You are investing $5,000 and can invest for 2 years or 3 years at 1.75% and 1.25% interest rates, respectively. Which earns more interest

Answer:

Step-by-step explanation:

Perimeter of a rectangle = 2l + 2w

Area of a rectangle = l × w

where

l is the length

w is the width

From the question

The length of a rectangle six times its width which is written as

l = 6w

Area = 150cm²

Substitute these values into the formula for finding the area

That's

150 = 6w²

Divide both sides by 6

w² = 25

Find the square root of both sides

width = 5cm

Substitute this value into l = 6w

That's

l = 6(5)

length = 30cm

So the perimeter of the rectangle is

2(30) + 2(5)

= 60 + 10

Hope this helps you

Solve

Let's solve your equation step-by-step.

9x−3−8x=7−x

Step 1: Simplify both sides of the equation.

9x−3−8x=7−x

9x+−3+−8x=7+−x

(9x+−8x)+(−3)=−x+7(Combine Like Terms)

x+−3=−x+7

x−3=−x+7

Step 2: Add x to both sides.

x−3+x=−x+7+x

2x−3=7

Step 3: Add 3 to both sides.

2x−3+3=7+3

2x=10

Step 4: Divide both sides by 2.

2x

2

=

10

2

x=5

Answer:

x=5

Answer:

Hope this is easier, good luck.

Answer:

Percentage of home team supporters =65%

Percentage of visiting team supporters =35%

Step-by-step explanation:

Total attendees=2,000 people

Home team supporters=1,300

Visiting team supporters=700

What percentage of people attending supported the home team?

Percentage of people attending who supported the home team = home team supporters / total attendees × 100

=1,300/2,000 × 100

=0.65 × 100

=65%

Visiting team supporters = visiting team supporters / total attendees

× 100

=700/2000 × 100

=0.35 × 100

=35%

Alternatively,

Visiting team supporters = percentage of total attendees - percentage of home team supporters

=100% - 65%

=35%

Answer:

Step-by-step explanation:

x^2+20=4 first isolate the variable by subtracting 20 on both sides.

x^2=-16 again isolate the variable but this time you square root both sides.

[tex]\sqrt{x}^2[/tex]=[tex]\sqrt{-16[/tex] then simplify

x= ±4

Answer:

C) 100 cm²

Step-by-step explanation:

(14*6)/2*10

20/2*10

10*10

100

The area of the given shaded part of the rectangle is 100 square meters as shown.

The entire space filled by a triangle's three sides in a two-dimensional plane is defined as its area.

The fundamental formula for calculating the area of a triangle is A = 1/2 b h.

The area of the shaded part = area of the rectangle -  area of the triangle

The area of the shaded part = 14 × 10 - (1/2) × 8 × 10

The area of the shaded part = 140 - 80/2

The area of the shaded part = 140 - 40

Apply the subtraction operation, and we get

The area of the shaded part = 100 meters²

Thus, the area of the given shaded part of the rectangle is 100 square meters.

Learn more about the triangles here:

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Answer:

There is not sufficient sample evidence to support the claim that the population mean is not equal to 88.9.

Step-by-step explanation:

We are given the following hypothesis below;

Let [tex]\mu[/tex] = population mean.

So, Null Hypothesis, [tex]H_0[/tex] : [tex]\mu[/tex] = 88.9      {means that the population mean is equal to 88.9}

Alternate Hypothesis, [tex]H_A[/tex] : [tex]\mu\neq[/tex] 88.9     {means that the population mean is different from 88.9}

The test statistics that will be used here is One-sample t-test statistics because we don't know about population standard deviation;

                             T.S.  =  [tex]\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }[/tex]  ~  [tex]t_n_-_1[/tex]

where, [tex]\bar X[/tex] = sample mean = 81.3

             s = sample standard deviation = 13.4

            n = sample size = 7

So, the test statistics =  [tex]\frac{81.3-88.9}{\frac{13.4}{\sqrt{7} } }[/tex]   ~ [tex]t_6[/tex]

                                     =  -1.501

The value of t-test statistics is -1.501.

Also, the P-value of the test statistics is given by;

                    P-value = P([tex]t_6[/tex] < -1.501) = 0.094

Since the P-value of our test statistics is more than the level of significance as 0.094 > 0.01, so we have insufficient evidence to reject our null hypothesis as the test statistics will not fall in the rejection region.

Therefore, we conclude that the population mean is equal to 88.9.

Answer:

Divide by 30.48: It would be 0.0656168 feet.

Step-by-step explanation:

Answer:

0.0656

Step-by-step explanation:

2.54 cm = 1 in

12 in = 1 ft

2.54 * 12 = 30.48

2/30.48 = 0.0656167979

Answer:

[tex]log_{10}[/tex] 10000 = 4

Step-by-step explanation:

Using the rule of logarithms

[tex]log_{b}[/tex] x = n ⇔ x = [tex]b^{n}[/tex]

Here b = 10, n = 4 and x = 10000, thus

[tex]log_{10}[/tex] 10000 = 4 ← in logarithmic form

that is [tex]10^{4}[/tex] = 10000 ← in exponential form

Answer:

(3) y+2=2(x-8)

Step-by-step explanation:

Substitute the point into the equation and see if it is true

(8,-2)

(1) y+2=2(x+8)

    -2+2 = 2(8+8)

    0 = 2(16)

False

(2) y-2=2(x-8)

  -2-2 = 2(8-8)

  -4 =2 (0)

  False

(3) y+2=2(x-8)

  -2+2 = 2( 8-8)

  0 = 2(0)

 True

(4) y-2=2(x+8)

  -2-2 = 2(8+8)

  -4 = 2(16)

False

Answer:

[tex]\boxed{y+2=2(x-8) }[/tex]

Step-by-step explanation:

[tex]x=8[/tex]

[tex]y=-2[/tex]

[tex]\sf Check \ the \ third \ option.[/tex]

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

[tex]\sf Both \ sides \ must \ be \ equal.[/tex]

[tex]0=2(0)[/tex]

[tex]0=0[/tex]

This question is incomplete, here is the complete question:

Specifications for a part for a DVD player state that the part should weigh between 25.2 and 26.2 ounces. The process that produces the parts has a mean of 25.7 ounces and a standard deviation of .25 ounce. The distribution of output is normal. Use Table-A

a) What percentage of parts will not meet the weight specs? (Round your "z" value and final answer to 2 decimal places.

b) Within what values will 95.44 percent of sample means of this process fall, if samples of n = 8 are taken and the process is in control (random)

Answer:

a) What percentage of parts will not meet the weight specs = 4.56%

b) values within which 95.44 percent of sample means of this process falls are;

UCL = 25.88 ounces

LCL = 25.52 ounces

Step-by-step explanation:

Given that;

Mean u = 25.7 ounces

Std deviation = 0.25 ounces

a)

Z-score (Upper) = (X- u) / s = (26.2 - 25.7) / 0.25 = 2

Z-score (Lower) = ( 25.2-25.7 ) / 0.25 = -2

using the T - table

For Z = 2.0

the area in the tail of the curve to the right of the mean (upper) = 0.4772

therefore;

Number of defective = 0.5000 - 0.4772 = 0.0228

These are errors on one side of normal distribution.

To get the total error, we say

Total error = 2 × 0.0228

Total error = 0.0456 ≈ 4.56% ( 2 decimal place )

b)

given that;

n = 8,

standard deviation = 0.25 ounce

Standard deviation of X = Std deviation / √n

= 0.25 /√8 = 0.088

Now for 95.44% of confidence interval, Z = 2

UCL = Mean + Z × Standard deviation of X

= 25.7 + 2 × 0.088

= 25.88 ounces

LCL = Mean - Z × Standard deviation of X

= 25.7 - 2 × 0.088

= 25.52 ounces

Answer:

7.15 miles

Step-by-step explanation:

4/5 of a mile is equivalent to .8 miles.

32.95

-25.8

7.15

Answer:

Step-by-step explanation:

39.95 - 25.80 = 7.15 miles

Answer:

Step-by-step explanation:

[tex]distance = 15 miles\\time = 0.1 hours\\\\Speed = \frac{Distance}{time}\\ Speed = \frac{15}{0.1}\\ Speed =150[/tex]

Answer:

[tex]150mph[/tex]

Step-by-step explanation:

Given:

s=15miles

t=0.1hours

Required:

v=?

Formula:

[tex]v = \frac{s}{t} [/tex]

Solution:

[tex]v = \frac{s}{t} = \frac{15m}{0.1h} = \frac{150m}{1h} = 150mph[/tex]

Hope this helps ;) ❤❤❤

Answer:

1. Make a list of activities and the number of students:

Watching TV: 32

Talking on the phone: 41

Video games: 24

Reading: 15

2. Then combine the data in a bar graph as shown in the picture

Answer: 0.1 or 1/10

Step-by-step explanation:

[tex]\left(\frac{3}{4}-\frac{2}{3}\right)\cdot \:1\frac{1}{5}[/tex]

[tex]1\frac{1}{5}=\frac{6}{5}[/tex]

[tex]\left(\frac{3}{4}-\frac{2}{3}\right)\cdot \frac{6}{5}[/tex]

  [tex]\frac{3}{4}-\frac{2}{3}[/tex]    [tex]=\frac{9}{12}-\frac{8}{12}[/tex]

[tex]=\frac{1}{12}[/tex]

[tex]\frac{6}{5}\cdot \frac{1}{12}[/tex]

Cross, cancel common factor

[tex]\frac{1}{2}\cdot \frac{1}{5}[/tex]

[tex]=\frac{1}{10}[/tex]

Step-by-step explanation:

Hey, there!!

Look this figure, simply we find that;

In triangle ABC,

angle CBD is an exterior angle of a triangle.

and its measure is 90°

Then,

angle CBD= y +48° {sum of interior opposite angle is equal to exterior angle or from theorem}.

or, 90°= y + 48°

Shifting, 48° in left side,

90°-48°= y

Therefore, the value of y is 42°.

Hope it helps...

Answer:

a)2/7

b)1/2

c)9/14

d)6/7

Step-by-step explanation:

The jar contains 4 red marbles, numbered 1 to 4 which means

Red marbles = (R1) , (R2) , (R3) , (R4)

It also contains 10 blue marbles numbered 1 to 10 which means

Blue marbles = (B1) , (B2) , (B3) , (B4) , (B5) , (B6) , (B7) , (B8) , (B9) , (B10) .

We can calculate total marbles = 4red +10 blues

=14marbled

Therefore, total marbles= 14

The marbles that has even number = (R2) , (R4) ,(B2) , (B4) , (B6) , (B8) , (B10) =7

Total number of Blue marbles = 10

Blue and even marbles = 5

(a) The marble is red

P(The marble is red)=total number of red marbles/Total number of marbles

=4/14

=2/7

(b) The marble is odd-numbered

Blue marbles with odd number= (B1) , (B3) , (B5) , (B7) , (B9) ,

Red marbles with odd number = (R1) , (R3)

Number of odd numbered =(5+2)=7

P(marble is odd-numbered )= Number of odd numbered/ Total number of marbles

P(marble is odd-numbered )=7/14

=1/2

(C) The marble is red or odd-numbered?

Total number of red marbles = 14

Number of red and odd marbles = 2

The marbles that has odd number = (R1) , (R3) ,(B1) , (B3) , (B5) , (B7) , (B9) =7

n(red or even )= n(red) + n(odd)- n(red and odd)

=4+7-2

=9

P(red or odd numbered)= (number of red or odd)/(total number of the marble)

= 9/14

(d) The marble is blue or even-numbered?

