What is the measure of AC ?

Answer:

Option D

Step-by-step explanation:

step 1

Account 1

The simple interest formula is equal to

[tex]A=P(1+rt)[/tex]

where

A is the Final Investment Value

P is the Principal amount of money to be invested

r is the rate of interest  

t is Number of Time Periods

in this problem we have

[tex]t=10\ years\\ P=\$6,000\\r=4.5\%=4.5/100=0.045[/tex]

substitute in the formula above

[tex]A=6,000(1+0.045*10)[/tex]

[tex]A=6,000(1.45)[/tex]

[tex]A=\$8,700[/tex]

step 2

Account 2

The compound interest formula is equal to  

[tex]A=P(1+\frac{r}{n})^{nt}[/tex]  

where  

A is the Final Investment Value  

P is the Principal amount of money to be invested  

r is the rate of interest  in decimal

t is Number of Time Periods  

n is the number of times interest is compounded per year

in this problem we have  

[tex]t=10\ years\\ P=\$6,000\\ r=4\%=4/100=0.04\\n=1[/tex]  

substitute in the formula above

[tex]A=6,000(1+\frac{0.04}{1})^{1*10}[/tex]  

[tex]A=6,000(1.04)^{10}[/tex]  

[tex]A=\$8,881.47[/tex]  

step 3

Find the difference

[tex]\$8,881.47-\$8,700=\$181.47[/tex]

therefore

Susie should invest her money in Account 2 because the account will earn $181.47 more interest than Account 1 after 10 years

Answer:

= -16

Step-by-step explanation:

If x= -2, then replace it on Y=2(4)X

Y=2x(4)x(-2)

Y=-16

Note:

2 multiplied by 4 = 8

8 multiplied by -2 = -16

Answer:

Step-by-step explanation:

y= 2(4)(-2)

y = 8(-2)

y =-16

Answer:

There are a total of 495 people on the train

Step-by-step explanation:

Let's identify what we know:

1) The train has 3 passenger cars

2) Each passenger car has 4 columns, and each can accommodate 40 people.

3) All three passenger cars are full, but one of them has 15 additional people standing.

We can create a formula to model the problem:

x = ((3 x 4) x 40) + 15

x = the total number of passengers!

There are a total of 180 people sitting, and 15 additional people standing in one of the passengers cars, equaling a total of 495 passengers on the train.

The train has a total of 495 passengers.

To calculate the number of passengers on the train, we first need to determine the seating capacity of each car. Since each car has 4 columns of seats and each column holds 40 passengers, each car can seat a total of 4 x 40 = 160 passengers.

Next, we need to account for the 15 people standing in one of the cars. This means that one car has 160 + 15 = 175 passengers.

Finally, since the rest of the cars are full without anyone standing, we can assume that the other two cars also have 160 passengers each. Therefore, the total number of passengers on the train is 175 + 160 + 160 = 495.

https://brainly.com/question/31095924

#SPJ2

Final answer:

Using a system of equations, we established that there are 8 pigs and 11 ducks among the 19 animals with a total of 54 legs.

Explanation:

To solve the problem of determining how many pigs and ducks there are when there are 19 animals in total and 54 legs, we set up two equations. Let's assume the number of pigs is x and the number of ducks is y. Pigs have 4 legs, and ducks have 2 legs. We can summarize this information in the following system of equations:

Equation 1: x + y = 19 (because there are 19 animals total)

Equation 2: 4x + 2y = 54 (because the total number of legs is 54)

We can solve this system using the substitution or elimination method. Simplifying Equation 2 by dividing every term by 2 gives us 2x + y = 27, which we'll call Equation 3.

Equation 3: 2x + y = 27

We can now subtract Equation 1 from Equation 3 to find the value of x:

(2x + y) - (x + y) = 27 - 19

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

x = 8 (number of pigs)

Substitute x back into Equation 1:

x + y = 19

8 + y = 19

y = 19 - 8

y = 11 (number of ducks)

Therefore, there are 8 pigs and 11 ducks among the 19 animals.

