Daria pays x dollars for a pair of shoes. The tax on shoes is

Ahmad just put some money into a cd that pays 11.3% interest compounded semiannually according to the rule of 72 in approximatel

lilavasa [31]

The "rule of 72" says that the doubling time in years is approximately 72 divided by the interest rate in percent. To make the money grow by a factor of 4 requires that it double twice, so will take twice as long as the period to double once.
2×72/11.3 ≈ 12.7 . . . . years

_____
The "rule of 72" is an approximation. The actual quadrupling time for this interest rate and compounding is about 12.6 years. (The actual product of doubling time and nominal interest rate is about 71.25.)

5 0

2 years ago

ΔABC underwent a sequence of rigid transformations to give ΔA′B′C′. Which transformations might have taken place?

Papessa [141]

Answer: The correct option is second, a rotation $90^{\circ}$ clockwise about the origin followed by a reflection across the x-axis.

Explanation:

From the given figure it is noticed that the vertices of ΔABC are A(-6,4), B(-4,6), C(-2,2) and vertices of ΔA'B'C' are A'(4,-6), B(6,-4), C(2,-2).

It means if the point is P(x,y) then after transformation it will be P'(y,x).

If a point P(x,y) reflection across the y-axis followed by a reflection across the x-axis, then the image of point after transformation will be P'(-x,-y), therefore it is not the correct option.

If a shape is rotated $90^{\circ}$ clockwise about the origin then the point P(x,y) will be P'(y,-x) and after that reflect across the x-axis, so the point after transformation will be P'(y,x), therefore it is the correct option.

If a shape is rotated $270^{\circ}$ clockwise about the origin then the point P(x,y) will be P'(-y,x) and after that reflect across the x-axis, so the point after transformation will be P'(-y,-x), therefore it is not the correct option.

If a point P(x,y) reflection across the x-axis followed by a reflection across the y-axis, then the image of point after transformation will be P'(-x,-y), therefore it is not the correct option.

Hence, the correct option is second, a rotation $90^{\circ}$ clockwise about the origin followed by a reflection across the x-axis.

4 0

2 years ago

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The amounts of vitamin C (in milligrams) for 100g (3.57 ounces) of various randomly selected fruits and vegetables are listed. I

34kurt

Answer:

H0: sigma=12

H1:sigma≠12

This hypothesis test is a two tailed test.

Step-by-step explanation:

The null value described in the statement is 12 mg. So, the null hypothesis would be sigma=12. As the statement states that whether there is sufficient evidence to conclude that standard deviation differs from 12 mg, so the alternative hypothesis would be sigma ≠12. The alternative hypothesis contains inequality sign so, the hypothesis test is a two tailed test.

4 0

2 years ago

For what values of m does the graph of y = 3x^2 + 7x + m have two x-intercepts? a) m>12/49 b) m<12/49 c) m<49/12 d) m&g

den301095 [7]

The quadratic formula, has a part we call the "discriminant" defined by the variables that are inside the square root, and is denotated by "delta":

Δ=b2−4ac Whenever we solve a quadratic equation that is complete and we analyze the discriminant, we can get 3 scenarios: if→Δ>0=>∃x1,x2/ax2+bx+c=0 This just means: "if the discriminant is greater than zero, there will exist two x-intercepts" And for the second scenario: if→Δ=0→∃xo/ax2+bx+c=0 This means: "if the discriminant is equal to zero, there will be one and only one x-intercept" And for the last scenario: if→Δ<0→∃x∉R/ax2+bx+c=0 This means that :"if the discriminant is less than zero, there will be no x-intercepts" So, if we take your excercise and analyze the the discriminant: 3x2+7x+m=y we will find the values that satisfy y=0 : 3x2+7x+m=0 And we'll analyze the discriminant: Δ=72−4(3)(m) And we are only interested in the values that make the discriminant equal zero: 72−4(3)(m)=0 All you have to do is solve for "m".

6 0

2 years ago

What is the minimum number of points needed to determine the equation of a line containing those points?. The choices are the fo

vodomira [7]

I believe the correct answer among the choice presented above is the second option. The minimum number of points needed to determine the equation of a line containing those points is two. This is because two points is also needed to make or define a line.

5 0

2 years ago

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