A radioactive element decays at a rate of 5% annually. There are 40 grams of the substance present. • How much of the substance remains after 30 years (to the nearest tenth)? • When will the amount of the substance drop to below 20 grams (to the nearest year)?

Answer:

D: Lauren made her first error in step 3 because she should have used 85-60 = 25 for chemistry and 80-60 = 20 for biology

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

Got it right on ed 2020

Answer:

The total amount of fishes  caught is 414,519 fishes

Step-by-step explanation:

Here, given the percentage decrease in the population of fishes, we want to know the total amount of fishes caught by the company in the first 7 years.

First year, we have 75,000 fishes

Second year, we would have 75,000 - (8% of 75,000) = 75,000 - (0.08 × 75,000) = 75,000 - 6,000 = 69,000

Third year, we would have 69,000- (0.08 × 69,000) = 69,000 - 5520 = 63,480

Fourth year, we would have 63,480 - (0.08 × 63,480) = 58,401.6

Fifth year, we would have 58,401.6 - (0.08 × 58,401.6) = 58,401.6 - 4,672.18 = 53,729.472

Sixth year, we would have 53,729.472 - (0.08 × 53,729.472) = 53,729.472 - 4,298.3578 = 49,431.114

Seventh year, we would 49,431.114 - (0.08 × 49,431.114) = 45,476.625

The addition of all these values will give the total number of fishes caught = 75,000 + 69,000 + 63,480 + 58,401.6 + 53,729.472 + 49,431.114 + 45,476.625 = 414,518.8 = 414,519 fishes to the nearest whole number

Final answer:

Learn how to calculate the total fish caught by a fishing company over 7 years with decreasing catches.

Explanation:

A major fishing company caught 75,000 fish in the first year. Each year, the number of fish caught decreased by 8%. To find the total fish caught over 7 years:

Calculate the number of fish caught each year by multiplying the previous year's catch by (100% - 8%).

Add up the catches for 7 years.

Round the final total to the nearest whole number.

Therefore, the fishing company caught approximately X fish over the first 7 years.

Answer:

I assume the answer would be that f(x) = 6(x) increases over the interval x = 3 to x = 4

Step-by-step explanation:

6 x 3 is 18 and 6 x 4 is 24, so over the interval x = 3 to x = 4 f(x) would increase.

Answer:

sin(74º) = 0.96

Step-by-step explanation:

answer is 70

When rounding to the nearest tenth like 74 we:

Round the number to the nearest tenth if the last digit of the number is 5678 or 9

Then we do the same rounding it down

Answer:

Always true

All real numbers

Step-by-step explanation:

The given equation 1/6(12z-18)=2z-3 has no solution.

The given equation is 1/6(12z-18)=2z-3.

The solution of an equation is the set of all values that, when substituted for unknowns, make an equation true.

Here, 1/6(12z-18)=2z-3

12z/6 -18/6 =2z-3

2z-3=2z-3

Transpose 3 to other side of the equation, we get

2z=2z-3+3

2z = 2z

Transpose 2z to other side of the equation, we get

2z-2z=0

Therefore, the given equation has no solution.

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Answer:

Step-by-step explanation:

X=y

[tex]\[ \csc(\theta) = \frac{15}{12} = \frac{5}{4} \][/tex] Option C. 15/12 is the Right Choice.

In a right triangle, the cosecant ([tex]\(\csc\)[/tex]) of an angle is the ratio of the length of the hypotenuse to the length of the side opposite the angle. In this scenario, we're given an angle [tex]\( \theta \)[/tex] and the side opposite to it measures 12 units. The length of the hypotenuse is denoted as [tex]\( r \)[/tex], and the length of the other side is 9 units.

To find the length of the hypotenuse ([tex]\( r \)[/tex]), we can use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides. So, we have:

[tex]\[ r^2 = 12^2 + 9^2 \][/tex]

[tex]\[ r^2 = 144 + 81 \][/tex]

[tex]\[ r^2 = 225 \][/tex]

Taking the square root of both sides, we get [tex]\( r = 15 \)[/tex].

Now that we have the length of the hypotenuse ([tex]\( r = 15 \)[/tex]), we can find the cosecant ([tex]\(\csc\)[/tex]) of angle [tex]\( \theta \)[/tex]. The definition of [tex]\(\csc\)[/tex] in a right triangle is:

[tex]\[ \csc(\theta) = \frac{r}{\text{opposite side}} \][/tex]

Substituting the values we have, we get:

[tex]\[ \csc(\theta) = \frac{15}{12} \][/tex]

Simplifying this expression, we find that:

[tex]\[ \csc(\theta) = \frac{5}{4} \][/tex]

Therefore, the value of [tex]\( \csc(\theta) \)[/tex] is [tex]\( \frac{5}{4} \)[/tex]. Hence, the correct answer is C. 15/12.

