Which of the following rates is proportional to $2.50 for 5 cans?

A. $2.00 for 3 cans
B. $4.00 for 7 cans
C. $4.50 for 9 cans
D. $1.50 for 1 can

Final answer:

To find the product of (5.2 · [tex]10^-^6[/tex]) and (8 · 10³), multiply the base numbers and add the exponents. The result is 41.6 × [tex]10^-^3[/tex], which simplifies to 4.16 × 10^-2.

Explanation:

The student asked to find the product of two numbers expressed in scientific notation: (5.2 · [tex]10^-^6[/tex]) and (8 · 10³). When multiplying numbers in scientific notation, you multiply the base numbers and add the exponents.

Step-by-Step Solution:

Simplified Result:

This can further be simplified by writing 41.6 × [tex]10^-^3[/tex]as 4.16 × [tex]10^-^2[/tex], by moving one decimal place to the left in the base number and increasing the exponent by 1 to balance it.

Answer:

An employee can legitimately claim the following as exemptions:

B. Self

C. Dependents

Step-by-step explanation:

We know that an employee can claim the health and medical insurance ( which is also known as Medicare and Social security deductions)  for himself or for himself, his/ her spouse and his family members or dependents.

Hence,  

An employee can legitimately claim the following as exemptions:

B.  Self

C. dependents.

Hence, option B and C are the correct options.

Answer:

A)

Step-by-step explanation:

The equivalent expression of [tex]2^{\frac{1}{3} }[/tex] in radical forms is ∛2

Radical are expression that uses a root, such as square root, cube root . They are numbers represented in radical symbols.

Therefore,

[tex]2^{\frac{1}{3} }[/tex] in radical form can be represented as follows:

Using indices rule

[tex]a^{\frac{1}{b} } = \sqrt[b]{a}[/tex]

Therefore,

[tex]2^{\frac{1}{3} } = \sqrt[3]{2}[/tex]

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The perimeter of the triangle will be 48  cm. The correct option is D.

A perimeter is the total length of the boundary or outer edge of a two-dimensional shape. It is the sum of the lengths of all the sides of the shape.

For example, the perimeter of a rectangle is the sum of the lengths of all four sides, while the perimeter of a circle is the distance around its circumference. The perimeter is usually measured in units such as meters, centimeters, inches, or feet, depending on the context of the problem.

Whenever we have two tangents outside the circle and they are in contact with each other, it means their lengths are the same

The perimeter of the triangle will be calculated as,

Perimeter = sum of all the sides

Perimeter = ( 11 + 11 + 7 + 7 + 6 + 6 )

Perimeter = 48 cm

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To find the housing block dimensions, we set up a system of equations based on the total fencing and area given, and then solve for the length and width.

The student has asked about finding the dimensions of a housing block where a new fence is constructed on three sides and the total area of the block is 240 m2. Given that 52 m of fencing is used, to determine the dimensions, we need to solve a system of equations derived from the perimeter and area provided.

Let's assume the length of the block is L meters, and the width is W meters. The area of the block (A) can thus be defined as A = L × W. Given that A = 240 m2, we have L × W = 240. Since the fence covers three sides, the total length of fencing used would be L + 2W, which is equal to 52 meters. Therefore, we have L + 2W = 52 meters.

To solve for L and W, we set up the system of equations:

From the second equation, we can express L as L = 52 - 2W and then substitute into the first equation to find W. Finally, we can determine the value for L using the found value of W.

The expression that represents the situation is 40 + 3p.

The correct option is D.

Equations whose variables have a power of one are called linear equations. One example with one variable is where ax+b = 0, where a and b are real values and x is the variable.

The essay is worth 40 points and each correctly answered multiple-choice question is worth 3 points.

If Rasha answered p multiple-choice questions correctly, she would earn a total of 40 + 3p points.

Therefore, the correct expression is D.

40 + 3p.

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Final answer:

The answer explains the calculation of the probability of an event occurring using provided probabilities and the intersection formula.

Explanation:

The probability of Kaitlyn going to the store and buying blueberries can be calculated using the formula for the intersection of two events.

We know that P(going to the store) = 0.3, P(buying blueberries) = 0.9, and we are looking for P(going to the store and buying blueberries).

Therefore, the probability of Kaitlyn going to the store and buying blueberries is 0.3 × 0.9 = 0.27 or 27%.

Answer:

B. [tex]x=62[/tex]; [tex]y=30[/tex]

Step-by-step explanation:

We have been given two similar triangles. We are asked to find the value of x and y for the given triangles.

[tex]\Delta SWK\sim \Delta EBT[/tex]

We know that the measure of corresponding angles of two similar triangles are equal.

[tex]m\angle S=m\angle E[/tex]

[tex]m\angle W=m\angle B[/tex]

[tex]m\angle K=m\angle T[/tex]

[tex]110=2x-14[/tex]

[tex]2x-14=110[/tex]

[tex]2x-14+14=110+14[/tex]

[tex]2x=124[/tex]

[tex]\frac{2x}{2}=\frac{124}{2}[/tex]

[tex]x=62[/tex]

[tex]m\angle S=m\angle E[/tex]

[tex]40=m\angle E[/tex]

Using angle sum property, we will get:

[tex]m\angle E+m\angle B+m\angle T=180[/tex]

[tex]40+y+110=180[/tex]

[tex]y+150=180[/tex]

[tex]y+150-150=180-150[/tex]

[tex]y=30[/tex]

Therefore, option B is the correct choice.

To find the cost of each taco and enchilada, set up a system of equations based on the given bills and solve for the variables T (taco) and E (enchilada). The solution reveals that each taco costs $0.90 and each enchilada costs $2.00.

To solve the problem of determining the individual cost of a taco and an enchilada based on the two given bills, we can set up a system of linear equations. Let's denote the price of a taco as 'T' and the price of an enchilada as 'E'.

The first equation represents your order: 2T + 3E = $7.80.
The second equation represents your friend's order: 3T + 5E = $12.70.

To solve the system, you can use either the substitution or elimination method. For this example, we'll use the elimination method:

So, each taco cost $0.90 and each enchilada cost $2.00.

By determining the cost per song, which is $0.78, we can calculate that downloading ten songs from the website would cost $7.80.

To determine the cost to download ten songs, we first need to calculate the cost per song. We are given that six song downloads cost $4.68. By dividing this total cost by the number of songs, we find the cost per song:

Cost per song = Total cost for six songs / Number of songs

= $4.68 / 6

= $0.78 per song

Now, to find the cost of ten songs, we multiply the cost per song by ten:

Total cost for ten songs = Cost per song * Number of songs

= $0.78 * 10

= $7.80

Therefore, it would cost $7.80 to download ten songs from the website.

The surface area of a cone with diameter 28 cm and height 22 cm in terms of pi is:

        c.     561.1 pi cm²

The diameter of cone= 28 cm

Radius of cone is half the diameter this means that:

Radius(r) of cone= 14 cm

Also, height(h) of cone= 22 cm

We know that the surface area of cone is given by:

[tex]Surface\ Area=\pi r(r+\sqrt{h^2+r^2})[/tex]

Now as we know the value of h and r hence we will substitute these values in the formula to get:

        [tex]Surface\ Area=\pi \times 14(14+\sqrt{(14)^2+(22)^2})\\\\\\Surface\ Area=14\pi (14+26.07681)\\\\\\surface\ Area=14\pi\times 40.07681\\\\\\Surface\ Area=561.07534\pi cm^2[/tex]

  Hence, the surface area of cone is:  561.1π cm²

The exact values of the given expressions are 90 degrees or π/2 radians, 90 degrees or π/2 radians, and 60 degrees or π/3 radians respectively.

Question 8:

The inverse cosine (cos^{-1}) of 0 is the angle whose cosine is 0. In other words, cos^{-1}(0) will give you the angle whose cosine is 0. The only angle that satisfies this condition is 90 degrees or π/2 radians.

Question 9:

The inverse sine (sin^{-1}) of 1 is the angle whose sine is 1. In other words, sin^{-1}(1) will give you the angle whose sine is 1. The only angle that satisfies this condition is 90 degrees or π/2 radians.

Question 10:

The inverse tangent (tan^{-1}) of (√3/3) is the angle whose tangent is (√3/3). In other words, tan^{-1}(√3/3) will give you the angle whose tangent is (√3/3). The angle that satisfies this condition is 60 degrees or π/3 radians.

Final answer:

The amplitude of a wave is the coefficient A in the equation y(x, t) = A sin(kx - ωt + φ), and the period T can be calculated using T = 2π/ω, where ω is the angular frequency. Additional properties like wavelength and speed can be found using related equations involving the wave number and frequency.

Explanation:

To find the amplitude and period from the equation of a wave, look at the standard form of a sinusoidal wave function, which is generally y(x, t) = A sin(kx - ωt + φ). Here, the amplitude can be directly read from the equation as the coefficient A, which represents the maximum displacement from the rest position. As for the period, it can be derived from the angular frequency using the formula T = 2π/ω, where T is the period and ω is the angular frequency.

The wavelength (λ) and speed (v) of the wave can also be determined from the properties of the wave. The wavelength is related to the wave number by the equation λ = 2π/k, and the speed can be calculated if the frequency (f) is known, using the equation v = λf.

For example, if the amplitude is provided as 30 V/m and the frequency is given as 2.0 MHz, the period (T) would then be 5.0 × 10-7 s based on the relationship between frequency and period, T = 1/f.

Answer:

The answer is D. 6

Step-by-step explanation:

Therefore, the solution of given equation is [tex]28.[/tex]

What is the simplification?

Simplification is reducing the expression/fraction/problem in a simpler form. It makes the problem easy with calculations and solving.

Here given equation is

[tex]8[/tex] x [tex]6 + (12- 4)[/tex] which is divisible by [tex]2[/tex].

So,

[tex]\frac{8(6)+(12-4)}{2}\\\\=\frac{48+8}{2}\\\\=\frac{56}{2}\\\\=28[/tex]

Hence, the solution of given equation is [tex]28.[/tex]

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