Drag each equation to show if it could be a correct first step to solving the equation 2(x+7)=362(x+7)=36.

Answer: The probability that she will guess correctly on the third question [tex]=\frac{1}{4}[/tex]

Step-by-step explanation:

Given: The math test has 10 multiple choice questions, each with 4 answers.

To find  probability that she will guess correctly on the third question, we need to just look at only one question which has 4 options and one of them is the right answer, thus probability of choosing the right answer from 4 option is the fraction of 1 over 4.

The probability that she will guess correctly on the third question

[tex]=\frac{\text{answer of a question}}{\text{total options of a question}}[/tex]

[tex]=\frac{1}{4}[/tex]

option b) 5 km

1 km = 1000 m

Divide the number of meters by 1000:

5000 m / 1000

= 5 km

So, 5000 meters is equal to 5 kilometers.

The correct answer is 5 km.

The ship is approximately 26.16 nautical miles from the harbor after following the described path.

To find the distance of the ship from the harbor after sailing due west for 28 nautical miles and then S68°W for another 17 nautical miles, we can use trigonometry to calculate the resultant displacement.

Let's break down the two legs of the journey:

1. Due west for 28 nautical miles is a straight line.

2. Sailing S68°W for 17 nautical miles forms an angle of 68° with the west direction.

Using trigonometry, we can find the horizontal and vertical components of the second leg:

Horizontal component = 17 * cos(68°)

Vertical component = 17 * sin(68°)

The total horizontal displacement from both legs is:

Horizontal displacement = 28 - (17 * cos(68°))

The total vertical displacement from both legs is:

Vertical displacement = 17 * sin(68°)

To find the distance from the harbor, we use the Pythagorean theorem:

Distance = √(Horizontal displacement² + Vertical displacement²)

Calculating:

Horizontal component = 17 * cos(68°) ≈ 6.93 nautical miles

Vertical component = 17 * sin(68°) ≈ 15.52 nautical miles

Horizontal displacement = 28 - (17 * cos(68°)) ≈ 21.07 nautical miles

Vertical displacement = 17 * sin(68°) ≈ 15.52 nautical miles

Distance = √(21.07² + 15.52²) ≈ √(443.9749 + 240.5504) ≈ √684.5253 ≈ 26.16 nautical miles

Therefore, the ship is approximately 26.16 nautical miles from the harbor after following the described path.

That is to say, if c = -2, f(x) is continuous at x = 4. 

Because f is continuous for all over values of x, it now follows that f is continuous for all real nubmers [tex](-\infty, +\infty)[/tex]

The probability of getting a country CD out of all the CDs is the number of country CDs divided by the total number of CDs in Dante's Collection.

The total number of CDs in Dante's collection is [tex]6+12+8+4+10=40[/tex].

The total number of country CDs is 12.

So our required probability is [tex]\frac{12}{40}= \frac{3}{10}[/tex].

In percentage this is 3 divided by 10, and then multiply by 100. We get 30%. Answer choice D is correct.

ANSWER: D

Answer: D.) 30%

Step-by-step explanation:

From the given pie chart, we have the number of country CD = 12

The total number of CD's=[tex]12+8+4+6+10=40[/tex]

Now, the probability that a randomly chosen CD will be country is given by :-

[tex]\text{P(country)}=\dfrac{\text{Number of country CD}}{\text{Total CDs}}\\\\=\dfrac{12}{40}=\dfrac{3}{10}=0.3[/tex]

In percent, [tex]0.3\times100=30\%[/tex]

Hence, the probability that a randomly chosen CD will be country is 30%.

It is important to start saving for retirement decades before retirement age because of compound interest. When you start saving at a younger age, you have more time for your money to compound. In other words, you can start with a smaller amount of money and after 30 years of compounding, it can grow to a larger amount.

Compounding is the formula 1 + r to the n which means interest compounds into more interest over time.

Answer:

The correct answer is A. Yes, because there are two pairs of congruent corresponding angles.

Step-by-step explanation:

This is because to prove that two triangles are congruent, you need at least two pairs of corresponding angles.

Also, the degrees 30, 65, and 85 is equal to 180 degrees.

Hope this helps!

Steve can completely fill 3 carousels with his 276 slides as each carousel holds up to 75 slides.

Based on the provided data, Steve has 276 slides and each carousel holds up to 75 slides. To find out how many carousels can be completely filled, we have to divide the total number of slides by the number that each carousel holds.

So, the calculation would be: 276 (total slides) divided by 75 (slides each carousel can hold).

276 ÷ 75 equals about 3.68. Since we cannot have a fraction of a carousel, we round the number down to the nearest whole number. Hence, Steve can completely fill 3 carousels with his slides.

https://brainly.com/question/11856055

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Answer:

36

Step-by-step explanation:

Answer:

[tex]\angle CBD=105^{\circ}[/tex]

Step-by-step explanation:

We have been given a diagram. We are asked to find the measure of angle CBD using given diagram.

We can see that in triangle ABD two angles measure 60 degree. Using angle sum property of triangle, we can find measure of triangle angle ADB as:

[tex]\angle A+\angle B+\angle D=180^{\circ}[/tex]

[tex]60^{\circ}+60^{\circ}+\angle D=180^{\circ}[/tex]

[tex]120^{\circ}+\angle D=180^{\circ}[/tex]

[tex]120^{\circ}-120^{\circ}+\angle D=180^{\circ}-120^{\circ}[/tex]

[tex]\angle D=60^{\circ}[/tex]

Since all angles of triangle ABD are equal, so it is an equilateral triangle and its all sides will have same measure.