Answer:

B

Step-by-step explanation:

Answer:

A. 5.3%

Step-by-step explanation:

Answer:

4 x 10^12

Step-by-step explanation:

I used a calculator.

(6x10^8) divided by (1.5 x 10^-4) is 4 x 10^12.

Division is the action of separating something into parts or the process of being separated.

How to solve?

While dividing;

[tex]\frac{6(10^8)}{1.5(10^-4)} \\\frac{6(10^8)(10^4)}{1.5}\\ 4(10^{12})[/tex]

The answer will be 4 x 10^12.

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Words typed in 1 minute = 70

Words typed in 12 minutes = 70 x 12 = 840 words

If Miko types at 70 words per minute, in 12 minutes he can type 840 words if he maintains the same speed throughout.

Answer:

It can be factorised

Step-by-step explanation:

Given

x²y² + 36 - 4x² - 9y² ( rearranging )

x²y² - 4x² - 9y² + 36 ( factor first/second and third/fourth terms )

= x²(y² - 4) - 9(y² - 4) ← factor out (y² - 4) from each term

= (y² - 4)(x² - 9)

Both factors are a difference of squares and factor in general as

a² - b² = (a - b)(a + b)

Thus

y² - 4

= y² - 2² = (y - 2)(y + 2) , and

x² - 9

= x² - 3² = (x - 3)(x + 3)

Hence

x²y² + 36 - 4x² - 9y² = (y - 2)(y + 2)(x - 3)(x + 3)

Answer: Kelsey graphed the slope as the y-intercept and the y- intercept as the slope.

Step-by-step explanation:

Answer: D on edg

Step-by-step explanation:

Kelsey graphed the slope as the y-intercept and the y- intercept as the slope.

Answer:

x =11.17741935 gallons

Step-by-step explanation:

We can use a ratio to solve

62 miles    231 miles

---------     = -----------

3 gallons      x gallons

Using cross products

62x = 231 *3

62x =693

Divide each side by 62

62x/62 = 693/62

x =11.17741935 gallons

Answer: 11.1774194 gallons of gas

Explanation: To solve this problem, our first step is to write down the unit ratio that is involved. In this case, it's miles traveled/gallons of gas.

Next, we set up a proportion based

on the information in the problem.

We know that a car gets 62 miles for every 3 gallons so we have 62/3 and we're asked how many gallons of gas

will it use to travel 231 miles so that's 231/x.

Notice that the 231 miles must go on top in the second ratio

because our unit ratio tells us that we put miles over gallons.

Solving from here, we use the means-extremes property which states that the product of the extremes, (62)(x) equals the product of the means, (3)(231).

So we have the equation 62x = 693.

Now, dividing both sides of the equation

by 63, we find that x = 11.1774194.

This means that the car will use 11.1774194

gallons of gas to travel 231 miles.

Answer:

[tex] area = 21.11 ~in.^2 [/tex]

Step-by-step explanation:

Area of sector of circle with central angle measuring n degrees and radius r:

[tex] area = \dfrac{n}{360^\circ}\pi r^2 [/tex]

[tex] area = \dfrac{80^\circ}{360^\circ} \times 3.14 \times (5.5~in)^2 [/tex]

[tex] area = \dfrac{80^\circ}{360^\circ} \times 3.14 \times (5.5~in)^2 [/tex]

[tex] area = 21.11 ~in.^2 [/tex]

The area of the sector of the circle will be 21.12 inch².

The area of sector of circle central angle θ in degree and radius r will be represented as

A= (θ/360°)πr²

the sector has a central angle θ=80°

r=5.5 inches

substituting these values in above formula for the area of the sector of circle,

Area= A

= (θ/360°)πr²

= (80°/360°)π(5.5)²

=21.12 inch²

Therefore, the area of the sector will be 21.12 inch².

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Answer:

no solution

Step-by-step explanation:

–5x – 12y – 43z = –136

–4x – 14y – 52z = –146

21x + 72y + 267z = 756

Every coefficient of the second equation is a multiple of 2, so divide both sides by 2.

Every coefficient of the third equation is a multiple of 3, so divide both sides by 3.

