taber invested money in an account where interest is compounded every year. he made no withdrawals or deposits. the function A(t) = 525(1+0.05) represents the amount of money in the account after t years. how much money did taber originally invest?

Answer:

Hey there!

Angle 6 and 4 are alternate interior angles.

Thus, 4 is 5 degrees.

Let me know if this helps :)

36 complete ¼ cup servings can be made.

Olly's plan leads to the correct solution.

Let's analyze both Jake's and Olly's plans and determine which one will lead to the correct solution.
Jake's plan:
1. Find the # % servings in s in 8-1-
2. Find the # of servings in 1
3. Add to find total servings
Olly's plan:
1. Find total liquid in the punch (add)
2. How many ¼ cups in the total (divide)
Between the two plans, Olly's plan is the correct one.

Here's why:
1. Olly's plan starts by finding the total liquid in the punch, which means adding 8 cups of Sprite and 1 cup of lime-aid. This gives us the correct total liquid amount.
2. Then, Olly's plan instructs to determine how many ¼ cup servings can be made from the total liquid by dividing the total by ¼.
Following Olly's plan :

1. Total liquid: 8 cups (Sprite) + 1 cup (lime-aid) = 9 cups
2. Number of ¼ cup servings: 9 cups ÷ ¼ cup = 9 * (4/1) = 9 * 4 = 36 servings.

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Answer: 162000

Step-by-step explanation:

Reduce the expression, if possible, by cancelling the common factors.

162000

\(\displaystyle\\Answer:\ (\frac{6}{125})^4\)

Step-by-step explanation:

\(\displaystyle\\(\frac{125}{6} )^{-4}=\\\\(\frac{6}{125})^{-(-4)}= \\\\(\frac{6}{125})^4\)

Answer:

The calculated value of t= -1.118860 does not lie in the critical region t= -1.714 or t= -2.5. Therefore we accept our null hypothesis that the mean score for Group 1 is significantly lower than the mean score for Group 2 for both significance level of 0.05 and 0.01

Step-by-step explanation:

Groups               Sample Size      Mean        Standard Deviation

1                              11                      65                   4.7

2                            16                      74                    2.5

Formulate null and alternate hypotheses as

H0 : u1 < u2 against Ha: u1 ≥ u 2

That is the mean of the group 1 is lower than the mean of the group 2

Degrees of freedom is calculated df = υ= n1+n2- 2= 11+16-2= 23

The significance level alpha is chosen to be ∝ = 0.05

The critical region t ≤ -t (0.05, 23) = -1.714

And if we choose alpha = 0.01 the critical region would be  

t ≤ -t (0.05, 23) = -2.5

Here the difference between the sample means is x`1- x`2= 65-74= -9

The pooled estimate for the common variance σ² is

Sp² = 1/n1+n2 -2 [ ∑ (x1i - x1`)² + ∑ (x2j - x`2)²]

= 1/11+16-2 [ (65)²+(74)²]

= 1/23[ 4225+5476]

= 1/23[9701]

=421.782

Sp =√ 421.782=20.5373

The test statistic is

t = (x`1- x` ) /. Sp √1/n1 + 1/n2

t= -9/ 20.5373√1/11+ 1/16

t= -9/8.0439

t= -1.118860

The calculated value of t= -1.118860 does not lie in the critical region t= -1.714 or t= -2.5. Therefore we accept our null hypothesis that the mean score for Group 1 is significantly lower than the mean score for Group 2 for both significance level of 0.05 and 0.01

Answer:

y is the cube root of 27

Step-by-step explanation:

\( { \tt{ {y}^{3} = 27 }} \\ \\ { \tt{y = \sqrt[3]{27} }} \\ \\ { \tt{y = 3}}\)

Answer:

20/z thats the answer I hope u understand

We are given the diagrams:

We are required to find the length of AC

When two triangles are similar, the ratio of their corresponding sides are congruent.

Hence, we can write:

Solving for AC:

Answer: 10

17

18

10

that's the answer

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Answer:

40, 24, 54

Step-by-step explanation:

let the 3 numbers be x, y and z

then

\(\frac{x}{y}\) = \(\frac{5}{3}\) ( cross- multiply )

5y = 3x ( divide both sides by 5 )

y = \(\frac{3}{5}\) x

and

\(\frac{y}{z}\) = \(\frac{4}{9}\) ( cross- multiply )

4z = 9y ( divide both sides by 4 )

z = \(\frac{9}{4}\) y = \(\frac{9}{4}\) × \(\frac{3}{5}\) x = \(\frac{27}{20}\) x

The 3 numbers are now expressed in terms of x , then adding gives

x + \(\frac{3}{5}\) x + \(\frac{27}{20}\) x = 118

multiply through by 20 to clear the fractions

20x + 12x + 27x = 2360

59x = 2360 ( divide both sides by 59 )

x = 40 ← first number

y = \(\frac{3}{5}\) × 40 = 3 × 8 = 24 ← second number

z = \(\frac{27}{20}\) × 40 = 27 × 2 = 54 ← third number

The 3 numbers are 40, 24, 54

The answer is C because of distribution.

Answer: 11/9

Step-by-step explanation:

you would cross out the two 4s(using butterfly method) and make them 1s. So 11 x 1 and 1 x 9 = 11/9

Answer:

11/4 times 4/9 is 11/9

Step-by-step explanation:

We have to find,

(11/4) times 4/9

\((11/4)(4/9) = (11*4/4*9)\)

We can cancel the 4s from the numeratorand denominator to get,

\((11*4/4*9) = (11*1/1*9) = 11/9\\=11/9\)

The answer is 11/9

The independent Variable in the situation presented in the table is the temperature (T), which is measured in degrees Celsius (°C), and the dependent variable is the volume (V), which is measured in milliliters (mL).

The table above illustrates the relationship between the temperature of a substance and its volume. The independent variable is the temperature of the substance and the dependent variable is the volume of the substance.

The symbol or name used to represent the independent variable is "T" for temperature and its units are given as degrees Celsius or °C.The symbol or name used to represent the dependent variable is "V" for volume, and its units are given as milliliters or mL.

The temperature is the independent variable as it is being manipulated in the experiment while the volume is dependent on the temperature as it is changing based on the temperature.

An independent variable is a variable in an experiment that is being manipulated by the experimenter, while the dependent variable is the variable that is being measured in response to changes in the independent variable.

In summary, the independent variable in the situation presented in the table is the temperature (T), which is measured in degrees Celsius (°C), and the dependent variable is the volume (V), which is measured in milliliters (mL).

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The possible number of 3 -letter words that can be formed with given conditions.

(a) No condition is imposed: 343

(b) No letter can be repeated in a word: 210

(c) Each word must begin with the letter 'a' : 49  

(d) The letter 'c' must be at the end: 49

(e) The second letter must be a vowel: 98

In this question we have been given that 3 -letter words' are formed using the letters a, b, c, d, e, f, g.

We need to find the possible number of 3 -letter words that can be formed with given conditions.

(a) No condition is imposed.

the possible number of 3 letters words would be,

7³ = 343

(b) No letter can be repeated in a word.

Using the formula of Permutation,

^{7}P_3 = 7!/(7 - 3)!

             = 210    

(c) Each word must begin with the letter a.  

If each word begins with letter 'a' there would be possible combinations of remaining 6 letters at 2nd and 3rd position of 3-letter word.

So, the possible number of 3 letters words would be,

7² = 49  

(d) The letter c must be at the end.

If each word ends with letter c there would be possible combinations of remaining 6 letters at 1st and 2nd position of 3-letter word.

So, the possible number of 3 letters words would be,

7² = 49  

(e) The second letter must be a vowel.

In the 3 letter word, the second letter must be vowel which is either a or e.

So, the possible number of 3 letters words would be,

49 + 49 = 98

Therefore, the possible number of words would be (a) No condition is imposed: 343

(b) No letter can be repeated in a word: 210

(c) Each word must begin with the letter 'a' : 49  

(d) The letter 'c' must be at the end: 49

(e) The second letter must be a vowel: 98

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The complete question is:

3 -letter words'' are formed using the letters a, b, c, d, e, f, g. How many such words are possible for each of the following conditions?

(a) No condition is imposed.

(b) No letter can be repeated in a word.

(c) Each word must begin with the letter a.

(d) The letter c must be at the end.

(e) The second letter must be a vowel.

Answer:

+7 will be the opposite or reciprocal of -7

Step-by-step explanation:

Hope it Helps!!!!

The opposite of the number, -7, is its reciprocal, which is: 7.

The opposite of a number is its reciprocal or the value on the number line that would occupy the same distance from zero in the opposite direction.

For example, opposite of b is -b.

The reciprocal of -7 is 7. Therefore, the opposite of the number, -7 is: 7.

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Answer:

B. (f + g)(x) = x - 7

Step-by-step explanation:

→Set it up, like so:

-3x - 5 + 4x - 2

→Add like terms (-3x and 4x, -5 and -2):

x - 7

The value of x for the equation to have infinite solution is 12

For an equation to have infinite solution, the expression on both sides must be equal

Given the expression below

3x–18=3(x–10)+ x

expand

3x - 18 = 3x - 30 + x

Equate

-18 = -30 + x

x = -18 + 30

x = 12

Hence the value of x for the equation to have infinite solution is 12

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The converse of the parallelogram angle theorem is proved.

The term parallelogram is defined as a quadrilateral whose two pairs of sides are parallel to each and the four angles at the vertices are not equal to the right angle and then the quadrilateral.

Here we are given that  LM ≅ ON and  LO ≅ MN

Here we have also know that ∠LNO and ∠NLM are alternative and interior angles

Then according to the reflexive property, it can be written as

=> LN ≅ LN

Then as per the SSS similarity the given triangle is written as,

ΔLNO ≅ ΔNLM

Here we have also it can be written as ∠OLN ≅ ∠MNL and  ∠LNO ≅ ∠NLM

Then it can be written as LM || ON and  LO || MN

Then the LMNO is a parallelogram

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In geometry, The transformation is expressed as (x, y) (5x/3, 5y/3)

In geometry, object transformations constitute the foundation for the majority of proofs. Transformations allow for the modification of any image in a coordinate plane. The four different types of transformations are dilation, rotation, reflection, and translation.

There are four possible transformations of a point, line, or geometric figure, each of which changes the object's shape and/or location. Pre-Image denotes the shape of the object before transformation, while Image denotes the final position and shape of the object.

(x, y) (5x/3, 5y/3) represents the transformation that is depicted in the function's graph.

The coordinates indicate the three spots on the object.

C(0,3), Z(-3,3), and X(-6,6).

The image's Z'(-5,5), X'(-10,10), and C'(0,5) coordinates.

change the x coordinate for Z to Z': -5 / - 3 = 5 / 3

In light if this, the function connection that associates the item with the image is

Z'=5/3Z

The transformation is therefore expressed as (x, y) (5x/3, 5y/3)

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Answer:

{0,π/3,π,5π/3}

Answer:

D

Step-by-step explanation:

on edge

The perimeter of Max's sandbox is 21 feet.

The sum of each length of external sides or boundary of a given figure is called its perimeter. To determine the perimeter of an object, add up the length of its boundaries.

Given the dimension of the Ohio park, then we have to determine the representative fraction of Max's sandbox.

Representative fraction = 10/ 25

                                       = 2/ 5

So that;

x = 15 * 2/5

  = 6 ft

y = 12.5 *2/5

  = 5 ft

The perimeter of Max's sandbox = 10 + y + x

                                                      = 10 + 5 + 6

                                                      = 21 ft

The perimeter of Max's sandbox is 21 feet.

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So the best actor's age deviates from the mean, he receives the award at the most extreme age.

In response to this question:

Whichever z-score does have the highest absolute value, such that, the one that deviates the most from the mean, has a most extreme age.

Best actor: 31 years old, so.

The mean age of the best actors is 42.2 years, with a standard deviation of 8.2 years.

z = (x - μ)/σ

Put the values;

z = (31 - 42.2)/ 8.2

z = -1.36

Best actress:

So, at the age of 42,

The mean of the best actresses is 31.6 years, with a standard deviation of 10.3 years.

z = (x - μ)/σ

Put the values;

z = (42 - 31.6)/10.3

z = 1.01

Thus, Because the best actor's age is further from the mean, he has the most extreme age when receiving the award.

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Answer:

35/16

Explanation:

(5*7)/2^4

= 35/2^4

= 35/16

Note:

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Answer:

≅20.9%

Step-by-step explanation:

To find the percent decrease, we need to calculate the difference between the old value (349) and the new value (276), divide that by the old value, and then multiply by 100 to express it as a percentage.

The formula for percent decrease is:

percent decrease = ((old value - new value) / old value) x 100%

Substituting the given values, we get:

percent decrease = ((349 - 276) / 349) x 100%

percent decrease = (73 / 349) x 100%

percent decrease = 20.92%

Rounding to the nearest tenth of a percent, we get:

percent decrease ≈ 20.9%

Therefore, the percent decrease in the number of petty crimes this year is [approximately 20.9%.]

Answer:

Hope this helps you

Answer:

Here's the parallel line: y = 5x - 4

Answer:

Dont worry man take a deep breath just try your best and if worse case you do bad and on the test take your time and don’t feel pressured

Step-by-step explanation:

Answer:

nope. you only go to summer school if you flunked about 60% of your core subjects. and/or if you also flunked your PAT'S/SAT'S. don't worry buddy.

Answer:

try substituting it should get you the correct answer if not im sorry.

Step-by-step explanation: