Solve each problem.
1) Roger spent 22 minutes on his math homework and 25.08 minutes on his spelling
homework. He spent
percent more time on his spelling homework.

Dan spent 1.25 at each table.

The formula used to solve this problem is m = 16 - 6/8. The calculation is as follows: 16 is the total amount of money Dan spent, 6 is the admission fee, and 8 is the number of tables. The equation is set up to find the amount of money Dan spent at each table. Taking the total amount of money spent, 16, and subtracting the admission fee, 6, leaves us with 10. We then divide this amount, 10, by the number of tables, 8, to find the amount of money spent at each table, which is 1.25. Therefore, Dan spent 1.25 at each table.

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Answer:

x=-2 y=-3

Step-by-step explanation:

.

Answer:

0.06

Step-by-step explanation:

0x x it expand almost done ✅✅✅

Tracy gets $1299.375 interest after 8 years and 3 months for an investment of  $3,500 at a 4.5% annual interest rate.

What is Simple Interest?

Simple interest is calculated based on a loan's principal or the initial deposit into a savings account. Simple interest doesn't compound, therefore a creditor will only charge interest on the principal sum, and a borrower will never be required to pay further interest on the interest that has already accrued.

The formula for calculating Simple Interest is -

S.I. = (P×R×T)/100

where, P = initial principal balance, R = annual interest rate and T = time (in years)

So, the principal rate, P = $3,500, the interest value, R = 4.5%, and the Time is T= 8.25 years.

Applying the formula for Simple Interest -

S.I. = (P×R×T)/100

S.I. = (3500×4.5×8.25)/100

S.I. = 1299.375

Therefore, the interest amount obtained is $1299.375.

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(b) The probability that the call is not for medical assistance = 0.37

(c) The probability that two successive calls will both be for medical assistance = 0.3969

(d) The probability that the first is for medical assistance and the second is not for medical assistance = 0.2331

(e) The probability that exactly one of the next two calls is going to be for medical assistance = 0.4662

The probability of an event is the proportion of favourable outcomes to all other possible outcomes. The symbol x can be used to denote how many successful outcomes there were in an experiment with 'n' outcomes. The formula below can be used to determine a given event's probability:

Probability (Event) = Positive Results/Total Results

                                 = x/n

Given P (call for medical assistance) = 0.63

This means that out of all incoming calls to the fire station, the probability that the call is for medical assistance is 0.63 or 63%. The complement of this event, which is the probability that an incoming call is NOT for medical assistance, is:

P (Not Medical Assistance) = 1 - P (Medical Assistance)

                                            = 1 - 0.63

                                            = 0.37

Now, assuming that successive calls are independent of one another, the probability that two successive calls will both be for medical assistance will be:

P (2 calls for medical assistance)

= 0.63 × 0.63

= 0.3969

The probability that the first is for medical assistance and the second is not for medical assistance will be:

P (1st for medical assistance × 2nd for not medical assistance)

= 0.63 × 0.37

= 0.2331

The probability that exactly one of the next two calls is going to be for medical assistance will be:

P (Exactly 1 call for medical assistance)

= (0.63×0.37) + (0.63×0.37)

= 0.2331 + 0.2331

= 0.4662

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The value of x is 11x+4x=180 and x = 12

The correct option is option c)

What is interior angles?

When two lines cross at one point, a linear pair of angles is created. If the angles follow the intersection of the two lines in a straight line, they are said to be linear. A linear pair's total angles are always equal to 180°. These are also referred to as supplementary angles.

We are given that the value of two angle is 11x and 4x

Since both lines are parallel and a line intersects both the lines

Hence the sum of these angles is 180 degrees

Hence we get an equation

11x+4x= 180

15x =180

x=12

Hence the correct option is option c)

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Using the normal distribution, the probability that x is of at most 40, represented by option B, is given as follows:

\(P(X \leq 40) = 0.1587\)

The z-score of a measure X of a normally distributed variable with mean \(\mu\) and standard deviation \(\sigma\) is given by:

\(Z = \frac{X - \mu}{\sigma}\)

The mean and the standard deviation of the distribution are given, respectively, by:

\(\mu = 51, \sigma = 11\)

The probability that x is of at most 40 is the p-value of Z when X = 40, hence:

\(Z = \frac{X - \mu}{\sigma}\)

\(Z = \frac{40 - 51}{11}\)

Z = -1

Z = -1 has a p-value of 0.1587.

Hence the probability is:

\(P(X \leq 40) = 0.1587\)

Which is the part to the left of X = 40 of the distribution, hence option B is correct.

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Answer:

undefined

Step-by-step explanation:

because

the figure does not appear

Answer:

\(3x^3(x-1)(2x^3+2x^2+2x+3)\)

Step-by-step explanation:

We can start by factoring out x³ because it's the greatest factor of every term:

\(6x^7+3x^4-9x^3=x^3(6x^4+3x-9)\)

Next, notice that each coefficient is divisible by 3, so this can be factored out as well:

\(x^3(6x^4+3x-9)=3x^3(2x^4+x-3)\)

While it may not look like we can factor out 2x⁴+x-3, we actually can! Notice the following:

\(2x^4+x-3=(2x^4+2x^3+2x^2+3x)+(-2x^3-2x^2-2x-3)=x(2x^3+2x^2+2x+3)-1(2x^3-2x^2+2x+3)=(x-1)(2x^3+2x^2+2x+3)\)

By grouping, we were able to condense this factor. Thus:

\(6x^7+3x^4-9x^3=\bf{3x^3(x-1)(2x^3+2x^2+2x+3)}\)

Answer:

Step-by-step explanation:

The zeroes are the values of such that

m² - 11m + 18 = 0

Quadratic formula:

m = [11 ± √(11² - 4∘1∘18)]/[2∘1]

= [11 ± √49]/2

= [11 ± 7]/2

= 9, 2

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Answer: x=11

Explanation: See below!

I hope this helped!

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- Zack Slocum

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Answer:

Step-by-step explanation:

\(\sqrt{x - 2} + 8 = x\\ \sqrt{x - 2} = x - 8\\x - 2 = (x - 8)^2\\x - 2 = x^2 - 16x + 64\\x^2 - 17x + 66 = 0\\(x^2 - 11x) - (6x - 66) = 0\\x(x - 11) - 6(x - 11) = 0\\(x - 6)(x - 11) = 0\\x - 6 = 6 >> x = 6\\x - 11 = 0 >> x = 11\)

Answer:

SAS postulate says that if two sides and the included angle of a triangle are equal to two sides and the included angle of another triangle, then the two triangles are said to be congruent.

Answer:

Hello! answer: 17

Step-by-step explanation:

15 × 15 = 225

8 × 8 = 64

225 + 64 = 289

√289 = 17 17 × 17 = 289 Therefore the answer is 17 hope that helps!

Answer:

17

Step-by-step explanation:

\(a^{2} + b^{2} = c^{2}\)

\(8^{2} + 15^{2} = c^{2}\)

289 = \(c^{2}\)

square root both sides

c = 17

Answer:

t=-4

Step-by-step explanation:

t+6=7/3.5

t+6=70/35 (I expanded 7/3.5 by multiplying both numerator and the denominator by 10)

t+6=2 (I divided 70 by 35 to get 2)

t=2-6

t=-4

Answer:

t=-4

Step-by-step explanation:

i took the test on k12

Answer:

C) -2/9

Step-by-step explanation:

\(\displaystyle -\frac{1}{6}\biggr[3-15\biggr(\frac{1}{3}\biggr)^2\biggr]\\\\=-\frac{1}{6}\biggr[3-15\biggr(\frac{1}{9}\biggr)\biggr]\\\\=-\frac{1}{6}\biggr[3-\frac{15}{9}\biggr]\\\\=-\frac{1}{6}\biggr[\frac{27}{9}-\frac{15}{9}\biggr]\\\\=-\frac{1}{6}\biggr[\frac{12}{9}\biggr]\\\\=-\frac{1}{6}\biggr[\frac{4}{3}\biggr]\\\\=-\frac{4}{18}\\\\=-\frac{2}{9}\)

Answer:

Hence, Option (C) - 2/9 is the Answer:

Step-by-step explanation:

-1/6 [3 -15(1/3)^2]

-1/6(3 -15)(1/9))

-1/6(3 - 5/3)

-1/6 (4/3)

Hence, Option (C) - 2/9 is the Answer:

I hope it helps!

-1.5 is the difference in the sequence

An arithmetic sequence is a sequence of numbers where the differences between every two consecutive terms are the same.

The difference is usually called the common difference. For example, the sequence 3, 6, 9, 12 have a common difference of 3 i.e. 6-3 = 3 or 9-6 = 3

Given: the sequence 4.5,3,1.5,0

The difference = 3 - 4.5 = -1.5 or 1.5-3 = -1.5

Note: You can pick any two consecutive terms to get the difference

Therefore, the difference in the sequence is -1.5

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Answer:

x = 4

Step-by-step explanation:

if a line is parallel to a side of a triangle and it intersects the other two sides then id divides those sides proportionally.

