Dr. Silas studies a culture of bacteria under a microscope. The function b(t)=50(1.4)^t represents the number of bacteria t hours after Dr. Silas begins her study.

a) What is the y-intercept of the function? What does this mean in the context of the problem?
b) Is this exponential growth or decay? How do you know?
c) How many bacteria would there be 5 hours after Dr. Silas began her study?

Please show all your work!

Final answer:

The function √(x-1) is a horizontal translation of the function √x by 1 unit to the right along the x-axis.

Explanation:

The function √(x-1) represents a horizontal translation of the parent function √x. The translation is 1 unit to the right along the x-axis.

In function transformation terms, when a function f(x) is altered to become f(x - a), this translates the graph of the function to the right by 'a' units if 'a' is positive and to the left by 'a' units if 'a' is negative.

To illustrate, the graph of f(x) = √x is translated to become g(x) = √(x-1). Compared with the graph of f(x), every point on the graph of g(x) will be 1 unit to the right.

There are no changes vertically, so there is no translation up or down.

Answer: 3.6651

Step-by-step explanation:

The formula to convert [tex]\theta[/tex] degrees to radians is given by :-

[tex]\dfrac{\pi}{180^{\circ}}\times\theta[/tex]

Given : Angle : [tex]\theta=210^{\circ}[/tex]

Then , the measure of angle in radians is given by :-

[tex]\dfrac{\pi}{180^{\circ}}\times210^{\circ}[/tex]

Using the value of [tex]\pi=3.14159[/tex], we get

[tex]\dfrac{3.14159}{6}\times7\approx3.6651[/tex]

Answer:

t > 47

Step-by-step explanation:

Tara is  taller than Jeff. Jeff is 47 inches tall.

We need to write an inequality that compares   Tara's height to Jeff's height

Let t be the height of Tara

and j be the height of Jeff

Tara is taller than Jeff, we use greater than symbol for taller

So inequality becomes t > j

Given Jeff is 47 inches tall, so replace 'j' with 47

Answer is t > 47

Final answer:

To compare Tara's height to Jeff's, the inequality used is t > 47, indicating Tara is taller than Jeff.

Explanation:

The question asks you to write an inequality that compares Tara's height, represented by t, to Jeff's height, which is 47 inches. To represent that Tara is taller than Jeff using an inequality, you use the 'greater than' symbol (>). Therefore, the correct inequality to show that Tara is taller than Jeff is t > 47. This inequality means that Tara's height in inches is greater than 47 inches.

Answer:

The answer is 45, 000. if you multiply 3,750 times 12 thats what her yearly salary.

Answer:

26 1/4

Step-by-step explanation:

took the test 100% 4.08 Quiz: Finding the Volume of Rectangular Prisms and Problem Solving

Answer:

the answer is C: y = -0.875x^2 - 3.956x + 20.179

Step-by-step explanation:

To predict the temperature during the sixth hour, we need to find the regression equation of the line that best fits the given data. Using the slope and y-intercept, we can substitute x = 6 into the equation to find the predicted temperature, which is -3.42.

To predict the temperature during the sixth hour using the regression equation, we need to find the equation of the line that best fits the given data. The regression equation is of the form y = mx + b, where m is the slope of the line and b is the y-intercept.

First, we need to calculate the slope (m) and the y-intercept (b) using the given data points. Then, we can substitute x = 6 into the equation to find the predicted temperature.

Using the formula for the slope (m) and the y-intercept (b), we find that m = -5.07 and b = 22.2. Substituting x = 6 into the regression equation, we get y = -5.07(6) + 22.2 = -3.42. Therefore, the predicted temperature during the sixth hour is -3.42.

The least natural number that is divisible by three different primes is 30.

The positive whole numbers are termed as natural Numbers.

Numbers that have only two factors are termed as Prime Numbers.

According to the question, the least natural number that is divisible by three different primes is calculated by multiplying three least prime numbers as-

[tex]2\times 3\times 5=30[/tex].

Here, the natural number should be the least so, you need to take lowest three prime numbers only.

Hence, The least natural number that is divisible by three different primes is 30.

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Final answer:

To find the equivalent numerator, we can multiply both sides of the equation by the denominator.

Explanation:

The equivalent numerator can be found by multiplying both sides of the equation by the denominator, which is x³y². This will cancel out the denominator on the right side. The result will be the equivalent numerator.

For example, if we have the equation 2x³y² = 6, we can multiply both sides by x³y² to get rid of the denominator:

equation * (x³y²) = 6 * (x³y²)
The x³y² on the left side will cancel out, leaving us with the equivalent numerator:

equivalent numerator = 6 * (x³y²)
So, the equivalent numerator is 6x³y².

81y4 -16x, the difference of squares.

The expression (9y2 – 4x)(9y2 + 4x) is equivalent to 81y4 – 16x2, a difference of squares in mathematical terms.