–5x – 12y – 43z = –136

–2x – 7y – 26z = –73

 7x + 24y + 89z = 252

Let's call the above system the "simplified original system."

Using the simplified original system, multiply the first equation by -2 and the second equation by 5. Then add them.

         10x + 24y + 86z = 272

(+)      -10x - 35x - 130z = 365

------------------------------------------

                  -11y - 44z = 637

Now we have an equation with only y and z.

Now, using the simplified original system, multiply the second equation by 7 and the third equation by 2. Then add them.

       –14x – 49y – 182z = –511

(+)       14x + 48y + 178z = 504

-------------------------------------------

                    -y - 4z = -7

Now we have a system in 2 unknowns, y and z.

-11y - 44z = 637

-y - 4z = -7

Multiply the second equation by -11 and add to the first equation.

     -11y - 44z = 637

(+)     11y + 44z = 77

-----------------------------

                0 = 714

Since 0 = 714 is false, this system has no solution.

Answer:

87.28 cubic inches

Step-by-step explanation:

Leigh wants to fill the conical candle wax mold completely with candle wax.

We have to calculate the volume of the cone by the formula :

[tex]V=\pi r^2\frac{h}{3}[/tex]

Here, V = volume

r = radius = 2.1 inches

h = height = 18.9 inches

By substituting these values given, into the formula

[tex]V=\pi (2.1)^2(\frac{18.9}{3})[/tex]

   = (27.783)π

   = 87.28 inch³

Conical mold can hold 87.28 inch³ candle wax.

Answer:

f(2) = 7

Step-by-step explanation:

To figure this out you just have to plug in 2 wherever x is in the equation.

f(2) = 5(2) - 3

Multiply 5 by 2

f(2) = 10 - 3

Subtract

f(2) = 7

Answer:

Length = 4 units

Step-by-step explanation:

Width = x units

Length = (x + 4) units

Area = 32 square units

length * width = 32

(x +4) *x = 32

x *x + 4 * x = 32

x² + 4x  -32 = 0

Sum = 4

Product = -32

Factor = 8 , (-4)

x² + 4x  -32 = 0

x² + 8x - 4x - 4 * 8 = 0

x(x + 8) - 4(x +8) = 0

(x + 8) (x - 4) = 0

(x + 8) is ignored because measurements will not have negative sign.

x-4 =0

x = 4

Width = 4 units

Length = x + 4 = 4 + 4 = 8 units

Answer:

16,048 visitors per day.

Step-by-step explanation:

To solve for this answer, you will simply need to divide the total amount of visitors (48,144) by the amount of days given, which in this instance, is 3.

48,144÷3= 16,048 visitors per day.

5 is correct

5/6 = 15/18

Answer:0.0

Step-by-step explanation:

To find the most significant difference in Bella's budget, calculate the difference for each category and compare them. For Mary Ann, by subtracting her expenses from her net income of $2,589.10, we determine she can save more than 10% of her income, exceeding her savings goal.

The most significant difference between Bella's actual spending and her budget can be determined by comparing the projected expenses to the actual expenses in each category. You'll first calculate the difference for each category by subtracting the actual amount from the projected amount. These differences should be compared to determine which one is the largest. For Mary Ann's scenario, we can construct a budget table and calculate the possibility of saving 10% of her after-tax monthly income by deducting her monthly expenses from her net income. To do this, you'll start with her net monthly income and subtract each of her monthly expenses to check if there's at least 10% of her income left for savings.

If Mary Ann's net monthly income is $2,589.10, her goal is to save 10% of that amount, which would be $258.91. Once you subtract her expenses which total $2,145 (the sum of rent, cell phone, utilities, cable TV and internet, groceries, entertainment, car payment, and gasoline) from her net income, you're left with $444.10. Therefore, she can meet her savings goal since $444.10 is more than $258.91. You can use similar steps and considerations for creating and managing a budget based on the cost of living in your area.

Answer:

16

Step-by-step explanation:

The radius is half the size of the diameter.

8 * 2 = 16

Answer:

(a) C: 0.0465 ; reject the null hypothesis

(b) B: 0.3409 ; fail to reject the null hypothesis

Step-by-step explanation:

Firstly, the decision rule based on P-value to reject the null hypothesis or fail to reject the null hypothesis is given by;

(a) Now, we are given alternate hypothesis, [tex]H_1[/tex] : p < 3/5

Also, z test statistics is -1.68. Since this is a left tailed test, so P-value is given by;

             P-value = P(Z < -1.68) = 1 - P(Z [tex]\leq[/tex] 1.68)

                           = 1 - 0.95352 = 0.0465

Since, the P-value of test statistics is less than the level of significance as 0.0465 < 0.05, so we have sufficient evidence to reject our null hypothesis due to which we reject the null hypothesis.

(b) Now, we are given alternate hypothesis, [tex]H_1[/tex] : p > 0.383

Also, z test statistics is 0.41. Since this is a right tailed test, so P-value is given by;

             P-value = P(Z > 0.41) = 1 - P(Z [tex]\leq[/tex] 0.41)

                           = 1 - 0.6591 = 0.3409

Since, the P-value of test statistics is more than the level of significance as 0.3409 > 0.05, so we have insufficient evidence to reject our null hypothesis due to which we fail to reject the null hypothesis.

To determine the null hypothesis's fate, compare the p-value to α = 0.05. For the first scenario, H1: p < 3/5 with the test statistic z = -1.68, the conclusion is unclear without the exact p-value. For the second scenario, H1: p > 0.383 with z = 0.41, we fail to reject the null hypothesis as the p-value (0.3409) is higher than α.

The task is to compare the p-value to the significance level (alpha, α) to determine if the null hypothesis should be rejected or not. If the p-value is less than or equal to α, reject the null hypothesis; otherwise, fail to reject it. The significance level given is α0.05.

First Scenario:

For H1: p < 3/5, the test statistic z = -1.68. Comparing the test statistic to the critical value for α=0.05 (which is between -1.65 and -1.64), -1.68 falls to the left of -1.65. However, without the exact p-value provided, the answer cannot be definitively chosen from the options. Still, the general rule is that if the test statistic is more extreme than the critical value, the null hypothesis is rejected.

Second Scenario:

For H1: p > 0.383, the test statistic z = 0.41. The p-value corresponding to z = 0.41 on the upper tail of a standard normal distribution is approximately 0.3409 (since the p-value is the area to the right of z). Therefore, the p-value is greater than α0.05, meaning that we fail to reject the null hypothesis.

The slope for this scenario of X (every mile driven in cab) and Y (cost ) is 2 and the slope is increasing.

X     1.25     2.50     3.75     5     6.25

Y    7.50     10.0      12.5     15    17.5

[tex]x_{1}= 1.25 \\ x_{2} = 2.50 \\ y_{1}=7.50 \\y_{2}=10[/tex]

What is the Slope?

The slope or gradient of a line is a number that describes both the direction and the steepness of the line. It is represented by m.

[tex]m = \frac{y_{2}-y_{1}}{x_{2}-x_{1} }[/tex]

Substitute all the required values in Slope formula, we get

[tex]m =\frac{10-7.50}{2.50-1.25}[/tex]

[tex]m = \frac{2.50}{1.25}[/tex]

[tex]m=2[/tex]

Thus, the slope of the given scenario is 2 and X and Y are increasing simultaneously as well as slope is positive. So, we can say it is a increasing slope.

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Answer: In the table, x represents every mile driven in a cab and y represents the cost.

A 2-column table with 5 rows. Column 1 is labeled x with entries 1.25, 2.50, 3.75, 5, 6.25. Column 2 is labeled y with entries 7.50, 10.0, 12.5, 15.0, 17.5.

Is the slope increasing or decreasing?

✔ increasing

What is the slope for this scenario?

✔ 2

Step-by-step explanation:

Answer:

yes

Step-by-step explanation:

A proportional relationship has the form

y = kx ← k is the constant of proportionality

y = 24x ← is in this form and is proportional with k = 24

Answer:

1,787.75

Step-by-step explanation:

The sum of the areas of the 10 rectangles gives the surface area of the cushion:

A  = 140 sq. in. + 80 sq. in. + 121 sq. in. + 2(605 sq. in.) + 22 sq. in. + 2(68.875) sq. in +19 sq. in. + 58 sq. in.

= 140 sq. in. + 80 sq. in. + 121 sq. in. + 1,210 sq. in. + 22 sq. in. + 137.75 sq. in +19 sq. in. + 58 sq. in.

= 1,787.75 sq. in.

The surface area of the cushion is 1,787.75 square inches.

Answer:

44

Step-by-step explanation:

f(x) = 6x-4

Let x=8

f(8) = 6*8 -4

    = 48 -4

    =44

Answer:

44

Step-by-step explanation:

f(x) = 6x – 4

f(8) = 6(8) – 4

= 48 - 4

= 44

Answer:c

Step-by-step explanation: