After a 4% reduction, you purchase a new suit for $288. What was the original price of the suit?

The radioactive compound has a half-life of around 3.09 hours.

The period of time needed for a radioactive substance's initial quantity to decay by half is known as its half-life. The half-life of a drug may be calculated as follows if the rate of decay is proportionate to the amount of the substance existing at time t:

Let t be the half-life of the substance, then after t hours, the amount of the substance present will be,

100 mg × [tex]\dfrac{1}{2}[/tex] = 50 mg.

At time 6 hours, the amount of the substance present is,

100 mg × (1 - 3%) = 97 mg.

Given that the amount of material available determines how quickly something degrades,

The half-life can be calculated as follows:

[tex]t = 6 \times \dfrac{50}{ 97} = 3.09 \ hours[/tex]

Therefore, the half-life of the radioactive substance is approximately 3.09 hours.

Learn more about half-life:

brainly.com/question/24710827

#SPJ12

Answer:

- The center line is at 16.5 ounces.

- The standard deviation of the sample mean = 0.112 ounce.

- The UCL = 16.836 ounces.

- The LCL = 16.154 ounces.

Step-by-step explanation:

The Central limit theorem allows us to write for a random sample extracted from a normal population distribution with each variable independent of one another that

Mean of sampling distribution (μₓ) is approximately equal to the population mean (μ).

μₓ = μ = 16.5 ounces

And the standard deviation of the sampling distribution is given as

σₓ = (σ/√N)

where σ = population standard deviation = 0.25 ounce

N = Sample size = 5

σₓ = (0.25/√5) = 0.1118033989 = 0.112 ounce

Now using the 3 sigma limit rule that 99.5% of the distribution lies within 3 standard deviations of the mean, the entire distribution lies within

(μₓ ± 3σₓ)

= 16.5 ± (3×0.112)

= 16.5 ± (0.336)

= (16.154, 16.836)

Hope this Helps!!!

Answer:

9.34%

Step-by-step explanation:

p = 4%, or 0.04

n = Sample size = 667

u = Expected value = n * p = 667 * 0.04 = 26.68

SD = Standard deviation = [tex]\sqrt{np(1-p)} =\sqrt{667*0.04*(1-0.04)}[/tex] = 5.06

Now, the question is if the manager is correct, what is the probability that the proportion of flops in a sample of 667 released films would be greater than 5%?

This statement implies that the p-vlaue of Z when X = 5% * 667 = 33.35

Since,

Z = (X - u) / SD

We have;

Z = (33.35 - 26.68) / 5.06

Z = 1.32

From the Z-table, the p-value of 1.32 is 0.9066

1 - 0.9066 = 0.0934, or 9.34%

Therefore, the probability that the proportion of flops in a sample of 667 released films would be greater than 5% is 9.34%.

Answer:

Step-by-step explanation:sin

(

t

h

e

t

a

)

=

√

7

4

cos

(

t

h

e

t

a

)

=

3

4

tan

(

t

h

e

t

a

)

=

√

7

3

cot

(

t

h

e

t

a

)

=

3

√

7

7

sec

(

t

h

e

t

a

)

=

4

3

csc

(

t

h

e

t

a

)

=

4

√

7

7

Answer:

3

Step-by-step explanation:

Step 1: Isolate y

5y < 20

y < 4

When we figure out the inequality, we see that y has to be less than 4. Therefore, the highest integer value will have to be 3.

Answer:

[tex]\huge\boxed{Option \ 1}[/tex]

Step-by-step explanation:

Since, AE = CE and BE = DE , then E is the midpoint of AC and BD. Causius can use that to show that AC and BD bisect each other which means that they both are the diagonals of a parallelogram bisecting each other. Hence, It will be proved that ABCD is a || gm.

Hope this helped!

Answer:

Solution,

[tex]h(x) = f(x) + g(x) \\ \: \: \: \: \: \: \: = 2x - 1 + 7x - 12 \\ \: \: \: \: \: \: = 2x + 7x - 1 - 12 \\ \: \: \: \: \: \: = 9x - 13[/tex]

hope this helps...

Good luck on your assignment..

Answer:

h(x)=9x-13

Step-by-step explanation:

We want to find out what h(x) is. We know what h(x) is equal to, which is

h(x)= f(x)+g(x)

We know that f(x)=2x-1 and g(x)=7x-12. Substitute the expressions in.

h(x)= (2x-1)+(7x-12)

Simplify by combining like terms. Add all the terms with a variable (x), then all the terms without a variable, or constants.

h(x)=(2x+7x)+(-1+-12)

Add 2x and 7x.

h(x)=(2+7)(x)+(-1+-12)  

h(x)= 9x+(-1+-12)

Add -1 and -12.

h(x)= 9x+(-13)

h(x)=9x-13

Answer: $3267.40

Step-by-step explanation:

A = P (1+r/n)^nt

A= 2500 (1+0.055)^nt

A= 2500 x 1.30696

A = 3267.40

Answer:

11

Step-by-step explanation:

Answer: x=45°

Step-by-step explanation:

Angles opposite from each other are equal. The angle 160 degrees in red on the bottom encompasses two angles: BEG and CEG. Angle BEG is on the opposite side as FEA which means it is equal to x.

Since angle FED on the other side is 115, you subtract 115 from 160 to get 45 degrees.

Answer: x=45°

The angle BEG, which is opposite to the angle FEA, is determined to be 45 degrees.

According to the information provided, in a figure with an angle of 160 degrees (red angle on the bottom), there are two angles labeled as BEG and CEG. It is stated that the angle BEG is opposite to the angle FEA, making them equal, so we can represent this angle as x.

Additionally, it is mentioned that the angle FED on the other side measures 115 degrees.

To find the value of x, we subtract 115 degrees from the angle of 160 degrees.
=160-115
= 45

Thus, the solution is x = 45°.

For more details about the angle visit the link below: https://brainly.com/question/16959514

#SPJ4

Step-by-step explanation:

2) 63

3) 7000

4) 10

These are some answers

Answer:

x = 16.5

Step-by-step-explanation:

The height of the larger triangle is 11, and the height of smaller triangle is 2. Which means that the larger triangle height is 5.5 times greater than the smaller triangle's height.

If the base of the smaller triangle is 3, that means that base of the whole/larger triangle is 16.5 because 3 * 5.5 = 16.5

Answer:

Step-by-step explanation:

i think its 3

Answer:

0

Step-by-step explanation:

You cannot make any triangles with this angle

Answer:

Step-by-step explanation:

Let a = original amt in the savings account

"He spent $48 on a radio and 3/8 of what was left on presents for his friends."

Therefore he kept 5/8 of what was left

5/8(a - 48)

5/8(a - 30) left

:

John then put 2/3 of his remaining money into a checking account and donated the $100 that was left to charity.

a = 2/3(5/8a - 30) + 100

a = 5/12a - 20 + 100

a = 5/12a + 80

a - 5/12a = 80

7/12a = 80

a = $137.17 originally in his saving acct

Answer:

  see the attachment for a graph

Step-by-step explanation:

The vertex of f(x) is (0, 0). The transformation g(x) = f(x -h) +k moves the vertex to (h, k). That is, the graph is translated right by h units, and up by k units.

Your transformation has h = -2, and k = -4. That is, the original graph is translated left 2 units and down 4 units. The result is the blue curve in the attachment.

Answer:

101-120=4

Step-by-step explanation:

All that you need to do is count how many data points fall into this category. In this case, there are four data points that fall into the category of 101-120 pushups

Therefore, the answer to the blank is 4. If possible, please mark brainliest.

Answer:

There are 4 numbers between 101 and 120.

Step-by-step explanation:

101-120: 105, 111, 111, 113 (4 numbers)

Answer:

Hiking: 28%

Canoeing: 16%

Swimming: 24%

Fishing: 32%

Step-by-step explanation:

21 + 12 + 18 + 24 = 75 (there are 75 campers)

21 out of 75 = 28%

12 out of 75 = 16%

18 out of 75 = 24%

24 out of 75 = 32%

Hope this helps!

Please mark Brainliest if correct

Answer:

no solutions

Step-by-step explanation:

6-3x=4-x-3-2x

Combine like terms

6-3x =1 -3x

Add 3x to each side

6 -3x+3x = 1-3x+3x

6 =1

This is not true so there are no solutions

Answer:

No solutions.

Step-by-step explanation:

6 - 3x = 4 - x - 3 - 2x

Add or subtract like terms if possible.

6 - 3x = -3x + 1

Add -1 and 3x on both sides.

6 - 1 = -3x + 3x

5 = 0

There are no solutions.

Using the Central Limit Theorem, it is found that the measures are given by:

a) 2,500,000.

b) 88,388.35.

c) 2,500,000.

