The half-life of strontium-90 is
approximately 29 years. How much of a
150 g sample of strontium-90 will remain
after 116 years?
Remaining Amount = 150(1 - [?])
Remaining Amount = [(1 - r)t
0.
Enter

The interest rate required to pay a simple interest of $53.96

from a principal of $500.00 is 18.50%.

Simple interest is expressed as:

[tex]\sf I = \dfrac{P\times r \times t}{100}[/tex]

Where I is interest, P is principal, r is interest rate and t is time.

Given that:

Plug the given values into the above formula and solve for interest rate.

[tex]\sf I = \dfrac{P\times r \times t}{100}[/tex]

[tex]\sf r = \dfrac{I}{P\times t}[/tex]

[tex]\sf r = \dfrac{\$53.96}{( \$500 \times \frac{7}{12} )}[/tex]

[tex]\sf r = 0.18501[/tex]

[tex]\sf r = 0.18501\times100\%[/tex]

[tex]\sf r = 18.50\%[/tex]

Therefore, the interest rate is 18.50%.

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Answer:

x=335/336

Step-by-step explanation:

First of all, we open the parentheses. 17x+14 1/2-2 3/7+7x=36. Then, we subtract the mixed fractions. 14 1/2-2 3/7=12 1/14. Then, we add the x's. 17x+7x=24x. What we get is 12 1/14+24x=36. We have to subtract 12 1/14 on both sides. 24x=23 13/14. To find x, we do 23 13/14 divided by 24=335/336. x=335/336

If f(x)=3x²-2x+5 and g(x) = x³+4x²-1 then the function obtained by multiplying two functions is  3x⁵+10x⁴-3x³+17x²+2x-5

The two functions are f(x)=3x²-2x+5 and g(x) = x³+4x²-1

We have to find (f×g)(x)

(f×g)(x)= f(x)g(x)

=(3x²-2x+5)( x³+4x²-1)

=3x⁵+12x⁴-3x²-2x⁴-8x³+2x+5x³+20x²-5

Combine the like terms

=3x⁵+10x⁴-3x³+17x²+2x-5

Hence, the function obtained by (f×g)(x) is 3x⁵+10x⁴-3x³+17x²+2x-5

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Answer:

1.27 X 10²

Step-by-step explanation:

standard form is in format A X 10^n, where A is a number between 1 and 10

127 = 1.27 X 10²

Answer:

A' (12, 8), B'(4, 8), C'(12, -4), D'(4, -4)

Step-by-step explanation:

Since the dilation is in the center, we just need to multiply everything by our scale factor, 2.

A (6,4) → (12, 8)

B (2,4) → (4, 8)

C (6, -2)  → (12, -4)

D (2, -2) → (4, -4)

Hope this helps!

Answer:

[tex]\textsf{A.}\quad\dfrac{1}{3} \ln \left|\sec(3x+1)+\tan(3x+1)\right|+\text{C}[/tex]

Step-by-step explanation:

[tex]\displaystyle \int \text{f}(x)\:\text{d}x=\text{F}(x)+\text{C} \iff \text{f}(x)=\dfrac{\text{d}}{\text{d}x}(\text{F}(x))[/tex]

If differentiating takes you from one function to another, then integrating the second function will take you back to the first with a constant of integration.

Given integral:

[tex]\displaystyle \int \sec(3x+1)\; \text{d}x[/tex]

To evaluate the given integral, use the method of integration by substitution.

Let u = 3x + 1.

Find du/dx and rewrite it so that dx is on its own:

[tex]\dfrac{\text{d}u}{\text{d}x}=3 \implies \text{d}x=\dfrac{1}{3}\;\text{d}u[/tex]

Rewrite the original integral in terms of u and du and integrate:

[tex]\begin{aligned}\displaystyle \int \sec(3x+1)\; \text{d}x&=\int \dfrac{1}{3} \sec(u)\; \text{d}u\\\\&= \dfrac{1}{3}\int \sec(u)\; \text{d}u\\\\&= \dfrac{1}{3} \ln \left|\sec(u)+\tan(u)\right|+\text{C}\end{aligned}[/tex]

Finally, replace u with the original substitution.

[tex]\dfrac{1}{3} \ln \left|\sec(3x+1)+\tan(3x+1)\right|+\text{C}[/tex]

Answer:

Check Explanation

Step-by-step explanation:

The question is incomplete. But I can explain in a way that the full question can be easily solvable.

Note that the missing part of the question is percentage or fraction of the total college tuition cost that the scholarship covers.

For the sake of clarity, let us assume that the scholarship covers 60% of the total college tuition costs.

This means that Tamara still has to raise 40% of the total college tuition cost herself over the space of 2 years (24 months)

The total college tuition cost = $8240

Amount that Tamara still needs to raise = 40% × 8240 = $3296

She has to raise this amount over 2 years (24 months) on a monthly basis.

So, the amount she has to save monthly over 24 months = (3296/24) = $137.333

So, whatever the fraction or percentage of the total college tuition cost that the scholarship covers, just divide the rest of the college tuition cost after the scholarship has done its part (1 - fraction or 100% - percentage) by 24 months.

The answer is the amount that Tamara needs to save monthly.

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The derivative of the function [tex]f(x)=(x+2)^{x}[/tex] is [tex](x + 2)^x \left( \frac{x}{x + 2} + ln(x + 2) \right)[/tex] A, using logarithmic differentiation.

To find the derivative of the function [tex]f(x)=(x+2)^{x}[/tex] using logarithmic differentiation, take the natural logarithm of both sides of the equation. This gives us the following equation:

[tex]ln(f(x)) = x ln(x + 2)[/tex]

Then differentiate both sides of this equation with respect to x. This gives us the following equation:

[tex]\frac{f'(x)}{f(x)} = \frac{x}{x + 2} + ln(x + 2)[/tex]

Multiply both sides of this equation by f(x) and solve for f′(x). This gives us the following equation:

[tex]f'(x) = f(x) \left( \frac{x}{x + 2} + ln(x + 2) \right)[/tex]

Then substitute the function [tex]f(x)=(x+2)^{x}[/tex] into this equation. This gives us the following equation:

[tex]f'(x) = (x + 2)^x \left( \frac{x}{x + 2} + ln(x + 2) \right)[/tex]

Therefore, the derivative of the function [tex]f(x)=(x+2)^{x}[/tex] is [tex](x + 2)^x \left( \frac{x}{x + 2} + ln(x + 2) \right)[/tex]

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Line segment PT ≅ line segment PT by the reflexive property.

ΔPRT ≅ ΔTVP by the SSS triangle congruence theorem

The SSS congruence theorem (side-side-side congruence theorem) states that if all three sides of one triangle are congruent to the corresponding three sides of another triangle, then both are considered congruent triangles.

According to the reflexive property, a line or angle is equal to itself, therefore, Line segment PT ≅ line segment PT by the reflexive property.

This also implies that both triangles have three pairs of corresponding sides that  congruent, therefore, ΔPRT ≅ ΔTVP.

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To calculate the tax owed by a married couple filing jointly who report a taxable income of $97,025, we can use the 2021 tax brackets and rates provided by the IRS.

The first $19,900 of their income is taxed at a rate of 10%, which equals $1,990.

The next $60,050 of their income is taxed at a rate of 12%, which equals $7,206.

The remaining $17,075 of their income is taxed at a rate of 22%, which equals $3,756.50.

Adding these amounts together gives a total tax liability of $12,952.50.

Therefore, the tax owed by a married couple filing jointly who report a taxable income of $97,025 is $12,952.50.