DE is such a line , then

\(\frac{BD}{AD}\) = \(\frac{BE}{EC}\)  ( substitute values )

\(\frac{x+2}{x}\) = \(\frac{3}{2}\) ( cross- multiply )

3x = 2(x + 2)

3x = 2x + 4 ( subtract 2x from both sides )

x = 4

Answer:

C

Step-by-step explanation:

Hey There!

The answer is C because x would equal what 42% of 12 would be if that makes sense

The  evaluation of the function for the given f(-1), f(1)   input value is  mathematically given as

In the field of mathematics, an assignment of one element from set Y to each and every element in set X is the definition of a function. This particular set, X, is referred to as the function's domain, and this particular set, Y, is referred to as the function's codomain. Historically, functions have been seen as an idealization of the way in which one variable relies on another variable.

-1 and 1 are both considered to be input when evaluating the function f, which is represented by the graph.

Since the inputs are on the x-axis, the graph demonstrates that the value of the function f at -1 is about -8 when x equals -1.

When x equals 1, the value of the function f is close to -12.

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The expression 3x+11y cannot be factorized.

What is factorization?

To factorise an algebraic statement, we first identify the terms' highest common factors before organising the words in the appropriate way. An algebraic expression's factorization is, to put it simply, the process of expansion in reverse. The same way, as the product of their factors, are the algebraic expressions written in algebra. The only difference is that in an algebraic expression, variables and integers are combined to perform mathematical operations like addition or subtraction.

Here the given expression 3x+11y didn't have any common factors.

The given expression has two variables 3x and 11y and they didn"t have any common terms.

Hence the expression 3x+11y cannot be factored.

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The percentile of 6.2 in the given data set is 40%.

To determine the percentile of 6.2 in the given data set, we can use the following steps:

Arrange the data set in ascending order:

4.2, 4.6, 5.1, 6.2, 6.3, 6.6, 6.7, 6.8, 7.1, 7.2

Count the number of data points that are less than or equal to 6.2. In this case, there are 4 data points that satisfy this condition: 4.2, 4.6, 5.1, and 6.2.

Calculate the percentile using the formula:

Percentile = (Number of data points less than or equal to the given value / Total number of data points) × 100

In this case, the percentile of 6.2 can be calculated as:

Percentile = (4 / 10) × 100 = 40%

The percentile of 6.2 in the sample data set is therefore 40%.

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Answer:

The nth term of an arithmetic sequence is given by. an = a + (n – 1)

Answer:

The nth term of an arithmetic sequence is given by an = a + (n – 1)d. So, to find the nth term, substitute the given values a = 2 and d = 3 into the formula.

Step-by-step explanation:

Given:

Required: length?

the formula for the area of a rectangle :

let the length of the rectangle be l

Using the long division method

So, the spread of the numbers 4, 6, 7, 9, 9 is 5.

Spread can refer to different things depending on the context. Here are a few examples:

In finance, spread refers to the difference between the bid price and the ask price of a security or asset. The bid price is the highest price a buyer is willing to pay for a security, while the ask price is the lowest price a seller is willing to accept. The spread represents the cost of trading that security or asset and is typically measured in basis points (hundredths of a percentage point).

In sports betting, spread refers to the point spread or handicap that is assigned to a team in order to make the betting odds more even. For example, if a football team is favored to win by 7 points, they may be assigned a -7-point spread, meaning they would have to win by more than 7 points for a bet on them to be successful.

In epidemiology, spread refers to the transmission of a disease from one person to another. The spread of a disease can be influenced by a variety of factors, including the infectiousness of the disease, the proximity and frequency of contact between people, and the effectiveness of measures to prevent transmission (such as vaccines or masks).

In cooking, spread can refer to a variety of ingredients that are used to spread on bread or crackers, such as butter, jam, or peanut butter.

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Answer:

the expression of perimeter is 2(l+b)

Answer:

way too long

Step-by-step explanation:

jk, 3 hours and 55 minutes

Answer:

Total Earnings = 18,160

1) 1.07 * principal1 *  + 1.06  * principal2= 18,160

2) principal1 + principal2 = 17,000

We'll multiply equation 2) by -1.06

2) -1.06*principal1 -1.06*principal2 = -18,020 then adding equation 1)

1) 1.07 * principal1 *  + 1.06  * principal2= 18,160

.01*principal1 = 140

principal 1 = 14,000

and therefore principal 2 = 3,000

Step-by-step explanation:

Step-by-step explanation:

Each year the truck retains 85 % of its value   ( 85% + 15% = 100%)

45000 * .85 * .85 * .85 * .85   = $ 45 000 *  .85^4 = $ 23490.28

Answer:

The value of the truck would be $23,490.28 after 4 years.

Step-by-step explanation:

Main concepts:

Concept 1. Percentages

Concept 2. Depreciation

Concept 3. Distributive property

Concept 4. Repeated multiplication as a power

Concept 1. Percentages

A percentage is effectively a unit.  In the same way that 25¢ is the same as 0.25 US dollars, 15% is the same as 0.15 (unit-less number).

A common task is to find a percentage of a quantity.  For example, finding 25% of 40.  Mathematically, the word "of" here means multiply, so 25% of 40 means "25% * 40".  But, since a percentage can be converted to a regular unit-less number, this is also the same as "0.25 * 40" which is 10.  So, 25% of 40 is 10.

Concept 2. Depreciation

To depreciate means that the value of the thing decreases.  In this question, the value of the truck depreciates by 15% (per year), so its value would decrease by whatever 15% of its current value is.

15% of $45,000 is 0.15 * $45,000 = $6,750 (this is the amount that the value decreases by during the first year)

To find the value after 1 year, we need to subtract this from the original value.  We'll label this equation 1:

Common mistake: It is a common mistake for people to continue subtracting $6,750 for years 2, 3, and 4 thinking that this is subtracting another 15%.  However, each year, the 15% depreciation is based on the new value of the truck, so during the second year, the truck started at a value of $38,250 (from the end of the first year), and 15% of $38,250 will be different from 15% of $45,000.

15% of $38,250 is 0.15 * $38,250 = $5,737.50 (this is the amount that the value decreases by)

To find the value after 2 year, we need to subtract this from the value at the end of year 1.  We'll label this equation 2:

Concept 3. Distributive property

In Equation 1 above, the left side of the equation can be factored by using the distributive property in reverse, and factoring out "$45,000":

$45,000 - $6,750 is the same as

$45,000 * ( 1 - 0.15 ) = $38,250    -- Equation 1a

This expression illuminates what is happening to the value if we change the numbers inside the parentheses into percentages

$45,000 * ( 100% - 15% )

Notice that in the parentheses, we start with 100% (whatever 100% is), and we're subtracting 15%.

Similarly, in Equation 2, the left side of the equation can be factored by using the distributive property in reverse, and factoring out "$38,250":

$38,250 - $5,737.50 is the same as

$38,250 * ( 1 - 0.15 ) = $32,512.50   -- Equation 2a

Notice that in the parentheses, we again start with 100% (whatever 100% is), and we're subtracting 15%.

Concept 4. Repeated multiplication as a power

Quick recap from Equation 1a & Equation 2a:

For year 1, Equation 1a:  $45,000 * ( 1 - 0.15 ) = $38,250

For year 2, Equation 2a:  $38,250 * ( 1 - 0.15 ) =  $32,512.50

However, note the equivalence in bold above.  This means that we can replace the $38,250 in the "Year 2" equation with the entire left side of the equation from Year 1.

Thus, for Year 2, the equation become:

$45,000 * ( 1 - 0.15 ) * ( 1 - 0.15 ) =  $32,512.50

While the value at the end of year 3 could be written

$32,512.50 * ( 1 - 0.15 )

notice that the left side again starts with the value that ended the year before.  With another substitution, for Year 3, the equation becomes:

$45,000 * ( 1 - 0.15 ) * ( 1 - 0.15 ) * ( 1 - 0.15 ) =  Value at end of year 3

Continuing the pattern, we need the value at the end of the year before, times ( 1 - 0.15 ) to get the value for the end of the following year.  

$45,000 * ( 1 - 0.15 ) * ( 1 - 0.15 ) * ( 1 - 0.15 ) * ( 1 - 0.15 ) =  Value at end of year 4.

Notice that each year, we're multiplying by another factor of ( 1 - 0.15 )

Recall that multiplying by the same number or expression repeatedly can be simplified with an exponent.  For example, five 2s multiplied together: 2*2*2*2*2 can be written as \(2^5\).  

Therefore, the value of the truck at the end of year 2 can be written as

\(\$45,000 * (1-0.15)^{2}\)

The value of the truck at the end of year 3:  \(\$45,000 * (1-0.15)^{3}\)

The value of the truck at the end of year 4:  \(\$45,000 * (1-0.15)^{4}\)

Side note: the value of the truck at the end of any year "n" is \(\$45,000 * (1-0.15)^{n}\)

So, to answer the question, and find the value of the truck in 4 years, we just need to evaluate \(\$45,000 * (1-0.15)^{4}\)

\(\$45,000 * (1-0.15)^{4}=\)

\(=\$45,000 * (0.85)^{4}\)

\(=\$45,000 * 0.52200625\)

\(=\$23,490.28125\)

Rounded to the nearest penny, the value of the truck would be $23,490.28 after 4 years.