Chris borrows 450 dollars from Gavin. Gavin lets Chris choose either a simple interest loan for 10 years with a 3.5% interest rate or loan compound annually for 7 years with a 2% interest rate. Which should Chris choose if he wants the cheaper plan?

Answer:

[tex]y = 7 \\ x = 4 \\ r = \sqrt{33} \\ \cot(t) = \frac{4}{7} \\ \sin(t ) = - \frac{7}{ \sqrt{33} } \\ \cos(t) = - \frac{4}{ \sqrt{33} } [/tex]

Using the normal distribution, it is found that:

A. There is a 0.0228 = 2.28% probability that a randomly selected score is greater than 81 points.

B. 81.85% of students scores are between 69 and 78.

C. The student scored in the 99.87th percentile.

The z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

In this problem, the mean and the standard deviation are given, respectively, as:

[tex]\mu = 75, \sigma = 3[/tex].

Item a:

The probability is one subtracted by the p-value of Z when X = 81, hence:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{81 - 75}{3}[/tex]

Z = 2.

Z = 2 has a p-value of 0.9772.

1 - 0.9772 = 0.0228.

0.0228 = 2.28% probability that a randomly selected score is greater than 81 points.

Item b:

The proportion is the p-value of Z when X = 78 subtracted by the p-value of Z when X = 69, hence:

X = 78:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{78 - 75}{3}[/tex]

Z = 1.

Z = 1 has a p-value of 0.8413.

X = 69:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{69 - 75}{3}[/tex]

Z = -2.

Z = -2 has a p-value of 0.0228.

0.8413 - 0.0228 = 0.8185.

81.85% of students scores are between 69 and 78.

Item c:

The percentile is the p-value of Z when X = 84, multiplied by 100, hence:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{84- 75}{3}[/tex]

Z = 3.

Z = 3 has a p-value of 0.9987.

The student scored in the 99.87th percentile.

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Answer:

slope = 1/3 , y-int = -5

Step-by-step explanation:

y = mx + b

hope this helps!

Answer:

w = 1.2 or 6/5

Step-by-step explanation:

math

Answer:

Step-by-step explanation:

Area of triangle is given by the formula:

1/2*a*b*sinC

= 1/2*433*520*sin(37degrees)

= 67752 sq ft

Answer:

Step-by-step explanation:

applying sine rule for area of triangle

Area = 1/2absin(c)

= 1/2x433x520xsin(37)

= 67752ft^2

Answer:

The answer is 90 mm squared

Step-by-step explanation:

First off, Surface Area is the combined areas of the 2D shapes that make up a 3D shape. The formula for finding the area of a triangle (the 2D shape that makes up most of a pyramid) is a = 1/2 bh, which is basically area = 1/2 base (the un-slanted line) * the height, or the middle line.

Since there are 4 triangles, you would multiply this by 4 after solving, so

sa = 4(1/2bh)

Putting the numbers in, you'd get

sa = 4(1/2*5*9)

To solve:

sa = 4(1/2*45)

sa = 4(22.5)

sa = 90mm^2

Introduce a constant,

let it be (k)

Y=KX

-40 = K(7)

K= -5.7

Then,

Y =KX

51= -5.7(X)

X = -8.95~-9

Answer:

h = 4.22 cm

Step-by-step explanation:

Mathematically, we have the volume of a cylinder as;

V = pie * r^2 * h

We have it that the radius is 6 cm

V = pie * 6^2 * h

for the sphere, we have it that;

V = 4/3 * pie * r^3

V = 4/3 * pie * 4.5^3

We can proceed to equate both volumes;

pie * 6^2 * h = 5/3 * pie * 4.5^3

pie on both sides cancel out

6^2h = 5/3 * 4.5^3

36h = 151.875

h = 151.875/36

h = 4.22 cm

Answer:

x = 6

Step-by-step explanation:

Complementary angles always equal 90 degrees so something multiplied by 12 will have to equal something that will add up with 18 to get 90 so

12 × 6 = 72 and 72 + 18 = 90 Hope this helps you!

Answer:

C

Step-by-step explanation:

Answer:

parallelograms

Step-by-step explanation:

Answer: 5:10 A.M.

Step-by-step explanation:

First find the total time that Isabelle spent playing volleyball and hiking.

= 2 hours and 10 minutes + 1 hour and 55 minutes

= 4 hours and 5 minutes

If she finished both activities at 11:15 am, the time she started was:

= 11:15 - 4 hours 5 minutes

= 5:10 A.M.

Answer:

a

Step-by-step explanation:

Answer:

on a graph will (-5, -7) be found Quadrant III.

Answer:

98 cm

Step-by-step explanation:

If the base is half the height, the base would be 7 cm. 14 X 7 = 98

Answer: 0 = 23

Almost positiveee :))

Step-by-step explanation:

Answer:

Step-by-step explanation:

since RS || VU   ( parallel to )   then the angle V is equal to ∠ VRS , also we are given that ∠VRT = 71°  so subtract  ∠VRT from ∠VRS

103° - 71° = 32°

so ∠TRS = 32°

next find ∠U,  we know that ∠U + ∠VRT= 180°  ( b/c they are supplementary )

we are also told that  ∠VRT = 71°

∠U = 180 - 71

∠U = 109°

Since RS || VU (parallel to) then the angle V is equal to VRS, also we are given that VRT = 71°

So subtract VRT from VRS,

103° -71° = 32°

So, TRS = 32°

next find U, we know that ZU + ZVRT= 180° (b/c they are supplementary)

We are also told that <VRT = 71"

U = 180° - 71°

U = 109° is the answer.

Answer:

B) 9/10

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

Answer:

Option B

Step-by-step explanation:

A) 30w + 35 does not equal 65, because we are not given that w=1

B) 5(6w + 7) equals 30w + 35, so it is correct

C) 30w + 35 does not equal 65, because we are not given that w=1

D) 6w + 7 is (30w + 35)/5, which is not equal to (30w + 35)

E) N/A

Answer:

Step-by-step explanation:

Answer:

Step-by-step explanation:

The equation is a parabola, that opens up downwards,  and the point from which Sarah throws the ball is 5 feet off the ground.  so set the height to zero ( when the ball reaches the ground )  and solve for t

0 = -16[tex]t^{2}[/tex] + 18t + 5

use quadratic equation :)

-b +- sqrt([tex]b^{2}[/tex] - 4ac) / 2a

-18 +- sqrt[ [tex]18^{2}[/tex] - 4 (-16)(5) ] / 2(-16)

-18 +- sqrt[324 +320 ] / -32

-18 +- sqrt[644] / -32

-18 +- 25.377155 / -32

do the positive choice :

-18 + 25.377155 / -32

7.377155  / -32

-0.2305  ( so this answer would be where the ball would hit the ground if the arc extended down to the ground behind where Sarah throws the ball from. so this answer doesn't count in our domain. Because it's before Sarah throws the ball)

do the negative choice:

-18 - 25.377155 / -32

1.355536  ( this answer looks good, about 1.35 seconds for the ball to fly , this was more of a toss than a throw. )

t = 1.4 seconds ( rounded to nearest 10th )

Answer:

Motor 1) 7 ½ horsepower single phase, 230 volts 40 ampere) ; Motor 2) 5 ... for a 2 horsepower 115 volt motor that has a full-load current rating of 24 ampere, ... Simultaneously disconnects all conductors of the circuit.

Answer:

A. -6

Step-by-step explanation:

Answer:

-6

Step-by-step explanation:

Common difference of an arithmetic sequence=t2-t1

=39-45

=-6

Answer:

Step-by-step explanation:

The sampling method employed in the given example is convenience sampling.

Convenience sampling is a non-probability sampling technique where the sample is selected based on its accessibility and convenience. In this case, the post office manager selected three delivery people from the total of 11 available. This selection was based on convenience, as they were already working for the post office.

The population in this scenario consists of all the customers the post office manager works with. Let's denote this population as N.

The post office manager used convenience sampling to select a subset of the population to participate in the study. The size of the sample is not explicitly mentioned, but we can assume it is the total number of customers on the three selected delivery routes. Let's denote the sample size as n.

Since convenience sampling does not involve random selection, the sample selected may not be representative of the entire population. The customers on the selected delivery routes may not be a fair representation of all the post office customers. This introduces a potential sampling bias.

It's important to note that convenience sampling can be quick and easy to implement but may not provide reliable or generalizable results. In this case, the post office manager may obtain information about customer satisfaction from a limited group, potentially leading to skewed or unrepresentative findings. For a more accurate and representative study, a different sampling method, such as random sampling or stratified sampling, could be employed.

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Answer:

I have got,

x = 14

y = 12.1

Using trigonometric ratio.

Step-by-step explanation: Do You Want Me To Find All The Values ?

Parallel lines intersected by a common transversal form 8 angles

The required values of y and x are;

The reasons why the above values are correct are given as follows:

Given the lines are parallel lines cut by a common transversal, we have;

Angles with measure (2·y - 1)° and (9·x - 38)° are same side interior angles

Angles with measure (4·x + 23)° and (2·y - 1)° are alternate interior angles

Which gives;

(2·y - 1)°+ (9·x - 38)° = 180°...(1)

(4·x + 23)° = (2·y - 1)°...(2)

From equation (1), we get;

y = 109.5 - 4.5·x

From equation (2), we get;

y = 2·x + 12

The common solution is given by; 109.5 - 4.5·x = 2·x + 12

From 109.5 - 4.5·x = 2·x + 12, we get;

x = 15,  

6) (9·x + 42)° and 15·x° are vertical angles, and therefore are equal

(9·x + 42)° = 15·x°

∴ x = 7

(4·y - 13)° and (9·x + 42)° are supplementary, therefore

(4·y - 13)° = (9·x + 42)°, which gives;

(4·y - 13)° = (9×7 + 42)° = 105°

7) (3x + 11) + (x + 21) = 180

∴ x = 37

(14·y - 4)° = 3x + 11 = 3 × 37 + 11 = 122°

8) (13·x - 33) = 10·x

∴ x = 11

10·x + 5·y = 180

10 × 11 + 5·y = 180

[tex]y = \dfrac{70^{\circ}}{5} = 14^{\circ}[/tex]

9) (27·x + 4) + (8·x + 1) = 180

∴ x = 5

y + 10 = 8·x + 1 = 8 × 5 + 1 = 41

y = 41 - 10 = 31

10) 16·x - 4 = 9·x - 6 + 58 = 9·x + 52

7·x = 56

x = 8

11) (6·x - 58)° + (x + 8)° = 90°

7·x - 50 = 90

7·x = 90 + 50 = 140

[tex]x = \dfrac{140}{7} = 20[/tex]

12) 7·x - 7 = 3·x + 45°

4·x = 52

[tex]x = \dfrac{52}{4} = 13[/tex]

x = 13°

(3·x + 45)° + 63° + (y - 6)° = 180°

(3×13 + 45)° + 63° + (y - 6)° = 180°

147 + (y - 6)° = 180°

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Answer:

you have 2 options!!!

Step-by-step explanation:

hoped I helped!

Answer:

Parenthesis is answered first

Step-by-step explanation

Using the pemdas strategy the "p" stands for parenthesis therefore it would be (9-4)

The answer to the problem is 11

24987.2 meters cubed.

Step-by-step explanation:

A Hemisphere is 1/2 of a sphere, so let's find the volume of a sphere and then cut it in half.

The volume of a sphere is V= (4/3)πr3

The diameter is double the size of the radius, so we can find r, the radius, by dividing the diameter,

45.7m, by 2. So r = 22.85 meters

so the volume of the sphere is (4/3)π(22.85 meters)3, which is 49974.35787 meters cubed.

Since we're actually looking for the Hemisphere, we can divide this volume in half to get the volume of the hemisphere as 24987.17894 meters cubed.

And because the answer must be to 1/10th of a cubic meter, that means we only want one decimal point. So we round to 24987.2 meters cubed.

Answer:

7 x 7 x 8 = 392

15 x 7 x 7(14 - 7) = 735

735 + 392 = 1,127 in^3 is your answer.

Let's split the figure:

Answer:

m<ZA = 109

Step-by-step explanation:

Supplementary angles mean the angles add up to 180 so:

8x - 27 + 4x + 3 = 180

12x - 24 = 180

12x = 180 + 24

12x = 204

x = 17

m<ZA:

8x - 27

8(17) - 27

136 - 27

109