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2 years ago

55) A shirt that usually costs $30 is on sale for $20. Find the percent of the discount.

Mathematics

2 answers:

Natasha2012 [34]2 years ago

5 0

Answer:

Percentage of Discount :---

$\frac{(30 - 20)}{30} \times 100 = \frac{10}{30} \times 100=\boxed{33.33\%}$

ivanzaharov [21]2 years ago

4 0

Find the amount of the discount and divide by the original price:

30-20 = 10

10/30 = 0. 333

Multiply by 100 for percent:

0.333 x 100 = 33.3333%

Round the answer as needed.

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Solve 9^x + 4 = 11 for x using the change of base formula log base b of y equals log y over log b.

Sauron [17]

Answer:

If you meant $9^x+4=11$ , then the answer is approximately 0.866.

If you meant $9^{x+4}=11$ , then the answer is approximately -2.909 which looks like what you meant based on the choices.

Step-by-step explanation:

$9^x+4=11$

First step is to get the exponential part by itself. The part that has the variable exponent which is the $9^x$ term.

To do this we need to subtract 4 on both sides:

$9^x=11-4$

Simplify:

$9^x=7$

The equivalent logarithmic form is:

$\log_9(7)=x$

I always say to myself the logarithm is the exponent that is how I know what to put opposite the side containing the log.

Anyways if you don't have options for computing $\log_b(a)$ in your calculator you need to use the change of base formula.

$\frac{\log(7)}{\log(9)}=x$

So $x \approx 0.8856$

I don't see this as a choice so maybe you actually meant the following equation:

$9^{x+4}=11$

Let's see if this is the correct interpretation.

So the exponential part is already isolated.

So we just need to put in the equivalent logarithmic form:

$\log_9(11)=x+4$

Now we subtract 4 on both sides:

$\log_9(11)-4=x$

Again if you don't have the option for computing $\log_b(a)$ in your calculator, you will have to use the change of base formula:

$\frac{\log(11)}{\log(9)}-4=x$

$x \approx -2.909$

6 0

3 years ago

What is the growth factor associated with the following growth rate: 30% decrease

fenix001 [56]

Given:

Growth rate = 30% decrease

To find:

The growth factor associated with the given growth rate.

Solution:

The general exponential function is:

$y=a(1+r)^x$

$y=a(b)^x$

Where, a is the initial value, r is the growth rate in decimal and $b=1+r$ is the growth factor.

It is given that the growth rate is 30% decrease. So,

$r=-30\%$

$r=-\dfrac{30}{100}$

$r=-0.3$

Now,

$b=1+r$

$b=1+(-0.3)$

$b=1-0.3$

$b=0.7$

Therefore, the growth factor is 0.7.

5 0

2 years ago

Help mee

Rina8888 [55]

Answer:

a percent is a variable of proportionality describing the part of the whole.

4 0

2 years ago

40% of 50 is what number

nikitadnepr [17]

Step-by-step explanation:

Step 1:

Let the number be 50 and to find 40% of 50 is given interms of expression as follows

To express the percentage the following strategy is used

Eg: 40% = $40/100$

∴ To express 40% of 50 is

$(40/100)*50$

Step 2:

On simplification the above expression we could get

$0.4*50$

= 20

4 0

2 years ago

Read 2 more answers

Which equation represents a parabola that opens upward, has a minimum at x = 3, and has a line of symmetry at x = 3?

densk [106]

Answer:

$A.\ y = x^2 - 6x + 13$ is the correct answer.

Step-by-step explanation:

We know that vertex equation of a parabola is given as:

$y = a(x-h)^2+k$

where $(h,k)$ is the vertex of the parabola and

$(x,y)$ are the coordinate of points on parabola.

As per the question statement:

The parabola opens upwards that means coefficient of $x^{2}$ is positive.

Let $a = +1$

Minimum of parabola is at x = 3.

The vertex is at the minimum point of a parabola that opens upwards.

$\therefore$ $h = 3$

Putting value of a and h in the equation:

$y = 1(x-3)^2+k\\\Rightarrow y = (x-3)^2+k\\\Rightarrow y = x^2-6x+9+k$

Formula used: $(a-b)^2=a^{2} +b^{2} -2\times a \times b$

Comparing the equation formulated above with the options given we can observe that the equation formulated above is most similar to option A.

Comparing $y = x^2 - 6x + 13$ and $y = x^2-6x+9+k$

13 = 9+k

k = 4

Please refer to the graph attached.

Hence, correct option is $A.\ y = x^2 - 6x + 13$

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2 years ago

Read 2 more answers