Find the length of the third side of the right triangle.

Answer:

  $5599.20

Step-by-step explanation:

The quarterly interest rate for the first two years was ...

  7%/4 = 0.0175

So, the multiplier each quarter for those 8 quarters was 1+0.0175 = 1.0175. At the end of the first 8 quarters, the account value had been multiplied by ...

  1.0175^8

For the next 8 quarters, the quarterly interest rate was 10%/4 = 0.025. So at the end of those 8 quarters, the balance had been multiplied by ...

  1.025^8

Then the balance at the end of 4 years was ...

  $4000(1.0175^8)(1.025^8) ≈ $5599.20

The balance was $5599.20.

Answer:

a. 990   b. 243   c. 693

Step-by-step explanation:

a.  1,800 * 0.55 = 990

b. 1,800 * 0.45 = 810

810 * 0.3 = 243 pretzels

c. 1,800 * 0.55 = 990

990 * 0.7 = 693 croissants

There are 990 croissants in the bakery shop. Out of 810 pretzels, 243 are coated with chocolate, and out of 990 croissants, 693 are coated with chocolate.

Number of Croissants and Coated Pastries

Let's begin by calculating the number of croissants in the bakery shop. If 45% of the pastries are pretzels, then the remaining 55% are croissants. We can calculate the number of croissants as follows:

Number of croissants = 55% of 1800
= 0.55 × 1800
= 990

This means there are 990 croissants in the bakery shop.

Next, let's find out how many pretzels are coated with chocolate. We already know that 45% of the pastries are pretzels, so first we determine the total number of pretzels:

Number of pretzels = 45% of 1800
= 0.45 × 1800
= 810

Now, 30% of these pretzels are coated with chocolate:

Chocolate-coated pretzels = 30% of 810
= 0.30 × 810
= 243

So, 243 pretzels are coated with chocolate.

Finally, we need to calculate how many croissants are coated with chocolate. We determined that there were 990 croissants, and 70% of them are coated with chocolate:

Chocolate-coated croissants = 70% of 990
= 0.70 × 990
= 693

Therefore, 693 croissants are coated with chocolate.

Answer:

The mass of a lead cube whose sides have length 1.5 cm is 40.5 grams

Step-by-step explanation:

1. Let's review the information given to us to answer the question correctly:

Mass of the cube made out of lead = 12 grams

Side of the cube = 1 cm

2. What would be the mass of a lead cube whose sides have length 1.5 cm?

For answering the question, let's calculate the volume of the cube and then its density, this way:

Volume = Height * Width * Length

Volume = 1 * 1 * 1

Volume = 1 cm³

Let's recall the formula of the density:

Density = Mass/Volume, therefore:

Density of the lead = 12/1 = 12 gr/cm³

Now, let's calculate the volume of the second cube:

Volume = Height * Width * Length

Volume = 1.5 * 1.5 * 1.5

Volume = 3.375 cm³

Finally, let's calculate the mass, using the density of the lead we already know:

Density = Mass/Volume

12 = Mass/3.375

Mass = 12 * 3.375

Mass = 40.5 grams

Answer:

y=-2x-7 D

Step-by-step explanation:

Answer: C

Example:

Bob bought stocks in a local company for $10. Now the stocks are showing a positive trend. Joe comes in and offers bob $5 for the stock. Bob says no because that would provide no good for him considering he is gaining money because of the positive trend, and he would not earn any money for the stock because he bought it for $5 more then Joe offered him.

We can actually infer that the situation that indicates that an investor shouldn't sell his or her stocks is: C. The price of the stock shows a positive trend, and the current stock price is lower than the investor's purchase price.

An investor refers to an individual whose takes the responsibility of releasing capital to a venture or business with an expectation of getting financial returns in future.

We can then see here that option C gives us a clear example of a situation that indicates that an investor shouldn't sell his or her stocks.

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Answer:

Humberto multiplied 4 by 3, but that is incorrect, you are supposed to first do 3^2 and the multiply the answer by 4 to get 36.

The correct value is:  36

Step-by-step explanation:

Step 1:  Set t to 3

4t^2

4(3)^2

4(9) -> Correct way

36 -> Correct

Humberto

4(3)^2

(12)^2 -> Made mistake

144 -> Incorrect

Humberto multiplied 4 by 3, but that is incorrect, you are supposed to first do 3^2 and the multiply the answer by 4 to get 36.

The correct value is:  36

Solution:

Given that,

zahra earns $80 each day plus a 6% commission on her sale at an appliance store

zahra has $900 in sales

Find the commission amount

commission amount = 6 % of 900

[tex]commission\ amount = \frac{6}{100} \times 900\\\\commission\ amount = 54[/tex]

Zara earnings including commission amount = 80 + 54 = 134

Thus Zara earned $ 134 on friday including commission

[tex]1)\ 3(2x + 5) = 6x + 15\\\\2)\ 7(p + 3q) = 7p + 21q\\\\3)\ 3m(n - 2m) = 3mn - 6m^2\\\\[/tex]

Solution:

Given that,

We have to expand the brackets

Use distributive property,

a(b + c) = ab + bc

Multiply the number in front of parenthesis with each term inside the parenthesis and then add them together

1)

[tex]3(2x + 5) = 3 \times 2x + 3 \times 5\\\\3(2x + 5) = 6x+15[/tex]

-------------------------------------------------

2)

[tex]7(p + 3q) = 7 \times p + 7 \times 3q\\\\7(p + 3q) =7p + 21q[/tex]

----------------------------------------------------

3)

[tex]3m(n-2m) = 3m \times n - 3m \times 2m\\\\3m(n-2m) = 3mn - 6m^2[/tex]

Thus the given expressions are expanded using distributive property

Answer:

The 3 pizzas will serve 12 players

Answer:

4.8 miles

Step-by-step explanation:

6 : 55

X : 44

X/44 = 6/55

X = 4.8

x/44 = 6:55

6(44) = 55

6 (44) = 264

55x = 264

Divide both sides by 55

55x/ 55 = 264/55

Cancel out: 55x/55 because that gives you 1

Keep: 264/55 because it gives us our answer

Thus x = 4.8

Your answer: 4.8

Good luck on your assignment and enjoy your day!

~LoveYourselfFirst:)

Answer:

y=-x+4

Step-by-step explanation:

Since the two lines are parallel, the slope would be negative x and the y intercept is 4

Answer:

y= - x + 4

Step-by-step explanation:

the two lines are parallel so the slope would be negative

Answer:

{1, 3, 5, 6, 7, 9}

Step-by-step explanation:

A u (B n C)

First we look at

(B n C)

n indicates intersects. Intersects means the common. The common number in B and C, we have

{6}

Now A u {6}

u means union. That is, joining both sets together, hence, we have

{1, 3, 5, 6, 7, 9}

A u (B n C} gives {1, 3, 5, 6, 7, 9}

Answer:

Part A: What would be worth the car's worth in 2 years?

V(2) = $ 391,114.50

Part B. In how many years will the car be worth $325,000?​

t = 7.2 years (rounding to the next tenth) or approximately 7 years, 2 months and 12 days

Step-by-step explanation:

Part A: What would be worth the car's worth in 2 years?

If V(t) = 420,000(0.965) ^t, therefore:

V(2) = 420,000(0.965)²

V(2) = 420,000 * 0.931225

V(2) = $ 391,114.50

Part B. In how many years will the car be worth $325,000?​

If V(t) = 420,000(0.965) ^t, therefore:

325,000 = 420,000(0.965) ^t

325,000/420,000 = (0.965) ^t

0.7738 = 0.965^t

t = log 0.965(0.7738)

t = log 0.7738/log 0.965

t = 7.2 years (rounding to the next tenth) or approximately 7 years, 2 months and 12 days

0.2 years = 0.2 * 12 = 2.4 months

Answer:

The y-coordinates are the same

Step-by-step explanation:

Answer:

12

Step-by-step explanation:

Let x be the number of gallons of water in lake Mead.

Given that  there is 326099 gallons in 1 acre-foot, we calculate Mead's gallons as:

[tex]1 acrefoot=326099g\\28945000acrefoot=x\\\\x=\frac{28945000acrefoot\times326099g}{1acrefoot}\\\\x=9.4\times 10^{12} \ gallons[/tex]

We now equate x to [tex]9.4\times10^a[/tex];

[tex]9.4\times 10^a=9.4\times 10^{12}\\\\a=12[/tex]

Hence, a=12

Answer:

3

Step-by-step explanation:

x              15

------  =   -----

20          100

20x5 is 100

What times 5 is 15? 3

Answer:

670$ gain

Step-by-step explanation:

After accounting for both the wage increase and the increased health insurance contribution, on average, each worker experiences a net gain of $670 annually.

The first step is to calculate the increase in wages due to the 3% increase in salary. This is calculated as follows: 3% of $39,000 is $1,170.

Next, we need to calculate the additional amount contributed toward health insurance, which has increased from 10% to 15%. This represents an increase of 5%. Thus, the added cost of health insurance is 5% of $10,000, which equals $500.

Finally, we can calculate the net change for the worker. This is achieved by subtracting the increase in health insurance contributions from the increase in wages. So, $1,170 - $500 equals $670 gain.

Hence, the correct option is (b), $670 gain.

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Answer:

Exact Form:

√485

Decimal Form:

22.02271554…

Step-by-step explanation:

Answer:

a = -92

Step-by-step explanation:

Step 1:  Subtract 29 from both sides

a + 29 = -63

a + 29 - 29 = -63 - 29

a = -92

Answer:  a = -92

Answer:

-92

Step-by-step explanation:

a + 29 = -63

  - 29  = -29

a = -63 - 29

a = -92

Height of Jaylah's fort =  243 inches

Step-by-step explanation:

Step 1:

Height of Cherie's fort = 181 inches

Height of Jaylah's fort = 62 inches taller than Cherie's fort

We need to find the actual height of Jaylah's fort

Step 2 :

Since we are given that Jaylah's fort is 62 inches taller than Cherie's fort the actual height of Jaylah's fort can be determined by adding the height of Jaylah's fort to that of Cherie's fort.

Hence

Height of Jaylah's fort = 181 + 62 = 243 inches

Step 3 :

Answer :

Height of Jaylah's fort =  243 inches

Step-by-step explanation:

[tex]10x - 4x + 6x = 12x = 6x + 6x \\ \\ 8(1 + 9y) = 8.1 + 8.9y = 8 + 72y[/tex]

Answer:

12x, 6x+6x for row one

8*1+8×9y, 8+72y for row two

Step-by-step explanation:

10x-4x is 6x, because they're like terms. 6x+6x=12x

Using the Distributive Property, 8(1+9y)=

(8*1)+(8*9y)

=

8+72y

Answer:

  144 square feet

Step-by-step explanation:

The 12-foot width apparently includes the garden and path, so the desired area is that of a 12-foot square:

  A = s² = (12 ft)² = 144 ft²

The area of the garden and path is 144 square feet.

Answer: Greater than

Step-by-step explanation:

1/7, no matter how small, is a positive number, and a positive number is always greater than a negative number, as visualized on a number line.

Answer:

6^x=x+32/9

Step-by-step explanation:

Answer:

A.) 55/8

Step-by-step explanation:

To make 6 7/8 an improper fraction, multiply the whole number by the denominator and add the result to the numerator.

That’s

6 x 8 = 48

48 + 7 = 55

Also, the denominator of the mixed number still remains the denominator of the improper fraction.

That’s

55/8

The mixed number 6 7/8 is equal to the improper fraction 55/8, making option A correct.

To convert a mixed number to an improper fraction, you multiply the whole number by the denominator of the fraction and then add the numerator of the fraction. The mixed number 6 7/8 can be converted to an improper fraction by following this method: Multiply 6 (the whole number) by 8 (the denominator) to get 48, and then add 7 (the numerator) to get 55. Therefore, 6 7/8 as an improper fraction is 55/8, which makes option A correct.

Janet's family should save $13,000 per year for the next 6 years to achieve their goal of $78,000 for her college education.

To calculate this, we divide the total cost by the number of years until Janet starts college.

Total cost for a four-year college education: $78,000.

Number of years until college: 6 years.

Annual savings required: Total cost / Number of years

= $78,000 / 6 years

= $13,000 per year.

Answer:

Step-by-step explanation:

First, replace f(x) with y

Replace every x with a y and replace every y with an x .

Solve the equation from Step 2 for y .

Replace y with f−1(x) f − 1 ( x ) .

Verify your work by checking that (f∘f−1)(x)=x ( f ∘ f − 1 ) ( x ) = x and (f−1∘f)(x)=x ( f − 1 ∘ f ) ( x ) = x are both true.

Final answer:

To find the inverse of a function, you reverse the original operation, whether it's an exponential with its natural log, a square with a square root, or logarithms with their exponential counterpart. These inverses, like ln(e^x) = x, demonstrate how they 'undo' each other. The inverse log can be used to find the original number from its logarithm.

Explanation:

Understanding Inverse Functions

To find the inverse of a function, you essentially want to reverse the original operation. For example, an exponential function and its inverse, the natural logarithm (ln), undo each other. If you have an equation y = ex, taking the natural logarithm of both sides would give you ln(y) = x, which effectively isolates x. This demonstrates that ln(ex) = x and eln(x) = x, showing how these functions are inverses of each other.

Similarly, other function pairs such as sine and arcsine, or a power function and its corresponding root function, act as inverse operations. For instance, if you have a2 = c2 - b2, as in the Pythagorean Theorem, you would take the square root of both sides to find a. This 'undoes' the square, showing that (√()2) is the inverse function of squaring.

When it comes to logarithms, the process of finding an inverse is similar. If you take a logarithm of a number, you can find the original number by taking the inverse log or calculating 10to the power of the logarithm. If you have log10(x) = y, then 10y = x.

For this case we must indicate an expression equivalent to:

[tex](3 ^ 6) ^ 3[/tex]

For properties of powers we have to:

[tex](a ^ n) ^ m = a ^ {n * m}[/tex]

So, the above expression can be rewritten as:

[tex](3 ^ 6) ^ 3 = 3^{6*3} = 3^{18}[/tex]

Thus, the resulting expression is: [tex]3^{ 18}[/tex]

Answer:

[tex]3^{ 18}[/tex]

Option D

Answer:

1) 10.1

2) 6 and 12

Step-by-step explanation:

1) median position: (31+1)/2 = 16th

15 are below 10, so 16th would be the first one to be greater than/equal to 10.

Which is 10.1

2) median = 12 of 9 values

So 5th value is 12

7,9,11,12,13,14,17,19 are the 8 values

To find the last measurement, use mean = 12

Mean = 12

Sum = 12×9 = 108

7+9+11+12+13+14+17+19+x = 108

102 + x = 108

x = 6

Final answer:

To determine the median of a data set with an odd number of measurements, find the middle value in the ordered list. In the first question, the median is 10.1cm. In the second question, the two missing measurements needed to maintain the given mean and median are 6 and 12.

Explanation:

To find the median of a given data set, one must first order the measurements from the smallest to the largest. Once the data are sorted, the median will be the middle value if there is an odd number of measurements. If there is an even number of measurements, the median will be the average of the two middle values.

We have 31 measurements with 15 being below 10cm and 12 above 11cm. The remaining four measurements are 10.1cm, 10.4cm, 10.7cm, and 10.9cm. Because there are 31 measurements (an odd number), the median will be the 16th value when sorted. The first 15 values are below 10cm, thus the 16th value is the first value above 10cm, which is 10.1cm. Therefore, the median is 10.1cm.

The mean and median of the data set are both 12. We are given seven of the measurements, and we need to find the remaining two that will keep the mean and the median at 12. To maintain the median at 12 for a set of nine measurements, the fifth datum must be 12. Among the given values, 13 is the smallest number that is bigger than 12, thus the two unknown values must be either less than or equal to 12 to not affect the median. To find these two unknown values we use the concept of mean, which is the sum of all the measurements divided by the number of measurements. Our equation to find the sum of the nine measurements is 7 + 9 + 11 + 13 + 14 + 17 + 19 + x + y = 9×12 (since the mean is 12). This simplifies to 90 + x + y = 108. Therefore, x + y = 18. Since we already have a 13 and we need a median of 12, one of the unknowns must be 12 to be the middle value and the other must be 6 to fulfill the equation x + y = 18. So the two unknown measurements are 6 and 12.

Answer:

19

Step-by-step explanation:

(x+2)/3 - (x+1)/5 = (x-3)/4 - 1

[5(x+2) - 3(x+1)]/15 = [(x-3) - 4]/4

(2x+7)/15 = (x-7)/4

4(2x+7) = 15(x-7)

8x+28 = 15x-105

7x = 133

x = 19