A quiz has 1 true-false question and 2 multiple choice questions that each have 4 answers. What is the probability that someone guessing all 3 answers will get 100% on the quiz?

...?

The total is: $ 1345.5

It is given that:

I would like to purchase 20 products at a cost 65.00 per product.

This means that the cost of 20 products will be:

[tex]20\times 65=\$\ 1300[/tex]

Also, there is a sales tax of 3.5%

This means that a person has to pay a extra 3.5% on the total cost of the items he purchased.

i.e. he need to pay 3/5% on $ 1300

This means that the amount of tax he need to pay is: 3.5% of 1300

                                                                              =  3.5%×1300

                                                                             = 0.035×1300

                                                                            = $ 45.5.

Hence, the total cost is: $ 1300+$ 45.5

This means that the total cost is: $ 1345.5

Calculating the total difference between what Bob and Tyree will pay over five years for borrowing $10,000 each involves simple interest calculation. Bob, with an 11.5% interest rate, pays $1,750 more than Tyree, who has an 8.0% interest rate. This demonstrates how credit scores affect loan costs.

The question involves calculating the total difference between what two consumers, Bob and Tyree, will pay for borrowing $10,000 each over five years, given their respective interest rates based on their credit scores.

First, to solve this, we'll use the simple interest formula I = PRT, where I is the interest, P is the principal amount (the initial amount borrowed), R is the annual interest rate, and T is the time in years.

The total difference between what Bob and Tyree pay is $5,750 - $4,000 = $1,750. Therefore, Bob will pay $1,750 more than Tyree over the five years due to his lower credit score and higher interest rate.

Answer:

i took the test

Step-by-step explanation:

ratio of voljumes = 3^3 : 4^3 or 27:64 small/large = 27 / 64 vol of smaller = 27 * 320 / 64 =135

Answer:

135 cubic inches.

Step-by-step explanation:

Given : The ratio of the base edges of two similar pyramids is 3:4

           The volume of the larger pyramid is 320 cubic inches.

To Find: What is the volume of the smaller pyramid?

Solution:

The ratio of the base edges of two similar pyramids is 3:4

The volume of the larger pyramid is 320 cubic inches.

The ratio of the volume of pyramids is equal to the ratio of the cubes of the sides of pyramids .

So, [tex]\frac{3^3}{4^3} =\frac{\text{Volume of smaller pyramid}}{320}[/tex]

[tex]\frac{27}{64} =\frac{\text{Volume of smaller pyramid}}{320}[/tex]

[tex]\frac{27}{64} \times 320 =\text{Volume of smaller pyramid}[/tex]

[tex]135 =\text{Volume of smaller pyramid}[/tex]

Thus the volume of smaller pyramid is 135 cubic inches.

The angle represents by 3.5 rotations in counterclockwise is 1260 degree or [tex]\frac{7}{2}\pi[/tex] radian.

In one complete rotation, the angle made is = 360 degree or [tex]\pi[/tex] radian

So, In 3.5 rotation, angle made is, = [tex]360*3.5=1260[/tex] degree

       Or,                                                   =  [tex]3.5*\pi=\frac{7}{2}\pi[/tex] radian

Therefore, The angle represents by 3.5 rotations in counterclockwise is 1260 degree or  [tex]\frac{7}{2}\pi[/tex] radian.

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Observe the figure below.

The given figure shows that the construction of line segment OS. We can observe clearly that OS is bisector of angle POS.

The bisector divides the angle into two equal angles.

So, [tex]\angle POS = \frac{1}{2} \angle POQ[/tex]

Let us observe the given options.

In first option, [tex]60^\circ = \frac{1}{2} \times 120^\circ[/tex]

Therefore, [tex]m \angle POS = 60^\circ, m \angle POQ=120^\circ[/tex]

So, Option A is the correct answer.

Let

m∠ABD--------> x degrees

we know that

The sum os the internal angles of a trapezoid is equal to [tex] 360 degrees [/tex]

So

[tex] 2*116+2*(24+x)=360\\ 232+48+2x=360\\ 2x=360-280\\ x=40degrees [/tex]

therefore

the answer is

The measure of the angle m∠ABD is [tex] 40 degrees [/tex]

The converse of the statement “If an angle is a right angle, then it measures 90 degrees” is “If an angle measures 90 degrees, then it is a right angle.”

The converse of the statement “If an angle is a right angle, then it measures 90 degrees” is “If an angle measures 90 degrees, then it is a right angle.” The converse of a conditional statement swaps the hypothesis and conclusion of the original statement. In this case, the original statement states that if an angle is a right angle (hypothesis), then it measures 90 degrees (conclusion). The converse states that if an angle measures 90 degrees (hypothesis), then it is a right angle (conclusion).

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The quadratic equation 3x^2+6x+7=0 has two complex solutions which is x=-1±√(48)i/6.

To solve the quadratic equation 3x^2+6x+7=0 using the quadratic formula, we first need to identify the coefficients a, b, and c from its standard form, which is ax^2+bx+c=0. In this case, a=3, b=6, and c=7.

The quadratic formula is given by x=(-b±√(b^2-4ac))/(2a).

Now, we will calculate the discriminant which is b^2-4ac. In this case, it is 6^2 - 4*3*7, which equals 36 - 84, or -48. Since the discriminant is negative, this means that there are no real solutions to the equation, but two complex solutions.

Applying the quadratic formula, we get the solutions:

x=(-6 ± √(-48))/(2*3)

This simplifies to:

x=(-6 ± √(48)i)/6

Therefore, the solutions are x=-1±√(48)i/6. The quadratic formula helped us to find the complex roots of the quadratic equation.

Line QR bisects angle PQS. Solve for x and find measure PQS:
m<PQS = 4x - 6, m<PQR = x + 11 ...?

 m<PQR  = (1/2) (m<PQS) = (1/2)( 4x - 6)

    so  x + 11 = 2x - 3 implies x =14

and then m<PQS = 4x - 6 =50°

Answer: if 3 for every 1000 students quit due serious health issues, then you can see the proportion doing the quotient between this numbers. This is:

3/1000 = 0.003

Then if you choose a random student, you have a 0.003 probability of choosing one who can have a health issue.

and a 0.997 probability to choose a student with no health issues.

Now, the company wins  $50 for the healthy students, and lose ($50 - $8000)  = -$7950 for each student that is sick (because they initially pay the 50$ and latter get the $8000).

Then the insurance company should expect to make in average:

0.997*$50 - 0.003*($7950) = $26

So the company should expect to make 26 dollars per student in a year.

The perimeter of the rectangle is 35.0 meters, and the area is 66.0 square meters, using the formulas for perimeter (2(length + width)) and area (length × width).

To calculate the perimeter and area of a rectangle, we apply the formulas: Perimeter = 2(length + width) and Area = length × width. In this case, the rectangle has a length of 5.50 m and a width of 12.0 m.

Calculating the Perimeter

Perimeter = 2(5.50 m + 12.0 m) = 2(17.5 m) = 35.0 m

Calculating the Area

Area = 5.50 m × 12.0 m = 66.0 m²

The perimeter of this rectangle is 35.0 meters, and the area is 66.0 square meters.

Answer:

1gm/ cm^3

Step-by-step explanation:

The total distance Joel walked is 3/4 of a mile.

To find the total distance, we add up the individual distances:

To add these fractions, they must have a common denominator. The least common denominator for 5, 10, and 20 is 20. So we convert the fractions:

Now we add the fractions:

8/20 + 6/20 + 1/20 = 15/20

Finally, we can simplify 15/20 by dividing both the numerator and the denominator by 5:

15/20 = 3/4

Therefore, the total distance Joel walked is 3/4 of a mile.

To find the cost of production for 170 units, consider both fixed costs and variable costs (the integral of the marginal cost function). The cost of producing 171 units can be estimated by adding the marginal cost for the additional unit.

The quantity of interest is C(170), the total cost to produce 170 units. To estimate this value, you can calculate the fixed costs plus the integral of the marginal cost from 1 to 170 (the number of items produced).

So, first, calculate the fixed costs which is given as $13000.

Next, estimate the total variable costs, which is the integral of the marginal cost function over the range from 1 to 170 units. Given marginal cost function is C'(q) = 0.006q^2-q+50. Use the power rule to integrate the function, then evaluate it at q=1 and q=170 and subtract.

The value of C'(170) is simply the value of the marginal cost function at q=170.

After finding the value of C(170) and C'(170), the total cost to produce 171 units, C(171), is approximately the total cost to produce 170 units plus the marginal cost to produce the 171st unit.

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Answer:

The complete factored form of given polynomial  [tex]21x^3+35x^2+9x+15[/tex] is [tex](7x^2+3)(3x+5)[/tex]

Step-by-step explanation:

Given polynomial  [tex]21x^3+35x^2+9x+15[/tex]

We have to factorize the given polynomial completely.

