Marco is studying a type of mold that grows at a fast rate. He created the function f(x) = 345(1.30)x to model the number of mold spores per week. What does the 1.30 represent? How many mold spores are there after 4 weeks? Round your answer to the nearest whole number

Answer:

6

Step-by-step explanation:

To solve, first plug in 4 as your x value for your g(x) equation.

[tex]g(4)=\sqrt{4-3} \\g(4)=\sqrt{1} \\g(4)=1[/tex]

Next, plug in the value of g(4) into your f(x) equation for x.

[tex]f(1)=-1+7\\f(1)=6[/tex]

Answer:

The answer in the procedure

Step-by-step explanation:

we know that

The volume of a rectangular pyramid is equal to

[tex]V=\frac{1}{3}LWH[/tex]

where

L is the length of the rectangular base

W is the width of the rectangular base

H is the height of the pyramid

If the pyramid is scaled proportionally by a factor of k

then

the new dimensions are

L=kL

W=kW

H=kH

substitute and find the new Volume V'

[tex]V'=\frac{1}{3}(kL)(kW)(kH)[/tex]

[tex]V'=\frac{1}{3}(k^{3})LWH[/tex]

[tex]V'=(k^{3})\frac{1}{3}LWH[/tex]

[tex]V'=(k^{3})V[/tex]

The new volume is equal to the scale factor k elevated to the cube multiplied by the original volume

Answer:

V = πr2h

V' = π × (k × r)2 × (k × h)

   = π × k2 r2 × kh

   = k3 × πr2h

   = k3 × V

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

Answer: OPTION C

Step-by-step explanation:

You need to follow these steps:

- Carry the number 1 down and multiply it by the number 2.

- Place the product obtained above the horizontal line, below the number 5 and add them.

- Put the sum below the horizontal line.

- Multiply this sum by the number 2.

- Place the product obtained above the horizontal line, below the number -14 and add them.

Then:

[tex]2\ |\ 1\ \ 5\ -14\\\\.\ \ |\ \ \ \ 2\ \ \ 14\\------\\.\ \ \ 1\ \ \ 7\ \ 0[/tex]

Therefore, the quotient in polynomial form is:

[tex]x+7[/tex]

Answer:

38.7°

Step-by-step explanation:

Use the Law of Cosines:

[tex]7^2=11^2+10^2-2(11)(10)cosT[/tex] and

49 = 121 + 100 - 220cosT so

-172 = -220cosT and

.781818181 = cosT

Using the inverse cosine function on your calculator, you find that angle T = 38.7 degrees

For the given equation, if b=30, then the value of a will be equal to 60.

Like the given equation is a linear equation with two variables (a and b). You can solve this equation replacing b for the informed value (30).

Here it is important to remember the rules to the addition and the mutiplication  of integers numbers:

The rules to addition of numbers are:

+  +  

Add  Final result (+)  

-   -    

Add  Final result (-)  

+  -    

Subtract  Final result (the sign of the integer having greater value )

-   +  

Subtract  Final result (the sign of the integer having greater value )

The rules to multiplication of numbers are:

+  +  or  -   -

The result presents a positive sign (+) because the signs are same.

+  - or   -   +

The result presents a negative sign (-) because the signs are different.

If b=30, then you can find the value for a from steps below.

                                          [tex]\frac{1}{2}*a +\frac{2}{3} *b=50\\ \\ \frac{1}{2}*a +\frac{2}{3} *30=50\\ \\ \frac{1}{2}*a +2*10=50\\ \\ \frac{1}{2}*a +20=50\\ \\ \frac{1}{2}*a =50-20\\ \\ \frac{1}{2}*a=30\\ \\ a=30*2\\ \\ a=60[/tex]

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Answer:

Cos function should be used for the determination of the length of the hypotenuse.

Answer:

$120.

Step-by-step explanation:

The amount he sells the tool kit for  = 80 + 20% of 80

= 80 + 16

= $96.

Let m be the marked price, then

m - 0.20m = 96

0.8m = 96

m = $120.

To make a 20 percent profit on tool kits costing $80, with a 20 percent discount applied, Harry should mark the tool kits for $120.

The subject of this question is profit calculation. This is a common topic in Mathematics, particularly in the field of business or financial mathematics. In order to understand this question, we need to consider the cost price with the profit margin and the discount offered.

In this case, if Harry buys tool kits for $80 and wants to make a 20 percent profit on his cost, he must initially price the tool kits in a way that both his profit is covered and the customer sees a discount of 20 percent.

Firstly, we calculate the 20 percent profit which is given by 0.2 x $80 = $16. This implies that the price before applying discount should be $80 (cost price) + $16 (profit) = $96.

Now, if Harry gives a 20% discount, the price $96 represents the 80% (100%-discount) of the final price (let's call it X). Therefore, we can write this as 0.8*X = $96. Solving for X gives X = $96 / 0.8 = $120. So, Harry should mark the tool kits for $120.

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Answer:

[tex]\large\boxed{\bold{Q1.}\ \angle W,\ \angle Y,\ \angle X}\\\boxed{\bold{Q2.}\ \angle D>\angle E}[/tex]

Step-by-step explanation:

Q1.

2x + 9 > 2x + 1     subtract 2x from both sides

9 > 2    TRUE → ∠Y > ∠W

∠Y = (2x + 9) and ∠W = (2x + 1) are acute angles

∠X is right angle

right angle > acute angle

Therefore:

∠W < ∠Y < ∠X

Q2.

Angles B, C, and E are acute angles.

Angles A, D and F are obtuse angles.

obtuse angle > acute triangle

Therefore

∠D > ∠E

Answer: 3.5308

Step-by-step explanation:

Claim : The firm's professionals volunteer an average of more than 15 hours per month.

i.e.  [tex]\mu>15[/tex]

Null hypothesis : [tex]H_0:\mu\leq15[/tex]

Alternative hypothesis : [tex]H_1:\mu>15[/tex]

Sample size : [tex]n=24[/tex]

The sample mean : [tex]\overline{x}=16.6\text{ hours}[/tex]

Sample standard deviation : [tex]\sigma=2.22\text{ hours}[/tex]

The test-statistics for the population mean is given by :-

[tex]z=\dfrac{\overline{x}-\mu}{\dfrac{\sigma}{\sqrt{n}}}[/tex]

i.e. [tex]z=\dfrac{16.6-15}{\dfrac{2.22}{\sqrt{24}}}=3.5307960256\approx3.5308[/tex]

Hence, the correct value of the test statistic for the appropriate hypothesis test is 3.5308.

A t-statistic can be computed using the formula: (sample mean - population mean) / (standard deviation / sqrt(sample size)). Applied to the given scenario, it would test the hypothesis of average volunteer hours vs the claimed 15 hours/month.

In this scenario, you are being asked to conduct a one-sample t-test.

Set up your null hypothesis (H0), which assumes no effect, so that the true volunteer hours would be equal to 15 hours/month, and the alternative hypothesis (Ha) would be that average volunteer hours are more than 15 hours/month.

The formula to calculate the t-statistic is: (sample mean - population mean) / (standard deviation / sqrt(sample size)). Using given values, it would look like this: (16.6 - 15) / (2.22 / sqrt(24))

Compute this, and the resulting value will be your t-statistic.

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Answer:

  x° = 109°

Step-by-step explanation:

x° is a "corresponding angle" to either of the upper left or lower right interior angles of the parallelogram. (The lines marked with a single arrow are parallel, as are the lines marked with a double arrow.)

Either of those angles is supplementary to the one marked 71°, so x° and all corresponding angles are 180° -71° = 109°.

Answer:

  B)  108π cm^2

Step-by-step explanation:

We assume the circumference measurement is the same as it would have been before the fruit was cut. In that case, the radius is found from ...