Number of Blue and even marbles = 5

Total number of Blue marbles = 10

Number of blue that are even= 5

The marbles that has even number = (R2) , (R4) ,(B2) , (B4) , (B6) , (B8) , (B10)

=7

n(Blue or even )= n(Blue) + n(even)- n(Blue and even)

= 10+7-5 =12

Now , the probability the marble is blue or even numbered can be calculated as

P(blue or even numbered)= (number of Blue or even)/(total number of the marble)

= 12/14

= 6/7

Answer:

B: 54

Step-by-step explanation:

for the first digit: 1 or 3 (2 choices)

for the second digit: 0, 1, or 3 (3 choices)

for the third digit: 0, 1, or 3 (3 choices)

for the forth digit: 0, 1, or 3 (3 choices)

2×3×3×3=54

Answer:

B) 54

Step-by-step explanation:

There are 3 numbers, but in the fourth positon (tens of thousands) if i put the zero no give value, then, in this position only have 2 options:

2*3*3*3 = 54

Answer:

$7,415.99

Step-by-step explanation:

Hello, please consider the following.

[tex]P\cdot (1+\dfrac{10.5\%\cdot 9}{12})=A = 8000 \\\\P = \dfrac{8000}{(1+\dfrac{31.5}{400})}=\dfrac{8000}{1.07875}\\\\=7415.990730...[/tex]

So it gives $7,415.99

Thank you.

Answer:

46.2÷m=x

Step-by-step explanation:

u divide the amount of water by the time it takes to fill up(m). Witch will equal the amount per minute (x).

16.5/min

time = m

gallons / minutes = rate

46.2  = 16.5 (m)

46.2 / 16.5 = 16.5 (m) / 16.5

2.8 = minutes

Answer:

No, it's not enough

Step-by-step explanation:

Given

Tilling Dimension = 4m by 2m

Tile Dimension = 400mm by 400mm

Required

Determine the 45 tiles is enough

First;

The area of the tiling has to be calculated

[tex]Area = Length * Breadth[/tex]

[tex]Area = 4m * 2m[/tex]

[tex]Area = 8m^2[/tex]

Next, determine the area of the tile

[tex]Area = Length * Breadth[/tex]

[tex]Area = 400mm * 400mm[/tex]

Convert measurements to metres

[tex]Area = 0.4m* 04m[/tex]

[tex]Area = 0.16\ m^2[/tex]

Next, multiply the above area result by the number of files

[tex]Total = 0.16m^2 * 45[/tex]

[tex]Total = 7.2m^2[/tex]

Compare 7.2 to 8

Hence, we conclude that the 45 tiles of 400mm by 400 mm dimension is not enough to floor his bathroom

Answer:

Step-by-step explanation:

[tex]3h\left(2\right)+2k\left(3\right)\\\\\mathrm{Remove\:parentheses}:\quad \left(a\right)=a\\\\=3h\times \:2+2k\times \:3\\\\\mathrm{Multiply\:the\:numbers:}\:3\times \:2=6\\\\=6h+2\times \:3k\\\\\mathrm{Multiply\:the\:numbers:}\:2\times \:3=6\\\\=6h+6k[/tex]

Answer:

Answers for E-dge-nuityyy

Step-by-step explanation:

(h + k)(2) = 5

(h – k)(3) = 9

Evaluate 3h(2) + 2k(3) = 17

Answer:

the interest is 195dollars

Step-by-step explanation:

csc θ sin θ

(1 / sin θ) sin θ

1

The simplified value of the given expression comes to be 1.

The given expression is:

[tex]cosec\theta.sin\theta[/tex]

The trigonometric ratio [tex]cosec\theta[/tex] is the ratio of the hypotenuse to the opposite side. It is the inverse of [tex]sin\theta[/tex].