Consider the given polynomial  [tex]21x^3+35x^2+9x+15[/tex]

We will solve it by grouping of terms,

Grouping is collecting terms having some factors common

Taking [tex]7x^2[/tex] common from first two term and 3 from last two terms , we have,

[tex]21x^3+35x^2+9x+15[/tex]

[tex]\Rightarrow 7x^2(3x+5)+3(3x+5)[/tex]

Now taking (3x +5) common from both terms , we have,

[tex]\Rightarrow (7x^2+3)(3x+5)[/tex]

Thus, the complete factored form of given polynomial  [tex]21x^3+35x^2+9x+15[/tex] is [tex](7x^2+3)(3x+5)[/tex]

The estimated quotient for 555 ÷ 8 would be 70.

To estimate the quotient for 555 ÷ 8, we can follow these steps:

We know that Quotients are number that is obtained by dividing one number by another number.

Dividend ÷ Divisor = Quotients

Round the dividend, 555, to the nearest ten:

555 rounds to 560.

Divide the rounded dividend, 560, by the divisor, 8:

560 ÷ 8 = 70.

Therefore, the estimated quotient for 555 ÷ 8 is 70.

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Final answer:

The area of grass that the goat can graze is calculated as a quarter-circle with a radius equal to the length of the rope, which is 6 metres, resulting in an area of approximately 28.27 square metres.

Explanation:

The area of grass a goat can graze when tethered by a 6 metre rope to the outside corner of a shed is a segment of the grassy field. To calculate this area, one must consider two scenarios based on the dimensions of the shed:

If the shed's dimensions of 4 metres by 5 metres do not allow the goat to reach the opposite corner, then the area grazed is a quarter-circle with the rope as the radius.

If the shed's dimensions allow the goat to reach around the corner, then additional area calculations are necessary for the extended grazing area beyond the corner.

In the stated problem, the rope's length does not allow the goat to graze beyond the opposite corner of the shed. Therefore, we calculate the area as a quarter-circle, which is a fraction (1/4) of the area of a full circle with radius 6 metres. The formula for the area of a circle is πr², where r is the radius.

To find the grazeable area, we use:

Area = (1/4) × π × radius² = (1/4) × π × 6² = (1/4) × π × 36

Area = 9π square metres (approximately 28.27 square metres)

The effective grazing area is 22.26 square meters.

The goat can graze in a quarter-circle sweep around the corner where the shed does not block its path.

Step-by-Step Calculation

The goat can graze around the corner up to a 6 metre radius, but the shed blocks its grazing in certain directions.

Calculate the total quarter-circle area the goat can cover:

Area = (1/4) * π * radius² = (1/4) * π * 6² = (1/4) * π * 36 = 9π square metres.

Subtract the area where the shed blocks grazing:

From one corner, the shed blocks a rectangular area measuring 4 meters by 6 meters.

Total area blocked by the shed: 6m * 4m = 24 square meters

Adjust for quarter-circle section, dividing the blockage by 4: 24 / 4 = 6 square meters

The area of grass the goat can graze = Total area - Blocked area

9π - 6 ≈ 28.26 - 6 ≈ 22.26 square metres

Thus, the total area grazed by the goat is 22.26 square meters.

Answer:

1 = b

Step-by-step explanation:

6.8 - 4.2b = 5.6b - 3

First you must add 4.2b to both sides.

Then you will get 6.8 = 9.8b - 3.

Next you must add 3 to both sides.

You will then get 9.8 = 9.8b

Finally divide both sides by 9.8.

You will be left with  1 = b

Answer:

[tex]\int {t\times \sec^2(2t)} \, dt \\\\ \text{Integrating by parts}\\\\=\frac{t\times \tan 2t}{2}-\int{(\frac{d}{dt}(t) \times \int{{\ sec^{2}(2t)}}) dt}\\\\=\frac{t\times \tan 2t}{2}-\int{\frac{\tan 2t}{2}} dt\\\\=\frac{t\times \tan 2t}{2}-\frac{\log sec 2t}{4}+C[/tex]

Where C is Constant of Proportionality.

Answer:

112

Step-by-step explanation:

Answer:  The required value of x is -52.

Step-by-step explanation:  We are given to find the value of x from the following equation :

[tex]x+58=6~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)[/tex]

To find the value of x, we need to solve the equation (i).

The solution of equation (i) is as follows :

[tex]x+58=6\\\\\Rightarrow x=6-58\\\\\Rightarrow x=-52.[/tex]

Thus, the required value of x is -52.