1200$ invested at a rate of 3.5% compounded quarterly; 4 years

To find the probability that a randomly selected person is shorter than 61.6 inches, calculate the z-score and use a standard normal distribution table or calculator to find the corresponding probability.

To find the approximate probability that a randomly selected person in the sample is shorter than 61.6 inches, we can use the standard normal distribution.

First, we need to calculate the z-score for 61.6 inches using the formula:
z = (x - mean) / standard deviation

z = (61.6 - 64.2) / 2.6 = -1.0

We can then use a standard normal distribution table or a calculator to find the area to the left of z = -1.0, which represents the probability that a randomly selected person is shorter than 61.6 inches. The probability is approximately 0.1587, or 15.87%.

Answer:

[tex]\frac{1}{6}[/tex]

Step-by-step explanation:

[tex]\frac{2}{3} - \frac{1}{2} =\frac{2x2}{3x3} -\frac{1x3}{2x3} =\frac{4}{6} -\frac{3}{6} =\frac{4-3}{6} =\frac{1}{6}[/tex]

Answer:

[tex]\frac{1}{6}[/tex]

Step-by-step explanation:

[tex]\frac{2}{3}-\frac{1}{2}=\\ \\=\frac{2*2-1*3}{6}\\ \\=\frac{4-3}{6}\\ \\=\frac{1}{6}[/tex]

Answer:

Step-by-step explanation:

250 divided by 20= 12.5

So 12.5 miles per gallon.

12.5. The answer ask for how many miles in 1 gallon. So, you do 250 divided by 20. 250 divided by 20 is 12.5, so he will drive 12.5 or 12 1/2 miles using each gallon of gas.

ANSWER : 12.5 or 12 1/2

Answer:

The tree is 17.5 ft tall

Step-by-step explanation:

We can use proportions to solve this.

Notice that Emily (5 feet tall) and her shadow (8 feet long) constitute the two legs of a right angle triangle (see attached image).

The nearby tree  (unknown height H), will also cast a shadow (28 ft long) with the same inclination as Emily does due to the unique position of the sun relative to them.

Then we can use the proportion associated with the sides of similar triangles:

[tex]\frac{5\,ft}{8\,ft} =\frac{H}{28\,ft}[/tex]

Then, we can solve for H in the equation:

[tex]\frac{5\,ft}{8\,ft} =\frac{H}{28\,ft} \\H=\frac{28*5}{8} \,ft\\H=17.5 \.ft[/tex]

Answer:

  23.6°

Step-by-step explanation:

The relevant trig relationship is ...

  Sin = Opposite/Hypotenuse

This tells you ...

  sin(Z) = XY/YZ = 6/15 = 2/5

The inverse sine (arcsine) function is used to find the angle when its sine is known.

  Z = arcsin(2/5)

  Z = 23.6°

To find the size of angle XYZ, we need additional information.

To find the size of angle XYZ, we need additional information. Typically, to determine the size of an angle, we need to know the measures of other angles or the lengths of the sides of the triangle. If we have such information, we can use the trigonometric ratios or the properties of triangles to find the size of angle XYZ. Could you please provide the missing information?

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Answer:

The discrimant of this equation is 144.

Step-by-step explanation:

First you have to move all the variables to one side to make the equation/expression into 0 by substracting 8x² to both sides :

9x² + 14x + 13 = 8x²

9x² + 14x + 13 - 8x² = 8x² - 8x²

x² + 14x + 13 = 0

It is given that the formula of discriminant is, D = b² - 4ac where a&b&c represent the number of the equation, ax²+bx+c = 0 :

x² + 14x + 13 = 0

D = b² - 4ac

= 14² - 4(1)(13)

= 196 - 52

= 144

Final answer:

The discriminant of the quadratic equation 9x²+14x+13=8x² is found by simplifying to x²+14x+13=0 and using the formula b² - 4ac, yielding a result of 144.

Explanation:

The student's question involves finding the discriminant of the quadratic equation 9x² + 14x + 13 = 8x². We simplify this equation by subtracting 8x² from both sides, resulting in x² + 14x + 13 = 0.

The discriminant of a quadratic equation ax² + bx + c = 0 is given by b² - 4ac. For this equation, a = 1, b = 14, and c = 13. Substituting these into the discriminant formula gives (14)² - 4(1)(13) = 196 - 52 = 144.

Since the discriminant is positive, there are two distinct real roots to the equation. This could be relevant if we were to graph the equation, indicating where it crosses the x-axis, or if further solving for x was required.

⁵/₉ of bafter a cup would go per cupcake .