  C = 2πr . . . . . . . . . formula relating circumference and radius

  12π cm = 2πr . . . . substitute given information

  6 cm = r . . . . . . divide by 2π

The surface area of a hemisphere is 3 times the area of the circular face:

  S = 3πr^2

  S = 3π(6 cm)^2 = 108π cm^2

The surface area of the grapefruit half is 108π cm^2.

Answer:

B) 108π cm2

Step-by-step explanation:

If a grapefruit is approximately spherical and Jane cuts the grapefruit in half and determines that the circumference of the resulting hemisphere is 12π centimeters, the surface area of one-half of the cut grapefruit is 108π cm2.

Formula: 2πr

S = 3π(6 cm)^2

Answer:

Earnings per share is $2.93

Step-by-step explanation:

Given data

shares = 450

assets =  $28,900

net income = $1,320

to find out

earnings per share

solution

Earnings per share is directly calculate by net income / total share

here we know net income and that share i.e.450

so

Earnings per share = net income / total share

Earnings per share = 1,320 / 450

Earnings per share = $2.93

so option C is right i.e. $2.93

Answer:

  a.  0.6975

  b.  0.833625

Step-by-step explanation:

a. The probability of both drives failing is 0.55² = 0.3025, so the probability that both drives won't fail is 1 -0.3025 = 0.6975.

__

b. The probability of all three drives failing is 0.55³ = 0.166375, so the probability that all three drives won't fail is 1 -0.166375 = 0.833625.

Answer:

  Case I, Case II

Step-by-step explanation:

For cases III and IV, you need the Law of Cosines.

The Law of Sines can be used when you have at least one side and the angle opposite. If you know two angles of a triangle, you know all three, so the given angles don't necessarily have to be opposite the given side if two angles are known.

The Laws of Sines can be applied to solve Case I and Case II.

Answer:

Explanation:

You can convert the percent markup into a multiplicative factor in this way:

Base price:                     15,800 . . . (cost to the seller)

Percent mark up:           115% . . .  (based on the cost to the seller)

Sale price:                      15,800 + 115% of x = 15,800 + 115 × 15,800 /100 =

                                        = 15,800 + 1.15 × 15,800 = 15,800 (2.15) = 33,970

The markup is:

And the percent markup based on the sale price is:

            = 53.49 %

Rounding to the nearest tenth percent that is 53.5 %.

Answer:

Part 1) The function of the First graph is [tex]f(x)=(x-3)(x+1)[/tex]

Part 2) The function of the Second graph is [tex]f(x)=-2(x-1)(x+3)[/tex]

Part 3) The function of the Third graph is [tex]f(x)=0.5(x-6)(x+2)[/tex]

See the attached figure

Step-by-step explanation:

we know that

The quadratic equation in factored form is equal to

[tex]f(x)=a(x-c)(x-d)[/tex]

where

a is the leading coefficient

c and d are the roots or zeros of the function

Part 1) First graph

we know that

The solutions or zeros of the first graph are

x=-1 and x=3

The parabola open up, so the leading coefficient a is positive

The function is equal to

[tex]f(x)=a(x-3)(x+1)[/tex]

Find the value of the coefficient a

The vertex is equal to the point (1,-4)

substitute and solve for a

[tex]-4=a(1-3)(1+1)[/tex]

[tex]-4=a(-2)(2)[/tex]

[tex]a=1[/tex]

therefore

The function is equal to

[tex]f(x)=(x-3)(x+1)[/tex]

Part 2) Second graph

we know that

The solutions or zeros of the first graph are

x=-3 and x=1

The parabola open down, so the leading coefficient a is negative

The function is equal to

[tex]f(x)=a(x-1)(x+3)[/tex]

Find the value of the coefficient a

The vertex is equal to the point (-1,8)

substitute and solve for a

[tex]8=a(-1-1)(-1+3)[/tex]

[tex]8=a(-2)(2)[/tex]