Answer: 15,734

Step-by-step explanation:

If you look at the table itself it has the answer however it says at least 97,000 but less than 97,050 and it says and you are-- right under married filing jointly is 15,734

Answer: 6ft

Step-by-step explanation:

180+40x+18x+4x^2=672

4x^2+58x+180x=672

4x^2+58x-492=0

2x^2+29x-246=0

(x=6)(2x+41)=0

x=6 or x=-20.5

Should be 6ft

Answer:

These triangles are not similar because the ratios of corresponding sides are not equal.

The 95% confidence interval for the population mean is (47.00, 48.90).

A sample of size n=78 is drawn from a normal population with a standard deviation of σ=5.1. The sample mean is x=47.95.

Using this information, we can estimate the population mean using the formula:

μ = x ± z*(σ/√n)

where μ is the population mean, x is the sample mean, z is the z-score for the desired level of confidence (e.g., 1.96 for a 95% confidence interval), σ is the population standard deviation, and n is the sample size.

Assuming a 95% confidence level, the z-score is 1.96. Plugging in the given values, we get:

μ = 47.95 ± 1.96*(5.1/√78)

Solving for the upper and lower bounds of the confidence interval, we get:

μ = 47.95 ± 0.95

So the 95% confidence interval for the population mean is (47.00, 48.90). This means that if we were to repeat this sampling process many times, we would expect the true population mean to fall within this interval 95% of the time.

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Answer:

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

Use the area formula:

We are given the circumference of the circle, which is C = 2πr.

So, we can set up an equation:

Now, we can plug this value of r into the area formula:

Therefore, the area of the circle is 42.25π or 132.73 square inches.

The first three terms of the Sequence are -2, 1, 6 and the tenth term is 97.

Given that the nth term of a sequence is n squared - 3.

We can find the first three terms by substituting n = 1, 2, and 3 into the formula.

When n = 1, the first term is:

a1 = 1² - 3 = -1

When n = 2, the second term is:

a2 = 2² - 3 = 1

When n = 3, the third term is:

a3 = 3² - 3 = 6

Therefore, the first three terms of the sequence are: -2, 1, 6.

To find the tenth term, we substitute n = 10 into the formula.

a10 = 10² - 3 = 97

Therefore, the tenth term of the sequence is 97.

In summary, the first three terms of the sequence are -2, 1, 6 and the tenth term is 97.

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The surface area of the cone is 553 cm².

The surface area of a three-dimensional object is the total area of all its faces.

To calculate the surface area of the cone, we use the formula below

Formula:

Where:

From the question,

Given:

Substitute these values into equation 1

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Answer:

0.4

Step-by-step explanation:

Let A be the event of selecting a bead with two holes and B be the event of selecting a red bead. We are given P(A) = 0.5 and P(A and B) = 0.2. We need to find P(B|A), the probability of selecting a red bead given the bead has two holes.

By definition of conditional probability, we have:

P(B|A) = P(A and B) / P(A)

Substituting the given values, we get:

P(B|A) = 0.2 / 0.5

Simplifying, we get:

P(B|A) = 0.4

Therefore, the probability of selecting a red bead given the bead has two holes is 0.4.

Answer: 0.2.

Step-by-step explanation:

The domain of a function is all of the possible x-values.

In the case of this function, we can see that the x-values begin at negative infinity, continue/change between -1 and 1, and pick up again to continue through positive infinity.

Therefore, the domain of the function is negative infinity to infinity, option D/#4.

Hope this helps!

On average, you would expect to have to ask 2.5 students before finding one who has jumper cables.

The distribution is the geometric distribution with the parameter p = 0.4.

We have,

a.

The variable of interest is the number of students who need to be stopped before finding one who has jumper cables.

The range of possible values is 1, 2, 3, 4, ...

b.

The probability that the third person asked would be the one who has a jumper cable can be found using the geometric distribution with parameter p = 0.4, where p is the probability of success (i.e., finding someone with jumper cables).

The probability can be calculated as:

P(X = 3)

= (1 - p)^(3-1) x p

= (0.6)^2 * 0.4

= 0.144

c.

The probability that the first person asked will be the one who has jumper cables.

P(X = 1)

= p

= 0.4

d.

The expected value (or mean) of the number of people who need to be asked before finding the first one with jumper cables can be calculated using the geometric distribution with parameter p = 0.4.

So,

E(X)

= 1/p

= 1/0.4

= 2.5

Thus,

On average, you would expect to have to ask 2.5 students before finding one who has jumper cables.

The distribution is the geometric distribution with the parameter p = 0.4.

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9x=28. x=28÷9

To solve this inequality for x, we need to isolate x on one side of the inequality sign. Let's begin by distributing the -2 on the right-hand side:

7x + 5 < -2(4x - 3)

7x + 5 < -8x + 6

Adding 8x to both sides, we get:

15x + 5 < 6

Subtracting 5 from both sides, we get:

15x < 1

So the equivalent inequality to 7x + 5 < -2(4x-3) is 15x < 1.

Therefore, the answer is: 15x < 1.

The function r(x) - 3f(x+1) transforms the parent function f(x)=x^2 by shifting it left by 1 unit, vertically stretching it by a factor of 3, and translating it downward by 3 units. The resulting graph is a parabola with vertex at (-1,-3) and a steeper shape.

The function r(x) - 3f(x+1) is a transformation of the parent function f(x)=x^2. Let's consider each transformation step by step.

First, the function f(x+1) represents a horizontal shift of the parent function f(x)=x^2 to the left by 1 unit. This means that the vertex of the parabola is shifted to the point (-1,0).

Next, the function 3f(x+1) vertically stretches the parabola by a factor of 3. This means that the distance between the vertex and the x-intercepts of the parabola is tripled, while the shape of the parabola remains the same.

Finally, the function r(x) subtracts a constant value from the transformed function. This translates the entire graph downward by 3 units.

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The 90% confidence interval for the mean body temperature of adults in the town is approximately (97.299, 98.529).

The given data points are:

97.1, 98.1, 98, 97.7, 97.4, 99.3, 96.8

Step 1: Calculate the sample mean (µ):

µ = (97.1 + 98.1 + 98 + 97.7 + 97.4 + 99.3 + 96.8) / 7 ≈ 97.914

sample standard deviation (s):

≈ 0.839

Step 3: Calculate the standard error (SE):

SE = s / sqrt(n)

≈ 0.839 / sqrt(7) ≈ 0.317

Step 4: Find the t-value for a 90% confidence interval with 6 degrees of freedom (n - 1 = 7 - 1 = 6).

Using a t-distribution table  we find that the t-value is approximately 1.943.

Step 5: Calculate the margin of error (ME):

ME = t-value * SE

≈ 1.943 * 0.317 ≈ 0.615

Step 6: Calculate the confidence interval:

Lower limit = µ - ME ≈ 97.914 - 0.615 ≈ 97.299

Upper limit = µ + ME ≈ 97.914 + 0.615 ≈ 98.529

So, the 90% confidence interval for the mean body temperature of adults in the town is approximately (97.299, 98.529).

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The distance from point A to point B is approximately 920 feet.

Let's call the distance from point A to point B as x.

From point A, the angle of elevation to the lighthouse's beacon-light is 8 degrees.

Using the tangent function to find the height of the lighthouse (h):

tan(8) = h/1083

h = 1083 tan(8) ≈ 157.6 feet

From point B, the angle of elevation to the lighthouse's beacon-light is 4 degrees.

Using the tangent function again to find the height of the lighthouse from point B (h'):

tan(4) = h'/(1083-x)

h' = (1083-x) tan(4) ≈ 78.6 - 0.07x

Since the height of the lighthouse should be the same from both points A and B, we can set h = h' and solve for x:

1083 tan(8) = (1083-x) tan(4)

x = 1083 - (157.6/tan(4)) ≈ 920 feet

Therefore, the distance from point A to point B is approximately 920 feet.

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Answer:

0.8475

Step-by-step explanation:

We can model the number of defective tablets in the shipment as a binomial distribution with parameters $n=26$ (the sample size) and $p=0.15$ (the probability of a defective tablet).

To calculate the probability that the whole shipment will be accepted, we need to find the probability that the number of defective tablets in the sample is at most 1, which means that the shipment meets the required specifications.

The range of the function is the set of all real numbers

From the question, we have the following parameters that can be used in our computation:

x: -2, -1, 0, 1, 2, 3

y: -11, -4, 1, 4, 5, 4

The range of a function is the set of y values of the function

using the above as a guide, we have the following:

Range = -11, -4, 1, 4, 5, 4

This can be expressed as

Range = -11 to 4

So, we can say that the range is the set of all real numbers

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Check the picture below.

[tex]\stackrel{ \textit{\LARGE Areas} }{\stackrel{ \textit{blue triangle} }{\cfrac{1}{2}(1)(2)}~~ + ~~\stackrel{ \textit{orange triangle} }{\cfrac{1}{2}(2)(1)}~~ + ~~\stackrel{ \textit{yellow rectangle} }{(2)(3)}~~ + ~~\stackrel{ \textit{purple triangle} }{\cfrac{1}{2}(3)(2)}} \\\\\\ 1+1+6+3\implies \text{\LARGE 11}[/tex]

The correct probability is indeed 0.25 or 25%.

When heterozygous pink (Pp) and white (pp) flowers are crossed, the Punnett square can be used to determine the probability of offspring having white flowers:

     |   P     p

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

 P  |  PP   Pp

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

 p  |  Pp   pp

From the Punnett square, we can see that there are four possible combinations of alleles for the offspring: PP, Pp, Pp, and pp.

Out of these four possibilities, only one combination (pp) corresponds to the white flower trait.

Therefore, the probability of an offspring having white flowers is 1 out of 4.

In terms of probability, this can be expressed as:

Probability of white flowers = Number of favorable outcomes / Total number of possible outcomes.

= 1 / 4

= 0.25

So, the correct probability is indeed 0.25 or 25%.

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To solve for the remaining angles and side of the triangles, we can use the Law of Sines and the Law of Cosines.

Triangle 1: (where angle A is acute)

Given:

B = 50°

b = 5

a = 6

Using the Law of Sines:

[tex]sin A / a = sin B / b[/tex]

sin A / 6 = sin 50° / 5

sin A = (6 x sin 50°) / 5

A = arcsin[(6 x sin 50°) / 5]

A ≈ 44.14°

Using the Law of Sines again:

sin C / c = sin B / b

sin C / c = sin 50° / 5

sin C = (c x sin 50°) / 5

Using the Law of Cosines:

c² = a² + b² - 2ab x cos C

c² = 6² + 5² - 2(6)(5) x cos C

c² = 36 + 25 - 60 x cos C

c² = 61 - 60 x cos C

c ≈ √(61 - 60 x cos C)

Triangle 2 (where A is obtuse):

Given:

B = 50°

b = 5

a = 6

Using the Law of Sines:

sin A / a = sin B / b

sin A / 6 = sin 50° / 5

sin A = (6 x sin 50°) / 5

A = arcsin[(6 x sin 50°) / 5]

A ≈ 44.14° (rounded to the nearest hundredth)

Using the Law of Sines again:

sin C / c = sin B / b

sin C / c = sin 50° / 5

sin C = (c x sin 50°) / 5

Since A is obtuse, C = 180° - A - B

C ≈ 85.86° (rounded to the nearest hundredth)

Using the Law of Cosines:

c² = a² + b² - 2ab x cos C

c² = 6² + 5² - 2(6)(5) x cos C

c² = 36 + 25 - 60 x cos C

c² = 61 - 60 x cos C

c ≈ √(61 - 60 x cos C)

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