By the Central Limit Theorem, the sampling distribution of sample means of size n for a population of mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] has the same mean as the population, but with standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex]

Hence, we have that for options a and c, the mean is of 2,500,000 users, while for option b, the standard deviation is given by:

[tex]s = \frac{\sigma}{\sqrt{n}} = \frac{625000}{\sqrt{50}} = 88,388.35.[/tex]

More can be learned about the Central Limit Theorem at https://brainly.com/question/24663213

Answer:

Let's solve your equation step-by-step.

[tex]x^7+64x^4=0[/tex]

Step 1: Factor left side of equation.

[tex]x^4(x+4)(x^2-4x+16)=0[/tex]

Step 2: Set factors equal to 0.

[tex]x^4=0[/tex]  or  [tex]x+4=0[/tex]  or  [tex]x^2-4x+16=0[/tex] 

[tex]x^4=0[/tex]  or  [tex]x=0[/tex]  

Answer:

I hope this help you :)

Answer:

We need a sample of at least 1937.

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.

[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

In which

z is the zscore that has a pvalue of [tex]1 - \frac{\alpha}{2}[/tex].

The margin of error is:

[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

For this problem, we have that:

[tex]\pi = 0.72[/tex]

95% confidence level

So [tex]\alpha = 0.05[/tex], z is the value of Z that has a pvalue of [tex]1 - \frac{0.05}{2} = 0.975[/tex], so [tex]Z = 1.96[/tex].

How large a sample should be if you want your estimate to be within 0.02 with 95% confidence.

We need a sample of at least n.

n is found when M = 0.02. So

[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

[tex]0.02 = 1.96\sqrt{\frac{0.72*0.28}{n}}[/tex]

[tex]0.02\sqrt{n} = 1.96\sqrt{0.72*0.28}[/tex]

[tex]\sqrt{n} = \frac{1.96\sqrt{0.72*0.28}}{0.02}[/tex]

[tex](\sqrt{n})^{2} = (\frac{1.96\sqrt{0.72*0.28}}{0.02})^{2}[/tex]

[tex]n = 1936.16[/tex]

Rounding up to the nearest number.

We need a sample of at least 1937.

Answer:

a prism is a three dimensional shape with the same width all the way through.

Step-by-step explanation:

Step-by-step explanation:

i think this will help.

Answer:

En álgebra, el teorema del factor es un teorema que vincula factores y ceros de un polinomio. Es un caso especial del teorema del resto polinómico.

Step-by-step explanation:

Answer:

The second graph.

Step-by-step explanation:

0-9: 6 numbers

10-19: 2 numbers

20-29: 1 number

30-39: 3 numbers

40-49: 1 number

50-59: 2 numbers

60-69: 0 numbers

70-79: 5 numbers

80-89: 3 numbers

90-99: 1 number

Answer:

1/5

Step-by-step explanation:

20*5 = 100, so 20 is 1/5

Answer:

x = 2

Step-by-step explanation:

the equation of the line can be found using the slope intercept form

y = mx +b

y= -3/2 x + 3

x intercept is found by setting y=0 bc that will give you the x-value at which the line crosses the x -axis so

0 = -3/2x+3 (subtract the 3 on both sides) would cancel out the + 3 and would

-3 = -3/2 x  (divide by -3/2 on both sides to cancel out the -3/2)  

x = 2

Answer:

A warranty of 6.185 years should be provided.

Step-by-step explanation:

When the distribution is normal, we use the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this question, we have that:

[tex]\mu = 8.2, \sigma = 1.3[/tex]

What warranty should be provided so that the company is replacing at most 6% of their blenders sold?

The warranty should be the 6th percentile, which is X when Z has a pvalue of 0.06. So X when Z = -1.55.

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]-1.55 = \frac{X - 8.2}{1.3}[/tex]

[tex]X - 8.2 = -1.55*1.3[/tex]

[tex]X = 6.185[/tex]

A warranty of 6.185 years should be provided.

Answer:

$394,772.11

Step-by-step explanation:

This requires using compound interest as follows:

Principal = $5,000

Time = 25 years

Interest rate per annum = 8%

1st year: principal = 5000

Interest capitalized (5000*0.08) = 400

Amount (5000 + 400) = $5400

2nd year: principal = 5400 + 5000 = 10,400

Interest capitalized (10,400*0.08) = 832

Amount (10,400 + 832) = $11,232

3rd year: principal = 11,232+5000 = $16,232

Interest capitalized (16,232*0.08) = 1,298.56

Amount (16,232+1,298.56) = $17,530.56

4th year: principal = 17,530.56+5000 = $22,530.56

Interest capitalized (22,530.56*0.08) = 1,802.45

Amount (22,530.56+1,802.45) = $24,333.01

5th year: principal = 24,333.01+5000 = $29,333.01

Interest capitalized (29,333.01 * 0.08) = 2,346.64

Amount (29,333.01 + 2,346.64) = $31,679.65

6th year: principal = 31,679.65 + 5000 = $36,679.65

Interest capitalized (36,679.65 * 0.08) = 2,934.37

Amount (36,679.65 + 2,934.37) = $39,614.02

7th year: principal = 39,614.02 + 5000 = $44,614.02

Interest capitalized (44,614.02 * 0.08) = 3,569.12

Amount (44,614.02 + 3,569.12) = $48,183.14

8th year: principal = 48,183.14 + 5000 = $53,183.14

Interest capitalized (53,183.14 * 0.08) = 4,254.65

Amount (53,183.14 + 4,254.65) = $57,437.79

9th year: principal = 57,437.79 + 5000 = $62,437.79

Interest capitalized (62,437.79 * 0.08) = 4,995.02

Amount (62,437.79 + 4,995.02) = $67,432.81

10th year: principal = 67,432.81 + 5000 = $72,432.81

Interest capitalized (72,432.81 * 0.08) = 5,794.63

Amount (72,432.81 + 5,794.63) = $78,227.44

11th year: principal = 78,227.44 + 5000 = $83,227.44

Interest capitalized (83,227.44 * 0.08) = 6,658.20

Amount (83,227.44 + 6,658.20) = $89,885.64

12th year: principal = 89,885.64 + 5000 = $94,885.64

Interest capitalized (94,885.64 * 0.08) = 7,590.85

Amount (94,885.64 + 7,590.85) = $102,476.49

13th year: principal = 102,476.49 + 5000 = $107,476.49

Interest capitalized (107,476.49 * 0.08) = 8,598.12

Amount (107,476.49 + 8,598.12) = $116,074.61

14th year: principal = 116,074.61 + 5000 = $121,074.61

Interest capitalized (121,074.61 * 0.08) = 9,685.97

Amount (121,074.61 + 9,685.97) = $130,760.58

15th year: principal = 130,760.58 + 5000 = $135,760.58

Interest capitalized (135,760.58 * 0.08) = 10,860.85

Amount (135,760.58 + 10,860.85) = $146,621.43

16th year: principal = 146,621.43 + 5000 = $151,621.43

Interest capitalized (151,621.43 * 0.08) = 12,129.71

Amount (151,621.43 + 12,129.71) = $163,751.14

17th year: principal = 163,751.14 + 5000 = $168,751.14

Interest capitalized (168,751.14 * 0.08) = 13,500.09

Amount (168,751.14 + 13,500.09) = $182,251.23

18th year: principal = 182,251.23 + 5000 = $187,251.23

Interest capitalized (187,251.23 * 0.08) = 14,980.10

Amount (187,251.23 + 14,980.10) = $202,231.33

19th year: principal = 202,231.33 + 5000 = $207,231.33

Interest capitalized (207,231.33 * 0.08) = 16,578.51

Amount (207,231.33 + 16,578.51) = $223,809.84

20th year: principal = 223,809.84 + 5000 = $228,809.84

Interest capitalized (228,809.84 * 0.08) = 18,304.79

Amount (228,809.84 + 18,304.79) = $247,114.63

21st year: principal = 247,114.63 + 5000 = $252,114.63

Interest capitalized (252,114.63 * 0.08) = 20,169.17

Amount (252,114.63 + 20,169.17) = $272,283.8

22nd year: principal = 272,283.8 + 5000 = $277,283.8

Interest capitalized (277,283.8 * 0.08) = 22,182.70

Amount (277,283.8 + 22,182.70) = $299,466.5

23rd year: principal = 299,466.5 + 5000 = $304,466.5

Interest capitalized (304,466.5 * 0.08) = 24,357.32

Amount (304,466.5 + 24,357.32) = $328,823.82

24th year: principal = 328,823.82 + 5000 = $333,823.82

Interest capitalized (333,823.82 * 0.08) = 26,705.91

Amount (333,823.82 + 26,705.91) = $360,529.73

25th year: principal = 360,529.73 + 5000 = $365,529.73

Interest capitalized (365,529.73 * 0.08) = 29,242.38

Amount (365,529.73 + 29,242.38) = $394,772.11

Answer:

Step-by-step explanation:

Ray

Answer:

ray

Step-by-step explanation:

ray is a part of a line that has an endpoint in one side and extends indefinitely on the opposite side. hence, the answer is ray

hope this helps