The expression you are asking about is equivalent to

81y4 – 16x2

, which is a special product known as

the difference of squares

. In mathematics, a difference of squares is a term that describes an expression of the form a^2 - b^2. It can be factored into the multiplication of two binomials: (a+b)(a-b). In your example, (9y2)^2 is 81y4 and (-2x)^2 is 16x2, so the final expression is 81y4 – 16x2.

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We need a table to do this. 3 rows and 3 columns. Across the top the columns are number of liters, % alcohol, and total. We will label the first row stuff with alcohol, the second row stuff with water, and the third row will be the mix of alcohol and water. In the first column we will put an x for alcohol since we don't know how much alcohol we have in the mix. In the second column we will put the decimal equivalent of the percent alcohol, which is .18. In the total column we will put the product of those 2, which is .18x. Now for the second row, water. We will put a y in the first column since we don't know how much water we have in the mix. In the second column we will put a 0, since water doesn't have any alcohol in it. In the third column we will put the product of the 2 which will be 0. In the third row, the mix row, we put a 10 since we want 10 L of this mix. We will put the decimal equivalent of how much alcohol we want in this mix which is .12. In the total column we put the product of those 2 which is 1.2. Since we are adding the alcohol and the water, x and y, to get a total of 10, this is our first equation. x+y=10. In the total column we will add the percent alcohol in the alcohol and the water to get 1.2. .18x + 0 = 1.2, or just .18x = 1.2. Let's divide both sides by .18 to find the amount of alcohol is in this mix. We get 6 2/3 liters of alcohol. If there is a total of 10 L of this mix, 10 - 6 2/3 = water, and the amount of water then is 3 1/3 L.

Answer:

  [tex]\dfrac{x+2}{x+1}[/tex]

Step-by-step explanation:

Factor the numerator and cancel common factors from numerator and denominator.

  [tex]\dfrac{x^2-4}{(x-2)(x+1)}=\dfrac{(x-2)(x+2)}{(x-2)(x+1)}=\dfrac{x+2}{x+1}[/tex]

Answer:

1/2 and -2 are the first answers to the question

1/16 and 1/16 are the next answers  

1/4 and 33/16 are the last ones

and for the multiple choice answer which is last is A

Step-by-step explanation:

To solve the quadratic equation 2x^2 + x - 4 = 0, we can use the quadratic formula: x = (-b ± √(b^2 - 4ac)) / (2a). Substituting the given values into the formula, we find two solutions: x = (-1 ± √33) / 4.

To solve the equation 2x2 + x - 4 = 0, we can use the quadratic formula. The quadratic formula states that for an equation of the form ax2 + bx + c = 0, the solutions for x can be found using the formula:

x = (-b ± √(b2 - 4ac)) / (2a)

For our equation, a = 2, b = 1, and c = -4. Substituting these values into the formula, we have:

x = (-1 ± √(1 - 4(2)(-4))) / (2(2))

Simplifying further, we get two solutions: x = (-1 ± √33) / 4.

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Answer:

No, because 8^2+12^2 doesn't equal 16^2

Step-by-step explanation:

The triangle ABC is not a right angle triangle

A triangle is a plane figure or polygon with three sides and three angles.

A Triangle has three vertices and the sum of the interior angles add up to 180°

Let the Triangle be ΔABC , such that

∠A + ∠B + ∠C = 180°

The area of the triangle = ( 1/2 ) x Length x Base

For a right angle triangle

From the Pythagoras Theorem , The hypotenuse² = base² + height²

if a² + b² = c² , it is a right triangle

if a² + b² < c² , it is an obtuse triangle

if a² + b² > c² , it is an acute triangle

Given data ,

Let the triangle be represented as ΔABC

Now , the measure of sides of the triangle are

The measure of side AB = 8 inches

The measure of side BC = 12 inches

The measure of side AC = 16 inches

Now , For a right angle triangle

From the Pythagoras Theorem , The hypotenuse² = base² + height²

Substituting the values in the equation , we get

AC² = AB² + BC²

16² = 8² + 12²

256 ≠ 64 + 144

256 ≠ 208

Therefore , it does not satisfy Pythagoras relation

Hence , the triangle is not a right angle triangle

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The student's expression is simplified by dividing 1.64 by 100 then expressing the result in scientific notation as 1.64  imes 10⁻².

The student's question involves simplifying a mathematical expression that uses scientific notation. The expression is 1.64 times 10⁰ divided by 2.0 times 10². Here's a step-by-step breakdown:

Identify the powers of ten: The denominator has 10 to the power of 2, which is 10 squared or simply 100. The numerator has 10 to the power of 0, which equals 1.

Simplify the expression: Divide 1.64 by 100 (2.0 times 10²), which gives a result of 0.0164.

Express in scientific notation: 0.0164 can be written as 1.64 times 10⁻².

Answer: Option c. $ 611.20 will be correct.

Explanation:

Since, the total amount of finance charge is [tex]A=P\frac{r(1+r)^n}{(1+r)^n-1}[/tex]

Where P is the principle, r is the rate, n is the times of compound interest (monthly or quarterly etc.) .

Here P=$4250 r=13.25%, and n=24.

So according to the formula So, the finance charge= [tex]4250\frac{13.25(1+13.25)^{24}}{(1+13.25)^{24}-1}[/tex] =  $ 611.20

The total finance charge for a $4,250 loan at 13.25% interest compounded monthly for 24 months is c) $611.20.

To calculate the total finance charge for a $4,250 loan at 13.25% interest compounded monthly for 24 months, we can use the following formula:

Total finance charge = Principal * (1 + Monthly interest rate)^Number of months - Principal

Where:

Principal is the amount of the loan ($4,250)

Monthly interest rate is the annual interest rate divided by 12 (13.25% / 12 = 1.1042%)

Number of months is the term of the loan in months (24)

Total finance charge = 4250 * (1 + 0.011042)^24 - 4250

Total finance charge = 611.20

Therefore, the answer is c. $611.20.

Note that this formula is for calculating the total finance charge over the entire term of the loan. If you want to calculate the monthly finance charge, you can simply divide the total finance charge by the number of months in the loan term. For example, the monthly finance charge for this loan would be $611.20 / 24 = $25.47.

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Answer:

[tex]t_{13} =7[/tex]

Step-by-step explanation:

[tex]t_{13}[/tex] here 1 represents that it is in 1st row whereas 3 represents that it is in 3rd column so the element placed in 1st row and 3rd column is 7

therefore answer is

[tex]t_{13} =7[/tex]

Answer:

Option A.

Step-by-step explanation:

The given expression is

[tex]\sqrt[3]{216x^3y^6z^{12}}[/tex]

We need to find the simplified form of the given expression.

It can be rewritten as

[tex]\sqrt[3]{6^3x^3y^6z^{12}}[/tex]

Using the properties of exponents, we get

[tex](6^3x^3y^6z^{12})^{\frac{1}{3}}[/tex]          [tex][\because \sqrt[n]{x}=x^{\frac{1}{n}}][/tex]

[tex](6^3)^{\frac{1}{3}}(x^3)^{\frac{1}{3}}(y^6)^{\frac{1}{3}}(z^{12})^{\frac{1}{3}}[/tex]         [tex][\because (ab)^x=a^xb^x][/tex]

[tex]6^{\frac{3}{3}}x^{\frac{3}{3}}y^{\frac{6}{3}}z^{\frac{12}{3}}[/tex]         [tex][\because (x^m)^n=x^{mn}][/tex]

[tex]6^{1}x^{1}y^{2}z^{4}[/tex]  

[tex]6xy^{2}z^{4}[/tex]  

Hence, the correct option is A.

To calculate the six-month emergency fund, we first determined the monthly net income after deductions from the gross monthly pay. Then, we found that 30% of the net income goes towards housing and fixed expenses. Multiplying this expense by six gives the total emergency fund needed, which is $2,848.20.

To calculate the amount needed for a six-month emergency fund, we first need to determine the monthly take-home pay after all deductions. The student earns $13.70 per hour and works 40 hours a week. Deductions include FICA (7.65%), federal tax withholding (11.55%), and state tax withholding (8.35%).

First, calculate the gross monthly income: $13.70/hr * 40 hrs/wk * 4 weeks/mo = $2,184/month.

Next, calculate total deductions: FICA (7.65% of $2,184) + Federal Tax (11.55% of $2,184) + State Tax (8.35% of $2,184) = $166.97 + $252.34 + $182.36 = $601.67.

Now calculate the net monthly income: $2,184 - $601.67 = $1,582.33.

The student's housing and fixed expenses are 30% of the net income, which amounts to $474.70/month. Therefore, for a six-month emergency fund, the student would need:

$474.70 * 6 months = $2,848.20 saved.

To save for a six-month emergency fund, you must first calculate your net monthly pay after deductions from your salary, which is determined to be $1,588.12. Then calculate 30% of this for your monthly fixed expenses, and finally, multiply that amount by six to determine the total savings required for the emergency fund, which amounts to $2,858.64.

To calculate how much you need to save for an emergency fund, we first need to determine your monthly take-home pay after deductions. Your gross pay per week is $13.70 per hour multiplied by 40 hours, which equals $548. Your gross pay per month is then $548 times 4 weeks, totaling $2,192. We will then subtract the deductions: FICA (7.65%), federal tax (11.55%), and state tax (8.35%). Let's calculate each:

FICA: $2,192 x 7.65% = $167.68

Federal Tax: $2,192 x 11.55% = $253.17

State Tax: $2,192 x 8.35% = $183.03

Your total deductions are $167.68 + $253.17 + $183.03 = $603.88.

So, your net monthly pay is $2,192 - $603.88 = $1,588.12.

Next, we calculate your fixed expenses which are 30% of your net income: $1,588.12 x 30% = $476.44.

To determine the amount needed for a six-month emergency fund, you multiply your monthly fixed expenses by six:

$476.44 x 6 = $2,858.64.

Therefore, you need to save $2,858.64 for your emergency fund.