To determine how many cups of cake batter to use for each of the 18 cupcakes when you have 10 cups of batter, you need to divide the total amount of batter by the number of cupcakes.

Divide the total cups of batter (10 cups) by the number of cupcakes (18):

= 10 ÷ 18

≈ 10 / 18

Divide both sides by 2 to simplify and get:

= 5 / 9

Answer:

When you are "multiplying" exponents, you're really just adding them together. So in the case of (x² ⋅ x⁴), you add the exponents:

2 + 4 = 6

[tex]x^{6}[/tex] would be the answer.

On the other hand, raising a power to a power, is actually multiplying them. So it would just be:

2 ⋅ 4 = 8

[tex]x^{8}[/tex] would be the answer.

Answer:

The correct answer is 2.45.

Step-by-step explanation:

Probability model of an office manager regarding reports from employees is given by:

X = 0; P(X) = 0.05

X = 1; P(X) = 0.15

X = 2; P(X) = 0.35

X = 3; P(X) = 0.25

X = 4; P(X) = 0.15

X = 5; P(X) = 0.05

Now expectation of number of emails that the manager would receive is given by X × P(X)

= 0 × 0.05 + 1 × 0.15 + 2 × 0.35 + 3 × 0.25 + 4 × 0.15 + 5 × 0.05

= 0 + 0.15 + 0.70 + 0.75 + 0.60 + 0.25

= 2.45

The correct answer is 2.45.

X = 0; P(X) = 0.05

X = 1; P(X) = 0.15

X = 2; P(X) = 0.35

X = 3; P(X) = 0.25

X = 4; P(X) = 0.15

X = 5; P(X) = 0.05

Now the number of emalis should be

= 0 × 0.05 + 1 × 0.15 + 2 × 0.35 + 3 × 0.25 + 4 × 0.15 + 5 × 0.05

= 0 + 0.15 + 0.70 + 0.75 + 0.60 + 0.25

= 2.45

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Answer:

1.- dR/dt   = 14 $/day

2.- dC/dt =  4.55 $/day

3.- dP/dt = 7,7 $/day

Step-by-step explanation:

By definition Profit is equal to Revenue minus total costs then.

We have

R(x) = 2*x

C(x) = 0,01*x²  + 0,4*x  + 30

Then Profit  P(x)  =  2*x  -  0,01*x²  - 0,4*x  - 30

P(x) = - 0.01*x²  +  1.6*x  - 30

1.- Find rate of change total revenue per day, when

x = 25  and dx/dt = 7 u/day

R(x) = 2*x

dR/dt   = 2*dx/dt      ⇒   dR/dt   = 2* 7

dR/dt   = 14 $/day

2.-

C(x) = 0,01*x²  + 0,4*x  + 30

dC/dt = 0,01*x* dx/dt  + 0,4*dx/dt

dC/dt = 0,01*25*7  +  0.4*7

dC/dt = 1.75 + 2.8

dC/dt =  4.55 $/day

3.-

P(x) = - 0.01*x²  +  1.6*x  - 30

dP/dt = - 2*0,01*x*dx/dt  + 1.6*dx/dt

dP/dt = - 2*0,01*25*7  + 1.6*7

dP/dt = - 3,5 + 11.2

dP/dt = 7,7 $/day

Answer:

Step-by-step explanation:

Given information

[tex]R(x)=2x\\C(x)=0.01x^2+0.4x+30[/tex]

When,

[tex]x=25\\dx/dt=7[/tex] units per day

As we know that

Profit = Revenue - Cost

Then, the Profit,

[tex]P(x)=2x-0.01x^2+0.4x-30\\P(x)=-0.01x^2+1.6x-30[/tex]

Now, The total Revenue per day

[tex]R(x)=2*x[/tex]

By differentiating both side with respect to [tex]t[/tex]

[tex]\\dR/dt=2*dx/dt\\dR/dt=2*7\\dR/dt=14[/tex]

Hence the rate of change of total revenue is $14 per day.

Similarly,

The total cost per day

[tex]C(x)=0.01x^2+0.4x+30[/tex]

By differentiating both side with respect to [tex]t[/tex]

[tex]dC/dT=0.01*x*dx/dt+0.4*dx/dt\\dC/dt=0.01*25*7+0.4*7\\dC/dt=1.75+2.8\\dC/dt=4.55[/tex]

Hence the rate of change of total cost is $4.55 per day

And the total Profit per day

[tex]P(x)=-0.01x^2+1.6x-30\\[/tex]

By differentiating both side with respect to [tex]t[/tex]

[tex]dP/dt=2*(-0.01)*x*dx/dt+1.6*dx/dt\\dP/dt=-2*(-001)*25*7+1.6*7\\dP/dt=-3.5+11.2\\dP/dt=7.7[/tex]

Hence the rate of change of total Profit is $7.7 per day

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Answer:

16 pi cm^2 or 50.27 cm^2

Step-by-step explanation:

In this question, we are told that by using a particular mug of coffee with a certain diameter, a baker was able to circular cookies from a big sheet of cookie dough so we need to know the area of each of the cookie.

