Find all solutions in the interval [0, 2π).

sec2x - 2 = tan2x

a) No solution

b) x = pi/3

c) x = pi/4

d) x = pi/6

"Since the ratio is 5:7 you can think in total there was 12 equal blocks of money invested. 5 of those blocks belonged to Jim and 7 of those blocks belonged to Gail. Since they invested $3,600 and then made $6,450 in total there is $10,050. Divide that total into 12 equal blocks of $837.50 and 5 of those blocks belong to Jim. So he will get $4,187.50"

The amount that Gail will get is $5862.5.

A ratio is a comparison of two quantities produced by dividing the first by the second. If a and b are two values of the same kind and with the same units, and b is not equal to zero, then the quotient a/b is known as the ratio between a and b. The colon sign is used to denote ratios (:). This means that the ratio a/b has no unit and can be expressed as a: b.

Given:

Jim and Gail invested a total of $3,600 in a stock, in a ratio of 5:7.

The stock made $6,450 on top of the initial capital.

Total they made

= 3600+ 6450

= $10, 050

The pay off Jim get

= 10, 050 x 5/12

= 4187.5

and, the pay off Gail  get

= 10, 050 x 7/12

= $5862.5

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There are [tex]728000[/tex] possibilities  of different licence plates.

The License plate is consist of [tex]4[/tex] digits followed by [tex]2[/tex] uppercase letters, i,e,

We have [tex]6[/tex] digits so let's first check  the choices of letter or digits over that.

Consider [tex]1[/tex]st Digit , according so question it should be odd so the choices we have for [tex]1[/tex]st Digits are [tex]1,3,5,7,9[/tex] i.e, [tex]5[/tex] choices we have as repitition not allowed.

Now consider [tex]2[/tex]nd Digit , according so question it should be odd so the choices we have for [tex]2[/tex]nd Digits are [tex]4[/tex] because [tex]1[/tex] odd digits has been used in  [tex]1[/tex]st Digit.

[tex]3rd[/tex] digit - [tex]2[/tex] digits has been used in [tex]1[/tex]st and [tex]2[/tex]nd digits so [tex]8[/tex] choices left.

[tex]4th[/tex] digit - This is left with [tex]7[/tex] choices.

[tex]5th[/tex]- On this [tex]2[/tex] uppercase letters required so choices we have are [tex]26[/tex].

[tex]6th[/tex]- On this we have to use uppercase so [tex]25[/tex] choices are left as repitition not allowed.

So Possibility of different license [tex]5 \times 4\times\times 8\times 7\times26\times 25=728000[/tex]

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True. Overdraft protection is a service offered by banks to their customers. When your account does not have enough money to cover a transaction, overdraft protection allows the bank to loan you the necessary funds to complete the transaction.

If you make a purchase or withdrawal that exceeds your account balance, the bank will cover the shortfall by lending you the needed amount. This ensures the transaction goes through, but typically comes with fees or interest. While convenient, it can lead to extra costs if used frequently.

Overdraft protection may apply to debit card purchases, checks, or automatic bill payments, depending on the account settings. Some banks offer this service automatically, while others require customers to opt in. It's a useful safety net but should be used responsibly to avoid accumulating unnecessary charges.

is a hope i helped you wlcome

Answer:

 Option C is the correct answer.  

Step-by-step explanation:

Volume = Length x Breadth x Height

Length = 10 feet = 3.33 yard

Height = 3 inches = 0.25 feet = 0.0833 yard

The price of concrete is $98 per cubic yard and total cost is  $72.59.

[tex]\texttt{Total concrete needed = }\frac{72.59}{98}=0.74yard^3[/tex]

We have

      Volume = Length x Breadth x Height = 0.74

      3.33 x Width x 0.0833 = 0.74

      Width = 2.67 yards = 2.67 x 3 = 8 feet

 Option C is the correct answer.  

To find the temperature that represents the 95th percentile, calculate the z-score using the given formula and substitute the values in the equation. Using a standard normal distribution table, the temperature is approximately 98.93°F.

To find the temperature that represents the 95th percentile, we need to calculate the z-score corresponding to the 95th percentile.

The z-score can be calculated using the formula: z = (x - μ) / σ, where x is the temperature, μ is the mean, and σ is the standard deviation. In this case, μ = 98.6°F and σ = 0.19°F.

By looking up the z-score in the standard normal distribution table, we can find the corresponding temperature.

Using a standard normal distribution table, we find that the z-score for the 95th percentile is approximately 1.645. Substituting the values into the formula, we get: 1.645 = (x - 98.6) / 0.19.

Solving for x, we find x ≈ 98.6 + (1.645 * 0.19) ≈ 98.9295°F.

Therefore, the temperature that represents the 95th percentile is approximately 98.93°F.

The dimensions of the rectangular fish aquarium are:

length = 31 inches, width = 13 inches and depth = 28 inches

If Simpson covers all the four glass walls of the aquarium.

We have to determine the covering he needs.

So, Covering required for four walls of the aquarium

= [tex]2(lh+bh)[/tex]

= [tex]2( (31 \times 28)+ (13 \times 28))[/tex]

= [tex]2( (868)+ (364))[/tex]

= [tex]2 \times 1232[/tex]

= 2464 square inches

So, Simpson needs 2464 square inches of covering to cover all the four glass walls of the aquarium.

By using the tangent formula, we will see that:

tan(x) = 5/12.

You just need to remember that we can write the tangent as:

tan(x) = sin(x)/cos(x).

In this case, we know that:

We can just replace these two in the tangent equation, we will get:

tan(x) = (5/13)/(12/13) = (5/13)*(13/12) = 5/12

tan(x) = 5/12

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Pi is a very special number in math and it’s so special that it even gets its own symbol. Mathematicians found out that when you try to write down what pi is, the decimal points keep going and going. This means that it’s impossible to find all the digits of pi.

I will only write down some digits.

π = 3.1415926535897932384626

Answer:

Step-by-step explanation:

1.

[tex](c+9)^2=64=8^2\\[/tex]

c+9=±8

either c=8-9=-1

c=-8-9=-17

so c=-1,-17

D

2.

8x^2-3=2

8x^2=5

[tex]x^2=\frac{5}{8}=\frac{10}{16}[/tex]

[tex]x=±\frac{\sqrt{10}}{4}[/tex]

so A

3.

[tex]x^2+4x+4=18\\(x+2)^2=9*2\\x+2=3\sqrt{2} \\x=-2  ±3\sqrt{2}[/tex]

so D

or

Answer: The answer is 2/3.

The 25.6 percentage of the number 82.5 is 21.12

Given data:

To find the percentage of 21.12 in relation to 82.5, the proportion is simplified as:

21.12 is to 82.5 as x is to 100.

This can be expressed as:

21.12/82.5 = x/100

On solving for x by cross multiplying:

21.12 * 100 = 82.5 * x

2112 = 82.5x

To isolate x, divide both sides by 82.5:

2112/82.5 = x

On simplifying:

25.6 ≈ x

Hence, 21.12 is approximately 25.6 percent of 82.5.

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To find the lateral area, surface area, and volume of a triangular prism, use the Pythagorean theorem to find the missing leg, then calculate the triangular base area, lateral area, and volume, and finally add the triangular base areas to the lateral area for the surface area.

Finding the Lateral Area, Surface Area, and Volume of a Triangular Prism

To find the lateral area (LA), surface area (SA), and volume of a triangular prism with a given hypotenuse, short leg, and height of the prism, we will follow these steps:

Determine the length of the other leg of the right-angled triangle using the Pythagorean theorem (since the triangular face is a right triangle given the hypotenuse and one leg).

Calculate the area of the triangular base using the formula for the area of a triangle (1/2 × base × height).

Compute the lateral area by multiplying the perimeter of the triangular base by the height of the prism.

Add the areas of the two triangular bases to the lateral area to get the surface area.

Find the volume by multiplying the area of the triangular base by the height of the prism.

Since the short leg is 5 m and the hypotenuse is 12 m, the other leg (long leg) can be found as √(12² - 5²) = √(144 - 25) = √119 m. The area of the triangular base (A) is then 1/2 × 5 m × √119 m. The perimeter (P) of the triangular base is 5 m + 12 m + √119 m. The lateral area is P × height of prism (5 m), and the surface area is LA + 2 × A. Lastly, the volume is A × height of prism (5 m).

The measure of the longest side of ∆ABC is 6 units. ∆ABC is a right scalene triangle. ∆ABD is also a right scalene triangle and the length of side AD is 5 units.

The measure of the longest side of ∆ABC can be found using the distance formula.

We calculate the distance between points A(1, 7) and B(-2, 2), between points B(-2, 2) and C(4, 2), and between points A(1, 7) and C(4, 2).

The longest distance is the measure of the longest side.

Using the distance formula, we find that the longest side is 6 units long.

∆ABC is a right scalene triangle.

This is because the lengths of its sides are all different and it has a right angle at point C, where the x-coordinate doesn't change but the y-coordinate does.

∆ABD is also a right scalene triangle.

The length of side AD can be found using the distance formula between points A(1, 7) and D(1, 2).

The length of side AD is 5 units.

Answer:

Step-by-step explanation:

Given that a study shows that, over the course of a lifetime, the average salary of college graduates is greater than the average salary of people with only a high school diploma.

The results were published claiming that graduating from college ensures you will make more money over the course of your lifetime.

Only means should not be compared. variances of each sample should be ascertained and test for comparison of two means to be done to conclude that one mean is greater than the other.

Hence here problem is correlation and causality.

Answer:

Step 3

Step-by-step explanation:

By asking the participants how delicious chocolate B is, you can possibly create bias in the test.  It is a leading question; these should not be asked to avoid creating bias.