Suppose you have $1750 in your savings account at the end of a certain period of time. You invested $1500 at a 3.72% simple annual interest rate. How long, in years, was your money invested?

Answer:

Step-by-step explanation:

It's 5/7

You get that by having a calculator that does that. If you don't then the way to do it is multiply the numerator and denominator by 1.25

4 * 1.25 = 5

5.6 * 1.25 = 7

Answer:

378 and 380

Step-by-step explanation:

The two even consecutive numbers that add up to 758 are going to be very close to half of 758. This is because two half of 758 are going to be the most similar addends of 758. This is important because the answers will be consecutive and therefore, must also be very similar. To solve, first, divide 758 by 2. This is 379, which is not an even number. So, to find the needed addends subtract and add 1 to 379. Both of these will be even and consecutive. These two numbers are 378 and 380. Then, to check you, can add them and see that they do sum 758.

Answer:

Step-by-step explanation:

Let the first number = x

Let the second number = x + 2

x + x + 2 = 758                      Collect like terms

2x + 2 = 758                         Subtract 2

2x = 758 - 2                          Combine

2x = 756                                Divide by 2

2x/2 = 756/2

x = 378

The first number is 378

The second number 380

If your teacher is really fussy, you can do it this way.

Let the first number = 2x

Let the second number = 2x + 2

The reason for this is to guarantee that both numbers were even to start with.

2x + 2x+2 = 758                    Combine like terms

4x + 2 = 758                          Subtract 2

4x = 756                                Divide by 4

x = 756/4

x = 189

Therefore 2x = 378

2x + 2 = 380                 Just as before.

Answer:a0 = 40 mg

a1 = 20 mg  after 28 years

a2 = 10 mg  after another 28 years

Step-by-step explanation:Set this up as

10 = 40 (1/2)t/28

and solve for t in years.

10/40 = (1/2)t/28

log(0.25) = (t/28) log(0.5)

t = 28 log(0.25) / log(0.5) years = 56 years

Answer:

40 mg

Step-by-step explanation:

10 = 40 (1/2)t/28   and solve for t in years.   10/40 = (1/2)t/28   log(0.25) = (t/28) log(0.5)   t = 28 log(0.25) / log(0.5) years = 56 years

Answer:

y"= 2 wich is positive

Step-by-step explanation:

Step-by-step explanation:

Our equation is: y=(x-3)²

x should be replaced by x-4

y=(x-3)²

y=[(x-4)-3]²

y=(x-4-3)²

y=(x-7)²

The graph is still a parabola but with a different vertex

The vertex here is :

y= (x-7)²

y= x²-14x-49

y'= 2x-14

solve y'=0

2x-14=0

2x=14

x=7

You can easily find it without derivating by dividing -14 by -2

since: x²-14x-49

a=1 b= -14  c=-49

-b/2a = 14/2 = 7

the image of 7 is:

y=(7-7)² = 0

so the coordinates of the new vertex are (7,0) and it's a maximum

since y">0

y'= 2x-14

y"= 2 wich is positive

Answer:

strong and fexible .

variable

Answer:

Step-by-step explanation:

Answer:

a1=6 a2=15 a3=33 a4=69 a5=141

Step-by-step explanation:

an=2an-1+3

We should attempt n=2 to find the second term

a2=2a1+3= 2*6+3=15

n=3 to find the third term

a3=2a2+3= 2*15+3=33

n=4 to find the fourth term

a4=2a3+3=2*33+3=69

n=5 to find the fifth term

a5= 2a4+3=2*69+3= 141

Answer:

B. Yes. By SSS~

Step-by-step explanation:

From the diagram given, we have the corresponding sides of both triangles as follows:

RQ/KL = 24/20 = 6/5

QP/LM = 18/15 = 6/5

RP/KM = 12/10 = 6/5

From the above, we can see that the ratio of the corresponding side lengths of both triangles are equal. This means that all three sides of one triangle are proportional to all corresponding sides of the other triangle.

The SSS similarity theorem states that if all sides of one triangle are proportional to all corresponding sides of another, then both triangles are similar to each other.

Therefore, ∆KLM ~ ∆RQP by SSS similarity.

Answer: -2

Step-by-step explanation:

g(-4) + f(1) = 7 + (-9) = 7 - 9 = -2

9514 1404 393

Answer:

  x = 8

Step-by-step explanation:

By AA similarity, ΔABD ~ ΔCDE. So, corresponding sides are proportional.

  AB/BD = CD/DE

  x/12 = 4/6

  x = 12(4/6)

  x = 8

Answer:

gang nem

Step-by-step explanation:

9514 1404 393

Answer:

  a. 5/10

  b. 2.5/10

  c. 1/10

  d. 4/10

Step-by-step explanation:

To find the numerator, multiply each fraction by 10.

  a. (1/2)(10) = 5, so 1/2 = 5/10

  b. (1/4)(10) = 2.5, so 1/4 = (2.5)/10 or (5/2)/10

  c. (3/30)(10) = 1, so 3/30 = 1/10

  d. (12/30)(10) = 4, so 12/30 = 4/10

Answer:

b(-2,-5)

Step-by-step explanation:

Answer:

$6.60

Step-by-step explanation:

12% = 0.12

12% of $55 = 0.12 x 55

=6.6

So, $6.60

Step-by-step explanation:

1. In an arithmetic sequence, the general term can be written as

xₙ = y + d(a-1), where xₐ represents the ath term, y is the first value, and d is the common difference.

Given the third term and the fifth term, and knowing that the difference between each term is d, we can say that the 4th term is x₃+d and the fifth term is the fourth term plus d, or (x₃+d)+d =

x₃+2d. =x₅ Given x₃ and x₅, we can subtract x₃ from both sides to get

x₅-x₃ = 2d

divide by 2 to isolate d

(x₅-x₃)/2 = d

This lets us solve for d. Given d, we can say that

x₃ = y+d(2)

subtract 2*d from both sides to isolate the y

x₃ -2*d = y

Therefore, because we know x₃ and d at this point, we can solve for y, letting us plug y and d into our original equation of

xₙ = y + d(a-1)

2.

Given the third and fifth term, with a common ratio of r, we can say that the fourth term is x₃ * r. Then, the fifth term is

x₃* r * r

= x₃*r² = x₅

divide both sides by x₃ to isolate the r²

x₅/x₃ = r²

square root both sides

√(x₅/x₃) = ±r

One thing that is important to note is that we don't know whether r is positive or negative. For example, if x₃ = 4 and x₅ = 16, regardless of whether r is equal to 2 or -2, 4*r² = 16. I will be assuming that r is positive for this question.

Given the common ratio, we can find x₆ as x₅ * r, x₇ as x₅*r², and all the way up to x₁₀ = x₅*r⁵. We don't know the general term, but can still find the tenth term of the sequence

Answer:

b) 9x² - 3x

Step-by-step explanation:

Area of a  rectangle = Length × Width

Area for the rectangle = 3x - 1 × 3x

Area = [tex](3x-1)(3x)[/tex]

Step 1. Multiply by combining like terms

3x · 3x = 9x²

Step 2. Multiply -1 by 3x

-1 · 3x = -3x

Step 3. Combine 9x² and -3x

9x² - 3x

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doomdabomb: All brainliest and thanks are appreciated

and would mean a lot to me, thanks!

Answer:

The area of a triangle is always one half the base b times the height h.

SEE PICTURE BELOW;

If the base is represented by the expression 4x + 2 and the height is represented by 3x, which expression gives the area of the triangle?

Step-by-step explanation:

Edge 2021

Answer:

Answer:f(2)=-3(2)^2+2*2+11

Answer:f(2)=-3(2)^2+2*2+11 =-3*4+4+11

Answer:f(2)=-3(2)^2+2*2+11 =-3*4+4+11 =-12+4+11

Answer:f(2)=-3(2)^2+2*2+11 =-3*4+4+11 =-12+4+11 =3

hence, f(2)=3

Answer:

A.  243

Step-by-step explanation:

[tex] 81^\frac{5}{4} = (3^4)^\frac{5}{4} = 3^{4 \times \frac{5}{4}} = 3^5 = 243 [/tex]

Answer: A

I just simplified it to 3^5, and that is also 243.

Answer:

[tex]308 \ m^3\\[/tex]

Step-by-step explanation:

The volume of a three-dimensional shape is the amount of space the figure takes up. This can be found by multiplying all of the dimensions of a figure together. In essence, the following formula can be used to find the volume.

[tex]A=l*w*h[/tex]

Where (l) represents the figure's length; (w) is the width: and (h) the height. Substitute the given values into the formula and solve for the volume.

[tex]A=l*w*h[/tex]

[tex]A=7*4*11[/tex]

Simplify,

[tex]A=7*4*11[/tex]

[tex]A=28*11[/tex]

[tex]A=308[/tex]

Answer:

Hello,

Step-by-step explanation:

AB=DC=b, AD=BC=a

p=BD, q=AC

angle ABC=x

[tex]AB^4+AD^4+AB^2*AD^2=AC^2*BD^2\\\\b^4+a^4+b^2a^2=(a^2+b^2+2abcos(X))(a^2+b^2-2abcos(X)\\\\(a^2+b^2+2a^2b^2)-a^2b^2=((a^2+b^2)^2-4a^2b^2*cos^2(X))\\\\\\4a^2b^2cos^2(X)=a^2b^2\\\\\\cos^2(X)=\dfrac{1}{4} \\\\(cos(X)-\dfrac{1}{2} )(cos(X)+\dfrac{1}{2} )=0\\cos(x)=\frac{1}{2} \ or\ cos(X)=\dfrac{-1}{2} \\\\\\X=60^o =\dfrac{\pi}{3} rad \ or \ X=120^o=\dfrac{4\pi}{3} rad\\\\\\\\Product=\dfrac{\pi}{3}*\dfrac{4\pi}{3} =\boxed{\dfrac{4\pi^2}{9}}\\[/tex]

Answer:

Step-by-step explanation:

This is a straight proportion problem.

15/42 = x/140                 Cross Multiply

15*140 = 42 * x

2100 = 42x                    Divide by 42

2100/42 = x            

x = 50 ml of HCl will be needed.

Answer:

7/16

Step-by-step explanation:

7/16>3/8

It would be 7/16 because 3/8 is what is being shown. If you make them both have a common denominator then it would be 6/16.

Answer:

It can be the point E or the point D

Answer: 33% is moisture content

Step-by-step explanation:

120kg - 80kg = 40kg

40 of 120 is %

Work:

40/120 = 0.33

0.33x100

= 33%

Answer:

a

Step-by-step explanation:

Lateral faces that are parallel is not a property of a regular pyramid. The correct option is A.

Any pyramid whose base is a regular polygon and whose lateral edges are all of the same lengths is said to be regular.

The properties of a regular pyramid are:-

Lateral faces that are congruent isosceles triangles. Lateral edges that are congruent and the volume of the pyramid is equal to one-third the product of the area of its base and its altitude.

Hence, option A is correct.

To know more about the regular pyramid follow

https://brainly.com/question/12298863

#SPJ2

Answer:

hello,

a) answer: 600

b) answer: 840

Step-by-step explanation:

a)

20=2²*5,25=5²,30=2*3*5,40=2³*5

l.c.m(20,25,30,40)=2³*3*5²=8*3*25=800

b)

24=2³*3, 42=2*3*7,35=5*7

l.c.m=(24,42,35)=2³*3*5*7=840

Answer:

B

Step-by-step explanation:

Reason...sum of angles in a triangle is equal to 180⁰

R+V+T=180⁰

60⁰+90⁰+x⁰=180⁰

150⁰+x⁰=180⁰

x⁰=180⁰-150⁰

:. x⁰=30⁰

===================================================

Explanation:

Ignore lines VS and SU. They're unnecessary clutter.

Triangle VRT is a right triangle with angles T = x, R = 60, V = 90

For any triangle, the angles must add to 180

T+R+V = 180

x+60+90 = 180

x+150 = 180

x = 180-150

x = 30

Or you could note that R+T = 90 Solves to T = 30 since triangle VRT is a right triangle. The rule with any right triangle is that the acute angles are always complementary (aka they add to 90 degrees).

Answer:

a) The p-value of the test is 0.0078 < 0.1, which means that there is sufficient evidence at the 0.1 level that the bags are underfilled.

b) 0.0078.

Step-by-step explanation:

Question a:

A manufacturer of potato chips would like to know whether its bag filling machine works correctly at the 421 gram setting.

At the null hypothesis, it is tested if the mean is of 421, that is:

[tex]H_0: \mu = 421[/tex]

It is believed that the machine is underfilling the bags.

At the alternative hypothesis, it is tested if the mean is of less than 421, that is:

[tex]H_a: \mu < 421[/tex]

The test statistic is:

[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]

In which X is the sample mean, [tex]\mu[/tex] is the value tested at the null hypothesis, [tex]\sigma[/tex] is the standard deviation and n is the size of the sample.

421 is tested at the null hypothesis:

This means that [tex]\mu = 421[/tex]

A 43 bag sample had a mean of 414 grams. Assume the population standard deviation is known to be 19.

This means that [tex]n = 43, X = 414, \sigma = 19[/tex]

Value of the test statistic:

[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]

[tex]z = \frac{414 - 421}{\frac{19}{\sqrt{43}}}[/tex]

[tex]z = -2.42[/tex]

P-value of the test and decision:

The p-value of the test is the probability of finding a sample mean below 414, which is the p-value of z = -2.42.

Looking at the z-table, z = -2.42 has a p-value of 0.0078.

The p-value of the test is 0.0078 < 0.1, which means that there is sufficient evidence at the 0.1 level that the bags are underfilled.

b. Find the P-value of the test statistic.

As found above, the p-value of the test statistic is 0.0078.

Answer:

a= 13.5

c=18.7

B= 46

Step-by-step explanation: