charlie wants to make a one time investment into an account that earns 6% interest compounded semi annually. to earn $338,893 after 26 years, approximately how much money did he invest?
[tex]s = p(1 + \frac{r}{m} ) {}^{mt}[/tex]
A.$72,866.33
B.$74,492.08
C.$528,673.08
D.$217,239.10​

The domain of the function is 0 ≤ x ≤ ∞.

Option 3 is correct

The range of values that we are permitted to enter into our function is known as the domain of a function. The x values for a function like f make up this set (x). A function's range is the collection of values it can take as input.

As per the given data:

The function is y = √x

Square root is not defined to for negative values. For negative values, the answer of square root is a complex number which is not in real domain.

So any such values, for which the expression is not defined, are not in the domain. So the domain of the square root of x will be all real numbers greater than or equal to 0.

Hence, the domain of the function is 0 ≤ x ≤ ∞

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9514 1404 393

Answer:

  no, the triangles are not similar

Step-by-step explanation:

The given ratios tell you corresponding side ratios are ...

  ED : DC : EC = 8 : 10 : 12 = 4 : 5 : 6

  AB : BC : AC = 12 : 15 : 21 = 4 : 5 : 7

Corresponding sides do not have the same ratios. The given information can be used to prove the triangles are NOT similar.

Answer:

15y^2-45

Step-by-step explanation:

5y^2+10y^2-45 = 15y^2-45

Answer:

(1, -1)

Step-by-step explanation:

If you end up at (2, -1), after moving 1 unit to the right, that implies that you started at (1, -1).  Note that 1 + 1 = 2.

Answer:

(1,-1)

Step-by-step explanation:

Because as it said go across 1 to the right , just go back 1 to the left so you are at were you started

Answer:21.88

Step-by-step explanation:

Answer:

112

Step-by-step explanation:

A = 2 (wl+hl+hw)

A = 2 (4 x 5 + 4 x 5 + 4 x 4)

A = 2 (20 + 20 + 16)

A = 2 x 56

A = 112

Answer:

C. Each calculator costs $80.

Step-by-step explanation:

Linear equation:

Has the following format:

[tex]y = mx + b[/tex]

In which m is the slope, and the meaning is how much the output changes when the input changes by 1 unit.

In this question:

Amount remaining after buying x calculators:

[tex]y = 1000 - 80x[/tex]

So the slope of -80 means that each calculator costs $80, since after buying a calculator, 80 is retired from the amount.

The answer is given by option C.

Answer:

28 divided by 7 is 4

Step-by-step explanation:

example: There 28 cupcakes if there are 7 people how many will each get? Ok so you have 28 groups of 7 and then you'll get your answer which is 4.

The mathematical expression for the phrase 28 divided by 7 is 28 ÷ 7 and the value of the expression is 4.

It is the basic arithmetic operation, in which you are separating the number into some parts. One of the fundamental mathematical operations is division, which involves breaking a bigger number into smaller groups with the same number of components.

Given:

28 divided by 7,

The mathematical expression for the above statement can be written as shown below,

28 ÷ 7

Calculate the value of the expression as shown below,

28 ÷ 7 = 4

Thus, the expression is 28 ÷ 7.

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Answer: x=4, y=-2

Step-by-step explanation: 4x+y=14, x-2y=8

4x+y-y=14-y

4x/4=14/4-y/4

x=14-y/4-(2y)(4)/4

4(14-9y)/4=(8)(4)

14-9y-14=32-14

-9y/-9=18/-9

y=-2

(14)-(-2)/4

14+2/4

16/4

4

x=4

x=4, y=-2

Answer:

Solution of given system of equations is: x=4, y=-2 or (4,-2)

Step-by-step explanation:

Solve the equation using substitution

4x+y=14

x-2y=8

Substitution method involves placing value of x or y from one equation to other equation.

We have

[tex]4x+y=14--eq(1)\\x-2y=8--eq(2)\\[/tex]

Finding value of x from equation 2

x-2y=8

x=2y+8

Put this value of x in equation 1

[tex]4x+y=14Put\:x=2y+8\\4(2y+8)+y=14\\8y+32+y=14\\9y=14-32\\9y=-18\\y=\frac{-18}{9}\\y=-2[/tex]

We get y=-2

Now, put value of y into equation 2 to find value of x

[tex]x-2y=8\\x-2(-2)=8\\x+4=8\\x=8-4\\x=4[/tex]

We get x = 4

So, solution of given system of equations is: x=4, y=-2 or (4,-2)

Answer:

1. The data that these cards allow stores to gather are customer data.

2. The stores want the data to enable them understand the customer, their buying goals, customer preferences, and spending patterns.  These data enable the stores to stock their stores to meet customers needs.  They also use the data to understand the individual customers credit history and buying habits.

Step-by-step explanation:

Customer data are essential assets which businesses use to understand their customers.  They obtain the data through firsthand responses from customers, through investigation, or by asking direct questions.  Many organizations use loyalty cards to help them gather customer data, such as individual preferences and spending patterns.

Answer: D on Edg

Step-by-step explanation:

Answer:

x=6

Step-by-step explanation:

32-21 = 11

28-11 = 17

17-11 = 6

x=6

Answer:

a) Range = 1.39

b) the sample variance is 0.1597

c) the sample standard deviation is 0.3996

Step-by-step explanation:

Given the data in the question;

a) Find the range.

To determine the range, we simple subtract the smallest value from the largest value. i.e

Range = largest value - smallest value

from data set; our smallest is 0.53 while our largest value is 1.92

so

Range = 1.92 - 0.53 = 1.39

b) Find the sample variance.

To determine our variance, we use the following formula;

∑([tex]X_{i}[/tex] - [tex]x_{bar}[/tex])² / n - 1 = [ ∑[tex]X_{i}[/tex]²/n-1 ] - [ [tex]\frac{n}{n-1}[/tex]([tex]x_{bar}[/tex])²]

where [tex]x_{bar}[/tex] =  ∑[tex]X_{i}[/tex]/n

n is sample size = 14 so lets calculate ∑[tex]X_{i}[/tex]

∑[tex]X_{i}[/tex] = 0.99 + 1.92 + 1.23 + 0.85 + 0.65 + 0.53 + 1.41  + 1.12 + 0.63 + 0.67 + 0.69 + 0.60 + 0.60 + 0.66

∑[tex]X_{i}[/tex]  =  12.55    

∑[tex]X_{i}[/tex]² = 0.99² + 1.92² + 1.23² + 0.85² + 0.65² + 0.53² + 1.41²  + 1.12² + 0.63² + 0.67² + 0.69² + 0.60² + 0.60² + 0.66²

∑[tex]X_{i}[/tex]² = 13.3253

so

our  [tex]x_{bar}[/tex] =  ∑[tex]X_{i}[/tex]/n = 12.55 / 14 = 0.8964

so our Variance  will be;

= [ ∑[tex]X_{i}[/tex]²/n-1 ] - [ [tex]\frac{n}{n-1}[/tex]([tex]x_{bar}[/tex])²]

= [ 13.3253 / 14-1 ] - [ [tex]\frac{14}{14-1}[/tex] (0.8964)²]

= 1.025 - 0.8653

= 0.1597

Therefore, the sample variance is 0.1597

c) Find the sample standard deviation.

we know that standard deviation is the square root of variance;

standard deviation = √Variance

standard deviation = √0.1597

standard deviation = 0.3996

Therefore, the sample standard deviation is 0.3996

Answer:

c = -20

Step-by-step explanation:

Isolate the variable, c. Note the equal sign, what you do to one side, you do to the other. Do the opposite of PEMDAS.

PEMDAS is the order of operation, and stands for:

Parenthesis

Exponents (& Roots)

Multiplication

Division

Addition

Subtraction

~

First, subtract 48 from both sides of the equation:

-2c + 48 = 88

-2c + 48 (-48) = 88 (-48)

-2c = 88 - 48

-2c = 40

Next, divide -2 from both sides of the equation:

(-2c)/-2 = (40)/-2

c = 40/(-2) = -20

c = -20 is your answer.

~

Answer:

40/100

Step-by-step explanation:

Answer:

40

Step-by-step explanation:

If 3/10 = 30/100, then 4/10 = 40/100

Answer:

The variance of this distribution is 42353.2

Step-by-step explanation:

For each visitor, there are only two possible outcomes. Either they clicked on the button, or they did not. Visitors are independent of each other. So we use the binomial probability distribution to solve this question.

Binomial probability distribution

Probability of exactly x sucesses on n repeated trials, with p probability.

Can be approximated to a normal distribution, using the expected value and the standard deviation.

The variance of the binomial distribution is:

[tex]V(X) = np(1-p)[/tex]

In this question:

226977 visitors, so [tex]n = 226977[/tex]

56330 clicked, so [tex]p = \frac{56330}{226977} = 0.2482[/tex]

Then

[tex]V(X) = 226977*0.2482*(1 - 0.2482) = 42353.2[/tex]

The variance of this distribution is 42353.2

Answer:

385

Step-by-step explanation:

Given that:

Margin of Error (MOE) = 5% = 0.05

Zcritical, 95% = Z(1-α/2) = Z0.025 = 1.96

MOE = Zcritical * (√p(1-p))/n)

p is taken as 0.5 when not stated ;

5 = 1.96 * sqrt[(0.5 * 0.5) / n]

5 = 1.96 * sqrt(0.25/n)

Square both sides

(0.05/ 1.96)² = 0.25/n

0.0006507 = 0.25/n

0.0006507 * n = 0.25

n = 0.25 / 0.0006507

n = 384.20162

Sample size = 385

Answer:

this could be wrong but for this question i put 10 as the first blank and for the second blank i put - and then for the third i put 5

Step-by-step explanation:

Im not sure on this. I have the same fsq and we haven't learned this yet but this is what I put because the sequence is subtracting 5  

Answer:

Step-by-step explanation:

the answers is 75,000,000

Answer:

19

Step-by-step explanation:

Answer:

19

Step by step explanation:

Answer:

The value of the test statistic is t = 2.19.

Step-by-step explanation:

Central Limit Theorem

For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]

Our test statistic is:

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

In which X is the sample mean, [tex]\mu[/tex] is the expected mean, [tex]\sigma[/tex] is the standard deviation and n is the size of the sample.

Sample of 1300 voters:

This means that [tex]n = 1300[/tex]

Found that 45% of the residents favored construction.

This means that [tex]X = 0.45[/tex]

A political strategist wants to test the claim that the percentage of residents who favor construction is more than 42%.

This means that [tex]\mu = 0.42[/tex], and by the Central Limit Theorem:

[tex]\frac{\sigma}{\sqrt{n}} = s = \sqrt{\frac{0.42*0.58}{1300}} = 0.0137[/tex]

So, the test statistic is:

[tex]t = \frac{X - \mu}{s}[/tex]

[tex]t = \frac{0.45 - 0.42}{0.0137}[/tex]

[tex]t = 2.19[/tex]

The value of the test statistic is t = 2.19.

Answer:

50.3 square units

Step-by-step explanation:

area of rectangle: 11 x twice the radius

radius = 2

A(rect): = 11(4) = 44 sq units

A (semi-circle) = (π·r²) / 2

A = 4π / 2 = 2π = 6.28 sq units

44.0 + 6.28 = 50.28

Answer:

(see below)

Step-by-step explanation:

First, you know that the first statement given is Given.

Now that you have that, you want to concentrate on your goal, and that goal is to prove that ΔGHI is an isosceles. To do this, you need to prove that the two base angles or two adjacent sides are congruent.

To do this, you can prove ΔGHJ ≅ ΔIHJ first, then use CPCTC.

Because HJ is the perpendicular bisector of GI, GJ ≅ IJ. this will be under Definition of Perpendicular Bisectors because it's a line which cuts a line segment into two equal parts at 90°.

This also means that ∠GJI and ∠IJH are right angles under Definition of Perpendicular Bisectors. Do not combine the two statements.

To clarify everything, ∠GJI ≅ ∠IJH because "all right angles are congruent."

It's also clear that these two triangles share a side, so HJ ≅ HJ. This is the Reflexive Property of Congruence, stating that for any real number a, a ≅ a.

Now you can prove these two triangles congruent by the SAS Postulate.

Using CPCTC, corresponding parts of congruent triangles are congruent, GH ≅ HI.

Your last statement should be ΔGHI is an isosceles because of Definition of Isosceles Triangle. You also want to state the statement exactly as given as the question.

Your proof should look something like IMAGE.A.

Answer:

so what is the question?

Answer:

The first graph.

Step-by-step explanation:

Just took the test, got it right. Every increase of ten pounds is an increase in 50 mg of treatment, and it should start at 0.

The best option is  first graph. The graph clearly shows the relationship between a dog's weight and the antibiotic dosage used to treat the dog.

A graph is "diagrammatic or pictorial representation of the collection of data in organized manner."

According to the question,

A veterinarian uses a specific formula to calculate the dosage of an antibiotic given to dogs with bacterial infections.  For each 10 pounds of a dog's weight, she treats the dog with 50mg of antibiotic per dose.

The horizontal line in the graph represents the dog's weight in (l b) and the vertical line in the graph represents the amount of dosage is used for treatment for bacterial infection of the dog.

Every increase of ten pounds is an increase in 50 mg dosage of treatment, and it should start at 0 in the graph.

Hence, the best option is  first graph. The graph clearly shows the relationship between a dog's weight and the antibiotic dosage used to treat the dog.

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Answer:

4/24

Step-by-step explanation:

[tex]\frac{1}{6} = \frac{1*4}{6*4}=\frac{4}{24}[/tex]

Answer:

approximately 7 CDs for her bonus

Answer:

Toris can buy about 7 CDs

Step-by-step explanation:

63 Divided by 9 = 7

Answer: 3 cents

Step-by-step explanation: multiply the price per pound by the amount of pounds purchased for both items and add them together. Then take the amount paid and subtract the total from what was paid to get the change.