Now this is pretty much straightforward. since we do know the diameter of the mug, finding the area of the cookie is simple!

How do we do this?

what to do simply is to apply the formula of a circle to find the area of a circle of diameter 8cm

mathematically, the area of a circle A = pi * r^2

Since we are given D in the question, we know quite well that we need r from the equation. Mathematically, d = 2r or more specifically r = d/2 = 8/2 = 4cm

now let’s find the area of a circle of radius 4cm

A = pi * 4^2 = 16 pi cm^2 or simply 50.27 cm^2

Answer: 49

Step-by-step explanation:

If iTs half of each square its the same

Answer:

Step-by-step explanation:

The number in the equation is 9.

A mathematical statement consisting of an equal symbol between two algebraic expressions with the same value is known as an equation in algebra.

Let the number be x

(2/3)x + 5 = (-2/6)x + 14 (Equation given)

x( 2/3 + 2/6 ) = 14 - 5

x( 2/3 + 1/3) = 9

x = 9

Hence, the number in the given equation is 9

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Answer:

19 5/8 miles

Step-by-step explanation:

First you convert all fractions into improper fraction which are

5 4/8 = 44/8

7 4/8 = 60/8

6 5/8 = 53/8

Then add just the numerators together as the denominator stays the same which looks like 157/8

Then see how many times 157 goes into 8 which is 19 with 5 left over

So you rewrite the answer as 19 5/8 miles

Answer:

4.5% (1dp)

Step-by-step explanation:

10500/11000x100=95.4545454545%

100-95.4545454545= 4.5454545455%

=4.5% (1dp)

I hope this helps!

Answer:

4.762%

Step-by-step explanation:

Change:

11,000 - 10,500 = 500

% change:

500/10500 × 100

100/21

4.761904762%

Answer:

I think its b

Step-by-step explanation:

A=2πrh+2πr2=2·π·5·12+2·π·52≈534

Answer:

median

Step-by-step explanation:

answer 1 is : 144

Answer2:21.60

Answer:

144 and 21.60

Step-by-step explanation:

Answer:

t represents the number of seconds after the rocket is released

Answer:

A

Step-by-step explanation:

answer is the number of seconds after the rocket is released

Answer:

The probability is 5/7

Step-by-step explanation:

Please check the attached files for more explanation

Answer:

a. 4 possible outcomes.

b. Possible outcomes - the spinner will fall on a 17, 3, 11 or N.

c. {17, 3, 11, N}

d. P(z) = 1/4.

Step-by-step explanation:

The probability of a specific value on one spin  P(z) = 1/4.

a) There are four possible outcomes in the experiment.

b) The possible outcomes are 17, 3, 11, and N.

c) The sample space for the experiment is  {17, 2, 11, N}.

d) P(z) = 1/4.

It is the total number of possible outcomes from a given set.

We have,

The square spinner has the following sections.

17, 3, 11, N.

Now,

a)

The number of possible outcomes.

= 17, 3, 11, N

= 4

b)

The possible outcomes are:

= 17, 3, 11, and N

c)

The sample space.

= {17, 3, 11, N}

d)

The probability of getting one specific outcome.

P(z) = 1/4

Thus,

The answers for a), b), c), and d) are given above.

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The probability that an individual's clotting time will be less than 6 seconds or greater than 11 seconds, under a normal distribution with a mean of 7.45 and a standard deviation of 3.6, is approximately 50.9%.

The subject in question pertains to the calculation of probabilities using the Normal Distribution. Given that the mean clotting time is 7.45 seconds with a standard deviation of 3.6 seconds, we need to find the probability that the clotting time will be either less than 6 seconds or more than 11 seconds.

First, we convert the clotting times to z-scores (the number of standard deviations away from the mean). The z-score for 6 seconds is (6-7.45)/3.6 = -0.40, and the z-score for 11 seconds is (11-7.45)/3.6 = 0.98. We can look these z-scores up in a Z-table to find the corresponding probabilities.

From the Z-table, we find that the probability of a z-score less than -0.40 is 0.345. The probability of a z-score less than 0.98 is about 0.836. Because we're asked to calculate the probability that the clotting time is either less than 6 seconds or greater than 11 seconds, we need to calculate the probabilities at the tails of the distribution. So we subtract the probability for 0.98 (0.836) from 1 to find the probability that clotting time is greater than 11 seconds, which is 0.164.

The probability of the clotting time being either less than 6 seconds or more than 11 seconds would be the sum of the two probabilities: 0.345 + 0.164 = 0.509 or 50.9%.

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The probability that an individual's blood clotting time is less than 6 seconds or greater than 11 seconds is approximately 0.5057, calculated using the Z-scores and the standard normal distribution.

The mean clotting time of blood is 7.45 seconds, with a standard deviation of 3.6 seconds. To find the probability that an individual's clotting time will be less than 6 seconds or greater than 11 seconds under normal distribution, we will use the Z-score formula:

Z = (X - mean) / standard deviation

Using Z-tables or standard normal distribution calculators:

Therefore, the total probability is:

P(X < 6 or X > 11) = P(Z < -0.40) + P(Z > 0.99) ≈ 0.3446 + 0.1611 = 0.5057

Answer:

B, D and E.

just trust me

The angle made by the apothem and the radius would be; 30 degrees. Then the correct option is B.

The polygon is a 2D geometry that has a finite number of sides. And all the sides of the polygon are straight lines connected to each other side by side.

The apothem of a regular hexagon = 8 cm.

Then the side length of the hexagon will be

[tex]\rm x = \dfrac{8}{\sin 60^o}= 9.24\ cm[/tex]

The perimeter of the hexagon;

Perimeter = 6 × 9.24 = 55.43 cm

The area of the hexagon;

Area = 0.5 × 8 × 9.24 = 36.95 cm².

The angle made by the apothem and the radius = 30 degrees.

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Answer:

(B) (7x - 6 ) ( 7x + 6)

Step-by-step explanation:

49x^2 - 36

This is the difference of squares

(7x)^2 - 6^2

We can factor this as

(a^2 -b^2) =(a-b) (a+b)

(7x)^2 - 6^2 = (7x-6) (7x+6)

Answer:

Incomplete question check attachment for diagram

Step-by-step explanation:

Two parallel lines, cross by a transversal

The angle between one of the line and the transfer is 125° and this angle is opposite to angle d, so it is vertical opposite angle

Vertically Opposite Angles are the angles opposite each other when two lines cross, so it was the transversal line that cross the parallel lines

and we know that, vertical opposite angle is equal.

Then, d = 125°

Answer:

(C) d=125

Step-by-step explanation:

Answer:

a. IT = 9.75 * X

b. GT = 4500 + 4.25 * X

c. G = 9.75 * X - 4500 - 4.25 * X

Step-by-step explanation:

With the data of the statement we can get a function. Let X be the number of pounds sold.

to. Monthly income

IT = 9.75 * X

b. Monthly expenses

GT = 4500 + 4.25 * X

c. Monthly Earnings (Monthly Income - Monthly Expenses)

G = 9.75 * X - (4500 + 4.25 * X)

G = 9.75 * X - 4500 - 4.25 * X

a. The IT function should be = [tex]9.75 \times X[/tex]

b. The GT function is = [tex]4500 + 4.25 \times X[/tex]

c. The function G is = [tex]9.75 \times X - 4500 - 4.25 \times X[/tex]

here we assume X be the number of pounds sold.

Since A coffee business should sell the coffee for $ 9.75. Monthly expenses are $ 4,500 along with $ 4.25 for each pound of coffee.

So,

a. The IT function is [tex]9.75 \times X[/tex]

b.  The GT function should be [tex]4500 + 4.25 \times X[/tex]

c. The function G should be [tex]G = 9.75 \times X - (4500 + 4.25 \times X)[/tex]

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Answer:

56%

Step-by-step explanation:

U reported me and the answer got deleted so

14:25*100 =

( 14*100):25 =

1400:25 = 56

here's your step by step explanation

and pls mark me brainliest

bye

Answer:

56%

Step-by-step explanation:

Is means equals and of means multiply.  Let P be the percent

14 = P * 25

Divide each side by 25

14/25 = 25P/25

.56 = P

Change to percent form

56% =P

Answer:

x = 5

Step-by-step explanation:

To solve this equation for x, subtract 2x from both sides, obtaining:

x = 5.

Answer:

m=3

Step-by-step explanation:

i hope today brings you joy and happiness :)))

Answer:

The answer is 3

Step-by-step explanation:

This is how you solve it

3m-2.4=6.6

   +2.4 .  +2.4

3m=9

/3 .  /3

m=3

Answer:

, a diagonal matrix is a matrix in which the entries outside the main diagonal are all zero

Step-by-step explanation: