved, the result is:

21v

The result of this mathematical sentence is v=6

First degree equation is a mathematical sentence - having at least one unknown. Its representation is given by ax + b = 0. To calculate an equation, as it is in the expression in the statement, simply: isolate x and divide the second to the first member.

*Note: Equal signs, the result will be equated as positive.

-3v = -18

v = -18/-3

v = 6

Therefore, the correct value of this equation is v = 6.

105600

Significant figures are used in scientific fields to show precision.

Multiplication

When rounding to significant figures you need to first do the operation shown. So, before we round we need to multiply 573.06 * 184.25.

This is an important step whenever you are rounding to significant figures. If you preround, you will be left with the wrong answer.

Significant Figures

Now that we have the answer before rounding, we need to know how to determine significant figures. If there is a decimal point present, then start counting significant figures at the first non-zero digit from the left.

For example:

If the decimal point is not present, then start counting significant figures from the first non-zero digit from the right.

For example:

Rounding

Finally, we can round our answer. Firstly, there are more than 4 digits before the decimal point. This means that our rounded answer will not have a decimal point, so when counting sig figs we will start from the right. Remember, even when rounding, a number should always have the same number of digits before the decimal point, even if they are not all significant.

Since we are rounding to 4 sig figs, we need to look at the 5th digit from the left, which is 8. This means we will round up.

So, write the first 4 digits of the number, but round the last one up. Then, write the remaining digits before the decimal point as 0.

Step-by-step explanation:

so, "- 1" is also part of the square root ?

sqrt(x - 1) = x - 3

it is clear that for any value x < 1 we have no solution in R (as this makes the argument of the square root negative, and there is so real number solution for the square root of negative numbers).

now square the whole equation.

x - 1 = (x - 3)² = x² - 6x + 9

x² - 7x + 10 = 0

the general solution for quadratic equations is

x = (-b ± sqrt(b² - 4ac))/(2a)

in our case

a = 1

b = -7

c = 10

x = (7 ± sqrt(49 - 4×1×10))/(2×1) =

= (7 ± sqrt(49 - 40))/2 = (7 ± sqrt(9))/2

x1 = (7 + 3)/2 = 10/2 = 5

x2 = (7 - 3)/2 = 4/2 = 2

x2 is probably (given the answer options) not a valid solution for the original problem, as it represents the negative solution of sqrt(x - 1).

sqrt(2 - 1) = 2 - 3

± 1 = -1

remember, every square root has always 2 solutions : a positive and a negative one.

your teacher clearly only wanted the positive solution, which is x1 = 5.

so, yes,

C. x = 5

is the correct answer.

but please send your teacher my regards and comments. he/she has to state that only the positive solution to the square root is required/allowed.

because, formally, also x = 2 is a valid solution.

and therefore, C. AND D. are correct answers !!!!

Answer: None

Step-by-step explanation:

There is only one pair of angles and one pair of sides, which is not sufficient to prove triangle congruence.

Answer:

24%

Step-by-step explanation:

there are 50 numbers total

number of 4's: 7
number of 7's: 5

it's asking for the odds of a 4 or a 7 meaning that they're fine with either one. that means you can ADD the number of them up!

7 + 5 = 12

to get the odds, we need to divide!

convert that into a percent!

24%

let me know if you're still confused :))

The new sample size based on the information will be B-M, B-C, B-R, 8.

Sample size is the number of participants or observations that are included in a study. This is usually represented by n.

When the boys and girls are to be chosen, the new sample size based on the information will be B-M, B-C, B-R, 8.

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Answer:

Step-by-step explanation:

B-M, B-C, B-R, 8.

The parameters of an Exponential Distribution is D. a > 0

This refers to the distribution of probability with respects to time taken in a Poisson point process.

Hence, we can see that from the previous knowledge of exponential distributions, it is stated that λ > 0 is the parameter of the distribution, and is supported on the interval [0, ∞).

Therefore, option D is correct.

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Answer:

3/4 cups

Step-by-step explanation:

3 1/2 divided by 2

The 73 customers who spend money in this store if a MOE of at most 0.075 with 80% confidence.

MOE is an error that provides an estimate of the percentage of errors in real statistical data.

The formula for finding the MOE:

MOE = z x s/√n

Where ,

Z = the z-score at the confidence interval

s =  the standard deviation

n = the number of samples.

We have p = 0.50 MOE = 0.075

Z = 1.282 at 80% confidence

0.075 = 1.282 x √0.50(1- 0.50)/ n

After solving,

n = (0.5)(0.5)/(0.0585)²

n = 73

Thus, the 73 customers who spend money in this store if a MOE of at most 0.075 with 80% confidence.

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Answer:

2 good scoops

Step-by-step explanation:

I got you I think

Answer:

Step-by-step explanation:

x^2 + 44^2 = 55^2

x^2 + 1936 = 3025

3025-1936 = 1089

sqrt(1089) = 33

x = 33

Answer:

X=33

Step-by-step explanation:

this is a right traingle so you can use pythagorean theorem

A^2 +B^2 =C^2

A^2 +44^2= 55^2

A^2 + 1936= 3025 subtract 1936 from both sides

A^2= 1089 now square root both sides

A=33

[tex]\textit{volume of a sphere}\\\\ V=\cfrac{4\pi r^3}{3}~~ \begin{cases} r=radius\\[-0.5em] \hrulefill\\ r=5.9 \end{cases}\implies V=\cfrac{4\pi (5.9)^3}{3}\implies V\approx 860.3~in^3[/tex]