Answer:

Plane speed: 480mph

Wind speed: 80mph

Step-by-step explanation:

Miami to Seattle: time = 7hrs

Speed (s) = 2800mph

D = speed/time = 2800/7

= 400mph

Seattle to Miami:

Same speed = 2800mp

Time = 5hrs

Distance (D) = speed/time

= 2800/5 = 560mph

Let p be speed of plane and w wind speed.

Therefore, P+w = 560. . .1

P-w = 400. . .2

2p = 960

P = 960/2 = 480

Therefore, P + w = 560

480 + w = 560

W = 80mph

While P = 480mph

Answer:

Yes each side will always be of the same size unless you are purposely trying to make an uneven shape

Step-by-step explanation:

Answer:

Step-by-step explanation:

Area of a square

Area = l*l

121=l^2

l=√121

L=11cm

The monthly rate is $45 for this cellphone plan.

Step-by-step explanation:

Given,

Amount charged for cell phone = $60

Amount paid by Regina for 24 month plan = $1140

Number of months = 24

Let,

m be the monthly rate for cellphone plan

Number of months * Monthly rate + cellphone charges = Amount paid

[tex]24m+60=1140\\24m=1140-60\\24m=1080[/tex]

Dividing both sides by 24

[tex]\frac{24m}{24}=\frac{1080}{24}\\m=45[/tex]

The monthly rate is $45 for this cellphone plan.

Keywords: subtraction, division

Learn more about subtraction at:

#LearnwithBrainly

Polynomial functions with an even degree have y-axis symmetry is a true statement.

Explanation:

A function symmetrical with respect to the y-axis is called an even function. A function that is symmetrical with respect to the origin is called an odd function. f(x). Since f(−x) = f(x), this function is symmetrical with respect to the y-axis.

So a function that has an even degree in it, be it a polynomial function, has a y-axis symmetry always. The equations with odd degrees may or may not have a y axis symmetry.

Answer:

$98.00

Step-by-step explanation:

$2000.00 x .049=$98.00

Answer:

0.5675

Step-by-step explanation:

We have that, the IQ of the ruling species is normally distributed with a mean of 118 and a standard deviation of 18.

We want to find the probability that a randomly selected person's IQ is over 115.

We need to find the z-score of 115

using

[tex]z = \frac{x - \mu}{ \sigma} [/tex]

We substitute x=115 to get:

[tex]z = \frac{115 - 118}{18} [/tex]

This implies that:

[tex]z = \frac{ - 3}{18} = - \frac{1}{6} = - 0.17[/tex]

We read from the normal distribution table to get;

P(X>115)=0.5675

By converting the IQ score of 115 into a Z score and finding the area to the right of this Z score in a standard normal distribution, we find that the probability of a randomly selected individual's IQ being over 115 is approximately 0.57 or 57%.

To answer this question, we need to understand how a normal distribution works. A random variable X, such as an individual's IQ, that is normally distributed can be converted into a standard normal variable Z, using the formula Z = (X - mean) / standard deviation.

In our case, the mean IQ is 118 and the standard deviation is 18. Therefore, to find the probability that a randomly selected individual's IQ is over 115, we convert 115 into a Z score using the aforementioned formula: Z = (115 - 118) / 18 = -0.167. This is the Z score for an IQ of 115.

To find the probability that a randomly selected individual's IQ is more than 115, we find the area to the right of Z = -0.167. From standard normal tables, we know that the area to the left of Z = -0.167 is approximately 0.4332. Therefore, the area to the right (which is the probability we want) is 1 - 0.4332 = 0.5668.

So, the probability that a randomly selected individual's IQ is over 115 is approximately 0.57 (or 57% when expressed as a percentage).

https://brainly.com/question/30390016

#SPJ3

Answer:

Step-by-step explanation:

y=−3x+5;5x−4y=−3

Step: Solve: y=−3x+5for y:

Step: Substitute: −3x+5foryin5x−4y=−3:

5x−4y=−3

5x−4(−3x+5)=−3

17x−20=−3 (you have to simplify both sides of the equation)

17x−20+20=−3+20(then add 20 to both sides)

17x=17

17x

17

=

17

17

(Divide both sides by 17)

x=1

Step: Substitute1forxiny=−3x+5:

y=−3x+5

y=(−3)(1)+5

y=2( again Simplify both sides of the equation)

The Answer Is:

x=1 and y=2

Am I incorrect?

answer is

o.7 liters 2000 milliliters and 4.1 liters  

Step-by-step explanation:

1 / 5

1 \text{ liter} ={1{,}000}\text{ milliliters}1 liter=1,000 milliliters1, start text, space, l, i, t, e, r, end text, equals, 1, comma, 000, start text, space, m, i, l, l, i, l, i, t, e, r, s, end text

So, 1 \text{ milliliter} = \dfrac1{1{,}000}\text{ liter}1 milliliter=  

1,000

1

​  

 liter1, start text, space, m, i, l, l, i, l, i, t, e, r, end text, equals, start fraction, 1, divided by, 1, comma, 000, end fraction, start text, space, l, i, t, e, r, end text

Hint #22 / 5

We know \maroonD{0.7}0.7start color #ca337c, 0, point, 7, end color #ca337c liters is less than \greenD{4.1}4.1start color #1fab54, 4, point, 1, end color #1fab54 liters. But where does \blueD{2{,}000}2,000start color #11accd, 2, comma, 000, end color #11accd milliliters fit?

We need to convert \blueD{2{,}000}2,000start color #11accd, 2, comma, 000, end color #11accd milliliters to liters before we can compare.

Hint #33 / 5

\begin {aligned}{\blueD{2{,}000} \text{ mL}}&= {\blueD{2{,}000} \text{ mL}}\times \dfrac{1 \text{ L}}{{1{,}000 \text{ mL}}} \\\\ &= {\dfrac{\blueD{2{,}000} \cancel{\text{ mL}}}{1}}\times \dfrac{1 \text{ L}}{{1{,}000 \cancel{\text{ mL}}}} \\\\ &=\dfrac{\blueD{2{,}000}\text{ L} }{1{,}000}\\\\ &=\blueD{2{,}000}\text{ L}\div1{,}000\\\\ &=\blueD{2}\text{ L} \end{aligned}  

2,000 mL

​  

=2,000 mL×  

1,000 mL

1 L

​  

=  

1

2,000  

mL

​  

×  

1,000  

mL

1 L

​  

=  

1,000

2,000 L

​  

=2,000 L÷1,000

=2 L

​  

Expression: [tex]\((x - 3)(x + 5)\)[/tex]. If original is 10 × 10, new is 105 sq ft. New is 5 sq ft larger.

1. **Expression representing the two binomials for the area of Talia's new bedroom:**

Let [tex]\( x \)[/tex] represent the original length of the square bedroom.

The original bedroom's dimensions: [tex]\( x \times x \)[/tex]

The new bedroom's dimensions: [tex]\( (x - 3) \times (x + 5) \)[/tex]

So, the expression representing the two binomials would be: [tex]\((x - 3)(x + 5)\)[/tex]

2. **Finding the difference in size between old and new bedrooms:**

If the original bedroom measured 10 feet by 10 feet, then [tex]\( x = 10 \)[/tex] (since it's a square).

Substituting into the expression: [tex]\( (10 - 3)(10 + 5) = (7)(15) = 105 \)[/tex] square feet.

So, the new bedroom's area is 105 square feet.

The original bedroom's area is [tex]\( 10 \times 10 = 100 \)[/tex] square feet.

The difference is: [tex]\( 105 - 100 = 5 \)[/tex] square feet.

Therefore, her new bedroom will be 5 square feet larger than her old bedroom.

The complete question is here:

Talia has a square bedroom. Her family is moving and her bedroom in her new apartment will be 3 feet shorter in one direction and 5 feet longer in the other direction. Write an expression that represents the two binomials you would multiply together to find the area of Talia's new bedroom.

2nd Part

If Talia's old bedroom measured 10 feet by 10 feet, how much larger or smaller will her new bedroom be?

Final answer:

The dilution ratio of a solution when 150 microliters of it contains 90 microliters of saline is 3:5. This means there are 3 parts saline to every 5 parts of the total solution.

Explanation:

If 150 microliters of a solution contains 90 microliters of saline, the dilution ratio of the solution can be described as the volume of saline to the total volume of the solution. To find this ratio, divide the volume of saline by the total solution volume:

Ratio = Volume of Saline / Total Volume of Solution

Ratio = 90 µL / 150 µL

By dividing the two volumes, you get a ratio of 0.6, which can also be expressed as 3:5 after multiplying both numerator and denominator by 10 to eliminate the decimal. This means there are 3 parts of saline to every 5 parts of the total solution.

The dilution ratio is therefore 3:5.

Answer:

B

Step-by-step explanation:

Answer: B

Step-by-step explanation:

Answer:

[tex]T_n=-1(-5)^n^-^1[/tex]

Step-by-step explanation:

We are given;

A geometric sequence;

-2,10,-50

Required to determine the nth term

The nth term in a geometric sequence is given by the formula;

[tex]T_n=a_1r^n^-^1[/tex]

where [tex]a_1[/tex] is the first term and r is the common ratio;

In this case;

[tex]a_1=-2[/tex]

r = 10 ÷ -2

  = -5

Therefore;

To get the nth term in the given geometric sequence we use;

[tex]T_n=-1(-5)^n^-^1[/tex]

Thus, the nth term is [tex]T_n=-1(-5)^n^-^1[/tex]

Answer:

112.5

Step-by-step explanation:

25/100 x450/1 =

11250/100=112.5

Answer:

The lines blue and green are perpendicular

Step-by-step explanation:

we know that

If two lines are perpendicular, then their slopes are opposite reciprocal (the product of their slopes is -1)

The formula to calculate the slope between two points is equal to

[tex]m=\frac{y2-y1}{x2-x1}[/tex]

step 1

Find the slope of the blue line

we have the points

(-1,-3) and (0,3)

substitute

[tex]m=\frac{3+3}{0+1}[/tex]

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

step 2

Find the slope of the red line

we have the points

(3,-3) and (4,2)

substitute

[tex]m=\frac{2+3}{4-3}[/tex]

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

step 3

Find the slope of the green line

we have the points

(-4,-1) and (2,-2)

substitute

[tex]m=\frac{-2+1}{2+4}[/tex]

[tex]m=-\frac{1}{6}[/tex]

step 4

Compare the slopes

Blue line ----> [tex]m=6[/tex]

Red line ----. [tex]m=5[/tex]

Green line ---> [tex]m=-\frac{1}{6}[/tex]

so

The slope of the blue line and the green line are opposite reciprocal ( their product is equal to -1)

therefore

The lines blue and green are perpendicular

Marlie's federal unsubsidized student loan will accrue $3,627.34 in interest over a 4.5-year non-payment period, given a 4.29% annual interest rate.

The subject of this problem is calculating interest accrued on an unsubsidized student loan. First, we need to understand that the 4.29% interest is an annual rate. So, for 4.5 years, the rate would become: 4.29% * 4.5 = 19.305%.

To calculate the amount of interest that will accrue during this period, we simply multiply this by the principal loan amount ($18,800). So, $18,800 * 19.305% = $3,627.34. Therefore, Marlie will accrue $3,627.34 in interest over this 4.5-year period.

https://brainly.com/question/35896917

#SPJ12

Marlie, who took a Federal Unsubsidized student loan that accumulates interest over time, will accrue $3,628.83 in interest during her 4.5 years of non-payment.

The subject of this question is about interest calculation on a Federal Unsubsidized student loan. Interest on an unsubsidized loan like Marlie's accumulates from the time the loan is disbursed until it's paid in full, including during the non-payment period. The interest that will accrue can be calculated using the formula I = PRT, where 'I' is the interest, 'P' is the principal amount (the initial amount of loan), 'R' is the annual interest rate in decimal, and 'T' is the time the money is borrowed for in years.

In Marlie's case, P = $18,800, R = 4.29/100 = 0.0429, and T = 4.5. Therefore, the interest accrued will be I = 18800 * 0.0429 * 4.5. After performing the calculation, the total interest that Marlie will accrue over the non-payment period is $3,628.83.

https://brainly.com/question/29011216

#SPJ11

Answer:

B. The probability that the second dart hits the center given that the

first dart hits the center

Step-by-step explanation:

P(BA) is also called the "Conditional Probability" of B given A.

B. The probability that the second dart hits the center given that the first dart hits the center

The following information should be considered;

Learn more: https://brainly.com/question/6789603?referrer=searchResults

Step-by-step explanation:

The number π is a mathematical constant. Originally defined as the ratio of a circle's circumference to its diameter.

It is an irrational number

[tex]\pi = 3.14159265359...[/tex]

Answer:

the right answer is b

Step-by-step explanation:

since its square root does not result in an integer

The initial number is 7.

Step-by-step explanation:

Let the initial number be 'x'.

⇒ 7x-4 = 45

⇒ 7x = 49

⇒ x = 7

The initial number is 300. Multiply by 7.4 to get 2220, subtract 2220, then divide by 9 to get 247. Confirming: 7.4(300) - 2220 = 247(9) = 5.

Let's denote the initial number as ( x ). According to the given information:

1. Multiply by 7.4: ( 7.4x )

2. Take away from the product: ( 7.4x - (7.4x) )

3. Finally, divide by 9:[tex]\( \frac{{7.4x - 7.4x}}{9} \)[/tex]

We know that this resulting expression equals 5:

[tex]\[ \frac{{7.4x - 7.4x}}{9} = 5 \][/tex]

Now, let's solve for ( x ):

[tex]\[ \frac{{0}}{9} = 5 \][/tex]

As ( 7.4x ) cancels out, we are left with ( 0 = 5 ), which is not a valid equation.

Answer:

Vestigial.

Step-by-step explanation:

It might have had a use in the past and man's evolution has rendered it of no known use.

Answer:

1.5,

Step-by-step explanation:

The examples of rational numbers are: a, d, and e.

A rational number is any number that can be expressed as the quotient or fraction of two integers, where the denominator is not zero.

Let's evaluate each option:

a. [tex]\( \sqrt{4} + \sqrt{16} = 2 + 4 = 6 \)[/tex]

This is a rational number because it can be expressed as the integer 6.

b. [tex]\( \sqrt{5} + \sqrt{36} = \sqrt{5} + 6 \)[/tex]

This is not a rational number because it involves the irrational square root of 5.

c. [tex]\( \sqrt{9} + \sqrt{24} = 3 + 2\sqrt{6} \)[/tex]

This is not a rational number because it involves the irrational square root of 6.

d. [tex]\( 2 + \sqrt{4} = 2 + 2 = 4 \)[/tex]

This is a rational number because it can be expressed as the integer 4.

e. [tex]\( \sqrt{49} + \sqrt{81} = 7 + 9 = 16 \)[/tex]

This is a rational number because it can be expressed as the integer 16.

f. [tex]\( 3\sqrt{12} = 3 \times \sqrt{4 \times 3} = 3 \times 2\sqrt{3} = 6\sqrt{3} \)[/tex]

This is not a rational number because it involves the irrational square root of 3.

So, the examples of rational numbers are: a, d, and e.

The complete Question is given below:

Which of the following are examples of rational numbers? Select all that apply

a. √4+√16

b. √5+√36

c. √9+√24

d. 2+√4

e. √49+√81

f. 3√12

Answer:

A- 4h 18min

Step-by-step explanation:

First you look at the data provided that shows that this is this latest time, so when it is 10:15 in buffalo, it is 9:15 in Dallas. He arrives in Dallas at 1:33, so you can either think in central time which is 9:15-1:33, or in eastern time which is 10:15-2:33. From there you can subtract 15 from 33 getting 18, and from 10 o’clock to 2 o’clock (or 9 o’clock to 1 o’clock) is 4 hours.