[tex]a=-2[/tex]

therefore

The function is equal to

[tex]f(x)=-2(x-1)(x+3)[/tex]

Part 3) Third graph

we know that

The solutions or zeros of the first graph are

x=-2 and x=6

The parabola open up, so the leading coefficient a is positive

The function is equal to

[tex]f(x)=a(x-6)(x+2)[/tex]

Find the value of the coefficient a

The vertex is equal to the point (2,-8)

substitute and solve for a

[tex]-8=a(2-6)(2+2)[/tex]

[tex]-8=a(-4)(4)[/tex]

[tex]a=0.5[/tex]

therefore

The function is equal to

[tex]f(x)=0.5(x-6)(x+2)[/tex]

For the first graph the function is f(x) = (x—3)(x + 1), for the second graph the function is f(x) = -2(x—1)(x + 3), and for the third graph the function is f(x) = 0.5(x-6)(x+2).

It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.

As we can see in the first graph, the x-intercepts are x = -1 and x = 3, and it is opening up-side, so the function:

f(x) = (x - 3)(x + 1)

Second graph: x-intercepts are x = -3 and x = 1 and opening down-side.

Also, the vertex is at (-1, 8) so the function:

f(x) = -2(x - 1)(x + 3)

Third graph: x-intercepts are x = -2 and x = 6, and it is opening up-side, Also the vertex is at (2, -8) so the function:

f(x) = 0.5(x-6)(x+2)

Thus, for the first graph the function is f(x) = (x—3)(x + 1), for the second graph the function is f(x) = -2(x—1)(x + 3), and for the third graph the function is f(x) = 0.5(x-6)(x+2).

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Answer:

Step-by-step explanation:

[tex]\bold{Q1}\\\\5x^2-50x+120=5(x^2-10x+24)=5(x^2-6x-4x+24)\\\\=5\bigg(x(x-6)-4(x-6)\bigg)=5(x-6)(x-4)\\\\\bold{Q2}\\\\64x^2-1=(8x)^2-1^2=(8x-1)(8x+1)\\\\\text{Used}\ a^2-b^2=(a-b)(a+b)[/tex]

Answer:

see explanation

Step-by-step explanation:

1

Given

5x² - 50x + 120 ← factor out 5 from each term

= 5(x² - 10x + 24)

To factor the quadratic

Consider the factors of the constant term (+ 24) which sum to give the coefficient of the x- term ( - 10)

The factors are - 4 and - 6, since

- 4 × - 6 = 24 and - 4 - 6 = - 10, hence

x² - 10x + 24 = (x - 4)(x - 6) and

5x² - 50x + 120 = 5(x - 4)(x - 6) → d

2

64x² - 1 ← is a difference of squares and factors in general as

a² - b² = (a - b)(a + b)

64x² = (8x)² ⇒ a = 8x and b = 1

64x² - 1

= (8x)² - 1² = (8x - 1)(8x + 1) → b

Answer:

D, J

Step-by-step explanation:

21)

recall for a linear equation in the form

y=mx + b, where m is the slope

the slope a a line that is perpendicular to the equation is given by m' = -1/m

in this case the line is given with the slope of 3/4

hence the slope of a perpendicular line must be,

-1 / (3/4) = -4/3  (Hence D is the answer)

22)

M is the midpoint between Q (a,d) and R (c,b). Using the midpoint formula (see attached), we find the coordinates of M to be:

M [ (a+c)/2 , (d+b)/2 ]

The distance between P(a,b) and M [ (a+c)/2 , (d+b)/2 ] is given by (see other attached formula):

√ [(a+c)/2 - a]² + [(d+b)/2 - b]²

= √ [(a+c)/2 - (2a/2)]² + [(d+b)/2 - (2b/2)]²

= √ [(a+c - 2a)/2]² + [(d+b-2b)/2]²

= √ [(c - a)/2]² + [(d-b)/2]² (J is the answer)

Check the picture below.

I assume the question is to find [tex](g\circ f)(-4)[/tex]

[tex](g\circ f)(x)=(-2x-5)^4\\\\(g\circ f)(-4)=(-2\cdot(-4)-5)^4=3^4=81[/tex]

Answer:

x=105÷7

Step-by-step explanation:

You have to split the candy with 7 people and you can't split people

For this case we have that the variable "x" represents the amount of candies that each child touches.

If there are a total of 105 candies and they want to be distributed equally among 7 children, then we have the following expression:

[tex]x = \frac {105} {7}[/tex]

Thus, the correct option is:

"x = one hundred five divided by seven"

Answer:

OPTION B

Answer:

The average price of a gallon of orange increased by $0.03 each month.

Step-by-step explanation:

It is 11 months between October 2013 and September 2014 so the price after 11 months =

f(11) = 6.12 + 0.03(11)

= 6.12 + 0.33

= $6.45.

This is an increase of 0.33 / 11 = 0.03 / month.

Answer:

20,000 ft

Step-by-step explanation:

This is a linear equation.  The negative sign in front of the 1100 indicates that the line is going from upper left to lower right, the path a plane would definitely travel when it is landing.  The 1100 is the speed at which the plane is traveling down.

The standard form of a linear equation is y = mx + b where m is the rate of change (which is the same as the slope), and b is the y-intercept, which is found by replacing x with 0 and solving for y.  This is also known as the "starting point" for a linear situation.  Since the t in our equation represents the time that has gone by since the plane started its descent in hours, if we replace x with 0, we are effectively saying that NO time has gone by (and the plane has not yet begun to descend).  That means that the plane begins its descent at 20,000 feet in the air.

Answer: 8359

Step-by-step explanation:

The formula for sample size needed for interval estimate of population proportion :-

[tex]n=p(1-p)(\frac{z_{\alpha/2}}{E})^2[/tex]

Given : The significance level : [tex]\alpha=1-0.95=0.05[/tex]

Critical value : [tex]z_{\alpha/2}}=z_{0.025}=\pm1.96[/tex]

Previous estimate of proportion : [tex]p=0.32[/tex]

Margin of error : [tex]E=0.01[/tex]

Now, the required sample size will be :-

[tex]n=0.32(1-0.32)(\frac{1.96}{0.01})^2=8359.3216\approx8359[/tex]

Hence, the required sample size = 8359

To estimate the proportion of adults with high-speed Internet access with a 95% confidence level and a margin of error of 0.01, a sample size of 752 should be obtained.

To estimate the proportion of adults who have high-speed Internet access with a 95% confidence level and a margin of error of 0.01, we can use the formula:

Sample Size = (Z^2 * p * (1-p)) / (E^2)

Where Z is the Z-score corresponding to the desired confidence level, p is the estimated proportion from a previous study, and E is the desired margin of error.

With a previous estimate of 0.32, a confidence level of 95% (corresponding Z-score of 1.96), and a margin of error of 0.01, the sample size required would be:

(1.96^2 * 0.32 * (1-0.32)) / (0.01^2) = 752

A sample size of 752 should be obtained to achieve the desired confidence level.

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Answer:

  D.  a1=23/100, r=1/100

Step-by-step explanation:

The repeating fraction can be written as the sum ...

[tex]0.\overline{23}=0.23+0.0023+0.000023+\dots[/tex]

The first term is a1 = 0.23 = 23/100, and each successive term is shifted 2 decimal places to the right, so is multiplied by the common ratio r=1/100.

Answer:

Step-by-step explanation:

Here, a1 = 0.23 and r = 0.01.  Thus, the sum of this infinite series will be

 a1          0.23          0.23

------- = ------------- = ----------- = 23/99.

1 - r      1 - 1/100      99/100

Check this by dividing 23 by 99 on a calculator.  Result:  0.23232323....

Answer:

  Both A and B . . . . . and 2 more answers

Step-by-step explanation:

Completing the square, you get

  tan²(x) -tan(x) +0.25 = 2.25 . . . . . add 0.25

  (tan(x) -0.5)² = 1.5²

  tan(x) = 0.5 ± 1.5 = {-1, 2}

For tan(x) = -1, the solutions are ...

  x = arctan(-1) = 135°, 315°

For x = 2, the solutions are ...

  x = arctan(2) ≈ 63.435°, 243.435°

Answer:

D. 1, 3, 5, and 7 are congruent / 2, 4, 6, and 8 are congruent

Step-by-step explanation:

Vertical angles (such as 5 and 7) are congruent.

This means that angles 5 and 7 are congruent,

angles 1 and 3 are congruent,

angles 6 and 8 are congruent,

and angles 2 and 4 are congruent.

Answer:

  a) 15

  b) 2

Step-by-step explanation:

a) The sum of the enrollments in chemistry (60), physics (45), and biology (30) counts those triply enrolled 3 times and those doubly-enrolled twice. This sum will exceed the total number of students by 1 times those double-enrolled and twice those triply-enrolled.

We know that there are 10 students triply-enrolled, so the difference ...

  (60 +45 +30) -2(10) = 15

is the number of doubly-enrolled students.

There are 15 students enrolled in exactly 2 science classes.

__

b) There are 9+4 = 13 students doubly-enrolled in physics and something else. Using the result from part A, there will be 15 -13 = 2 students doubly-enrolled in chemistry and biology, but not physics.

Answer:

a) 15

b) 2

Step-by-step explanation:

There are 15 students in 2 science classes.

2 students enrolled in both chemistry and biology, but not physics.

15 -13 = 2

Answer:

B. Discontinuity at (−2, 1), zero at (−3, 0)

Step-by-step explanation:

The given function is:

[tex]\frac{x^{2}+5x+6}{x+2}[/tex]

The expression in numerator can be expressed as factors as shown below:

[tex]\frac{x^{2}+5x+6}{x+2}\\\\ =\frac{x^{2}+2x+3x+6}{x+2}\\\\ =\frac{x(x+2)+3(x+2)}{x+2}\\\\ =\frac{(x+2)(x+3)}{x+2}[/tex]

Note that for x = -2, both numerator and denominator will be zero. When both the numerator and denominator of a rational function are zero for a given value of x we get a discontinuity at that point. This discontinuity is known as a hole. This means there is a hole at x = -2

Cancelling the common factor from numerator and denominator we get the expression f(x) = x + 3

Using the value of x = -2 in previous expression we get:

f(x) = -2 + 3 = 1

Thus, there is a discontinuity(hole) at (-2, 1)

For x = -3, the value of the expression is equal to zero. This means x = -3 is a zero or root of the function.

Thus, (-3, 0) is a zero of the function.

Therefore, option B would be the correct answer.

Answer:

  x = 8.75

Step-by-step explanation:

The measure of angle C is half the measure of arc RS, so ...

  6x = (1/2)(105)

  x = 105/12 = 8.75 . . . . divide by 6

Answer:

[tex]x=8.75[/tex]

Step-by-step explanation:

We have been given a circle. We are asked to find the value of x for our given circle.

Upon looking at our given circle, we can see that angle RCS is an inscribed angle of arc RS.

We know that measure of an inscribed angle is half the measure of its intercepted arc, so we can set an equation as:

[tex]m\angle RCS=\frac{\widehat{RS}}{2}[/tex]

[tex]6x^{\circ}=\frac{105^{\circ}}{2}[/tex]

[tex]6x^{\circ}=52.5^{\circ}[/tex]

[tex]\frac{6x^{\circ}}{6}=\frac{52.5^{\circ}}{6}[/tex]

[tex]x^{\circ}=8.75^{\circ}[/tex]

[tex]x=8.75[/tex]

Therefore, the value of x is 8.75 for the given circle and option A is the correct choice.