[tex]AB=BD=AD[/tex]

We have been given segment AB is equal to segment BC. Now, we will get:

[tex]AB=BD=AD=BC[/tex]

In triangle BCD sides two sides (BD and BC) are equal, so it is an isosceles triangle.

We know that angles corresponding to equal sides of an isosceles triangle have equal measure, so measure of angle BDC will be equal to angle BCD.

[tex]\angle BDC=\angle BCD=37\frac{1}{2}^{\circ}[/tex]

Now, we will use angle property of triangle to find measure of angle CBD as:

[tex]\angle CBD+\angle BCD+\angle BDC=180^{\circ}[/tex]

[tex]\angle CBD+37\frac{1}{2}^{\circ}+37\frac{1}{2}^{\circ}=180^{\circ}[/tex]

[tex]\angle CBD+\frac{75}{2}^{\circ}+\frac{75}{2}^{\circ}=180^{\circ}[/tex]

[tex]\angle CBD+\frac{150}{2}^{\circ}=180^{\circ}[/tex]

[tex]\angle CBD+\frac{150}{2}^{\circ}-\frac{150}{2}^{\circ}=180^{\circ}-\frac{150}{2}^{\circ}[/tex]

[tex]\angle CBD=\frac{360}{2}^{\circ}-\frac{150}{2}^{\circ}[/tex]

[tex]\angle CBD=\frac{210}{2}^{\circ}[/tex]

[tex]\angle CBD=105^{\circ}[/tex]

Therefore, the measure of angle CBD is 105 degrees.

Answer:

  about 473 mL

Step-by-step explanation:

For liquid measure, there are 16 cups in a US gallon, which is exactly 231 cubic inches. Each cubic inch is exactly 2.54³ = 16.387064 cubic centimeters--the same number of mL.

So, the exact conversion from cups to mL is ...

  1 cup = (231/16)(16.387064) mL = 236.5882365 mL

Multiplying this by 2 gives ...

  2 cups = 473.176473 mL

For many purposes, the nearest mL is sufficiently accurate:

  2 cups ≈ 473 mL

Answer:

○ [tex]\displaystyle y ≤ -7[/tex]

Step-by-step explanation:

Whenever you divide\multiply by a negative, you reverse the inequality symbol.

I am joyous to assist you anytime.

Final answer:

To find the volume of a regular hexahedron with a face diagonal of 8√2 inches, we first calculate the side length of the cube and then use it to determine the volume, resulting in a volume of 512 cubic inches.

Explanation:

The question asks to find the volume of a regular hexahedron (which is a cube), given the diagonal of one of its faces is 8√2 inches. Since we know the face of a hexahedron is a square, we can use the Pythagorean theorem to find the side of the square. The diagonal (d) of a square relates to its side (s) by the formula d = s√2. Therefore, we can solve for s: s = d / √2 = (8√2) / √2 = 8 inches. Now that we have the length of the side of the cube, we can compute the volume (V) using the formula V = s3. Substituting s = 8 inches, we calculate the volume as V = 83 = 512 cubic inches.

The maximum volume of the box is:

              1000 cm³

Let x be the length of the square base

and h be the height(h) of the box.

As we know that the length(l) and width(w) of the box is same( since the base is in the shape of square)

As we know that the surface area of box is given by:

[tex]Surface\ Area=2(lw+wh+hl)\\\\\\i.e.\\\\\\Surface\ Area=2(x^2+xh+xh)\\\\\\Surface\ Area=2(x^2+2hx)[/tex]

We are given surface area of box=600 cm²

Hence,

[tex]2(x^2+2hx)=600\\\\i.e.\\\\x^2+2xh=300\\\\i.e.\\\\h=\dfrac{150}{x}-\dfrac{x}{2}[/tex]

The volume of box is given by:

[tex]Volume(V)=l\times w\times h\\\\\\Volume=x^2h\\\\\\Volume=x^2(\dfrac{150}{x}-\dfrac{x}{2})[/tex]

Hence,

[tex]V=150x-\dfrac{x^3}{2}[/tex]

Now, for maxima or minima we have derivative equal to zero.

[tex]i.e.\\\\\\\dfrac{dV}{dx}=0\\\\\\i.e.\\\\\dfrac{d}{dx}(150x-\dfrac{x^3}{2})=0\\\\\\i.e.\\\\\\150-\dfrac{3x^2}{2}=0\\\\\\i.e.\\\\\\150=\dfrac{3}{2}x^2\\\\\\x^2=100\\\\\\i.e.\\\\\\x=\pm 10[/tex]

Now,

[tex]\dfrac{d^2V}{dx^2}=\dfrac{-6x}{2}\\\\\\=-3x[/tex]

Now, as we know if for a given x

[tex]\dfrac{d^2V}{dx^2}<0[/tex]

then that x is a point of maxima.

Hence, when we put x=10 we get:  [tex]\dfrac{d^2V}{dx^2}<0[/tex]

Hence, x=10 is a point of maxima

Also, the value of V at x=10 is:

[tex]V=150\times 10-\dfrac{(10)^3}{2}\\\\\\V=1500-\dfrac{1000}{2}\\\\\\V=1500-500\\\\V=1000\ cubic\ cm.[/tex]

       Hence, the maximum volume of the box is:

                     1000 cm³

Final answer:

Option c, 15/16, is the correct answer because it cannot be simplified to 7/8, making it not equivalent to 7/8, while the other options are equivalent after simplification.

Explanation:

The question asks us to identify which fraction is not equivalent to 7/8. To determine this, we need to compare each option with 7/8:

Hence, the correct answer is option c, which is not equivalent to 7/8.