[tex]cosec\theta=\frac{1}{sin\theta}[/tex]

We know that [tex]cosec\theta=\frac{1}{sin\theta}[/tex]

So [tex]cosec\theta.sin\theta[/tex]

[tex]=\frac{1}{sin\theta} .sin\theta[/tex]

=1

So, the simplified value is 1.

Hence, the simplified value of the given expression comes to be 1.

To get more about trigonometric ratios visit:

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Answer:

The lengths of the sides are 20 cm and 20 cm

Step-by-step explanation:

Given

Perimeter, P = 80cm

Represent the length and width with L and W, respectively;

[tex]P= 2*(L + B)[/tex]

Substitute 80 for P

[tex]80 = 2 * (L + B)[/tex]

Divide through by 2

[tex]40 = L + B[/tex]

[tex]L + B = 40[/tex]

Make L the subject of formula

[tex]L = 40 - B[/tex]

Area of a rectangle is calculated as thus;

[tex]Area = L * B[/tex]

Substitute 40 - B for L

[tex]Area = (40 - B) * B[/tex]

Express this as a function

[tex]A(B) = (40 - B)* B[/tex]

[tex](40 - B)* B = A(B)[/tex]

Set A(B) = 0 to determine the roots

Hence;

[tex](40 - B)* B = 0[/tex]

[tex]40 - B = 0[/tex] or [tex]B = 0[/tex]

[tex]40 = B[/tex] or [tex]B = 0[/tex]

[tex]B = 40[/tex] or [tex]B = 0[/tex]

The maximum area of a rectangle occurs at half the sum of the roots;

So;

[tex]B= \frac{B_1 + B_2}{2}[/tex]

[tex]B= \frac{40+0}{2}[/tex]

[tex]B= \frac{40}{2}[/tex]

[tex]B = 20[/tex]

Recall that [tex]L = 40 - B[/tex]

[tex]L = 40 - 20[/tex]

[tex]L = 20[/tex]

Hence the lengths of the sides are 20 cm and 20 cm

Answer:

a. the probability that her pulse rate is less than 76 beats per minute is 0.5948

b. If 25 adult females are randomly​ selected,  the probability that they have pulse rates with a mean less than 76 beats per minute is 0.8849

c.   D. Since the original population has a normal​ distribution, the distribution of sample means is a normal distribution for any sample size.

Step-by-step explanation:

Given that:

Mean μ =73.0

Standard deviation σ =12.5

a. If 1 adult female is randomly​ selected, find the probability that her pulse rate is less than 76 beats per minute.

Let X represent the random variable that is normally distributed with a mean of 73.0 beats per minute and a standard deviation of 12.5 beats per minute.

Then : X [tex]\sim[/tex] N ( μ = 73.0 , σ = 12.5)

The probability that her pulse rate is less than 76 beats per minute can be computed as:

[tex]P(X < 76) = P(\dfrac{X-\mu}{\sigma}< \dfrac{X-\mu}{\sigma})[/tex]

[tex]P(X < 76) = P(\dfrac{76-\mu}{\sigma}< \dfrac{76-73}{12.5})[/tex]

[tex]P(X < 76) = P(Z< \dfrac{3}{12.5})[/tex]

[tex]P(X < 76) = P(Z< 0.24)[/tex]

From the standard normal distribution tables,

[tex]P(X < 76) = 0.5948[/tex]

Therefore , the probability that her pulse rate is less than 76 beats per minute is 0.5948

b.  If 25 adult females are randomly​ selected, find the probability that they have pulse rates with a mean less than 76 beats per minute.

now; we have a sample size n = 25

The probability can now be calculated as follows:

[tex]P(\overline X < 76) = P(\dfrac{\overline X-\mu}{\dfrac{\sigma}{\sqrt{n}}}< \dfrac{ \overline X-\mu}{\dfrac{\sigma}{\sqrt{n}}})[/tex]

[tex]P( \overline X < 76) = P(\dfrac{76-\mu}{\dfrac{\sigma}{\sqrt{n}}}< \dfrac{76-73}{\dfrac{12.5}{\sqrt{25}}})[/tex]

[tex]P( \overline X < 76) = P(Z< \dfrac{3}{\dfrac{12.5}{5}})[/tex]

[tex]P( \overline X < 76) = P(Z< 1.2)[/tex]

From the standard normal distribution tables,

[tex]P(\overline X < 76) = 0.8849[/tex]

c. Why can the normal distribution be used in part​ (b), even though the sample size does not exceed​ 30?

In order to determine the probability in part (b);  the  normal distribution is perfect to be used here even when the sample size does not exceed 30.

Therefore option D is correct.

Since the original population has a normal distribution, the distribution of sample means is a normal distribution for any sample size.

Answer:

0.4

Step-by-step explanation:

we are required to find the probability that the ring is within 12 meters from nthe car.

we start by defining a random variable x to be the distance from the car. the car is the starting point.

x follows a normal distribution (0,30)

[tex]f(x)=\frac{1}{30}[/tex]

[tex]0<x<30[/tex]

probabilty of x ≤ 12

= [tex]\int\limits^a_ b{\frac{1}{30} } \, dx[/tex]

a = 12

b = 0

[tex]\frac{1}{30} *(12-0)[/tex]

[tex]\frac{12}{30} = 0.4[/tex]

therefore 0.4 is the probability that the ring is within 12 feet of your car.

Answer:

The number of ways is 13860 ways

Step-by-step explanation:

Given

Senior Members = 10

Junior Members = 12

Required

Number of ways of selecting 6 students students

The question lay emphasis on the keyword selection; this implies combination

From the question, we understand that

4 students are to be selected from senior members while 2 from junior members;

The number of ways is calculated as thus;

Ways = Ways of Selecting Senior Members * Ways of Selecting Junior Members

[tex]Ways = ^{10}C_4 * ^{12}C2[/tex]

[tex]Ways = \frac{10!}{(10-4)!4!)} * \frac{12!}{(12-2)!2!)}[/tex]

[tex]Ways = \frac{10!}{(6)!4!)} * \frac{12!}{(10)!2!)}[/tex]

[tex]Ways = \frac{10 * 9 * 8 * 7 *6!}{(6! * 4*3*2*1)} * \frac{12*11*10!}{(10!*2*1)}[/tex]

[tex]Ways = \frac{10 * 9 * 8 * 7}{4*3*2*1} * \frac{12*11}{2*1}[/tex]

[tex]Ways = \frac{5040}{24} * \frac{132}{2}[/tex]

[tex]Ways = 210 * 66[/tex]

[tex]Ways = 13860[/tex]

Hence, the number of ways is 13860 ways

Answer:

c is the answer

Step-by-step explanation:

-3h = 31

-9h-12h = -3h

54-23= 31

Answer:

[tex]\boxed{C. -3h = 31}[/tex]

Step-by-step explanation:

Hey there!

9h - 12h = 54 - 23

Simplify

-3h = 31

C. -3h = 31

Hope this helps :)

Answer:

See below.

Step-by-step explanation:

It depends on the sentence or phrase. If the sentence includes an operation of numbers or something related to comparing numbers, then maybe it can be translated into symbols. If the sentence or phrase has nothing to do with quantities, or operations or comparison of quantities, then probably it can't.

Examples:

1) The boy went for a walk.

There's nothing to translate into symbols in this case.

2) I had $10 in my bank account, then I deposited n dollars. Now I have $30 in my account.

In this case, I can translate the sentence into an equation.

10 + n = 30

Answer:

0

Step-by-step explanation:

0 because there is a $100 duty free exemption.

answer:

For this problem, use the tables and charts shown in this section.  

A United States Citizen returning to the States declares the following items at the customs office:

3 shirts at $8.50 each

2 dresses at $27.50 each

1 pair of gold cuff links at $17.50 per pair

If he has not used his duty free exemption yet, how much duty should he pay?

$0.00 !

$5.00

$10.00

$300