Item before tax?
3. Mrs. Noah's bill, before tax, is $50. The sales tax rate is 3%. Mrs. Noah
decides to leave a 2% tip for the gate keeper based on the pre-tax amount.
How much will the total bill be, including tax and tip?

(SHOW THE WORK PLEASE)

Answer: the present age of son is 15 years, and the present age of father is 45 years.

Step-by-step explanation:

Let the age of son be 'x' and that of his father be 'y'.

So according to the question, the 1st equation that can be formed will be:

y = 3(x) ->(1)

[as father's age is 3 times the age of son]

Now after 5 years:

Age of son = (x+5)

Age of father = (y+5)

So according to the question, the 2nd equation that can be formed will be:

(y+5) = 2.5×(x+5) ->(2)

[as father is now two and half times old as his son]

Substituting the value of equation (1) in (2), we get:

(3x+5) = 2.5×(x+5)

=> 3x + 5 = 2.5x + 12.5

=> 3x - 2.5x = 12.5 - 5

=> 0.5x = 7.5

=> x = 7.5/0.5 = 15

Thus, the present age of son is 15 years.

Note : we can calculate the age of father by putting the value of x in equation (1) or (2):

y = 3(x) = 3 × 15 = 45 (putting x in equation 1)

Thus, the present age of father is 45 years.

ANSWER:

14 blocks of hundreds

1 blocks of tens

4 blocks of ones

STEP-BY-STEP EXPLANATION:

The first thing is to decompose the number 1414, like this:

Since we have only hundreds, tens, and ones blocks.

Therefore, would be:

14 blocks of hundreds

1 blocks of tens

4 blocks of ones

Answer:

use ten 100 blocks,four 10 blocks,and fourteen 1s blocks.

Step-by-step explanation:

hope that helps.

Answer:

4.9 in

Step-by-step explanation:

6/11 = x/9

6/11 times 9 = x

x = 4.9

Answer:

Ron's ERA has a z-score of -2.03.

Karla's ERA has a z-score of -1.86.

Due to the lower z-score, Ron had a better yean than Karla relative to their peers.

Step-by-step explanation:

Z-score:

In a set with mean \(\mu\) and standard deviation \(\sigma\), the zscore of a measure X is given by:

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

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this question:

Since the lower the ERA, the better the pitcher, whoever's ERA has the lower z-score had the better year relative to their peers.

Ron

ERA of 3.06, so \(X = 3.06\)

For the males, the mean ERA was 5.086 and the standard deviation was 0.998. This means that \(\mu = 5.086, \sigma = 0.998\)

So

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

\(Z = \frac{3.06 - 5.086}{0.998}\)

\(Z = -2.03\)

Ron's ERA has a z-score of -2.03.

Karla

ERA of 3.28, so \(X = 3.28\)

For  the females, the mean ERA was 4.316 and the standard deviation was 0.558. This means that \(\mu = 4.316, \sigma = 0.558\)

So

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

\(Z = \frac{3.28 - 4.316}{0.558}\)

\(Z = -1.86\)

Karla's ERA has a z-score of -1.86.

Which player had the better year relative to their peers, Ron or Karla?

Due to the lower z-score, Ron had a better yean than Karla relative to their peers.

The number of bears that the researcher should be expected to see in the larger central Pennsylvania forest with about 1,000 total animals is given as follows:

95 bears.

To obtain the number of bears in the larger forest, first we must obtain the proportion in the smaller forest.

The proportion is given by the number of bears divided by the total number of animals, both of these amounts given by the bar graph presented at the end of the answer.

The number of bears is given as follows:

20.

The total number of animals is given as follows:

20 + 70 + 30 + 90 = 210.

Meaning that the proportion of bears is of:

20/210.

Hence, out of 1000 animals, the expected number of bears is of>

20/210 x 1000 = 20000/210 = 95 bears.

The bar graph is given by the image presented at the end of the answer.

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The equation of the line  4x + 5y = -30  in slope intercept form is y = - 4 / 5 x - 6

Equation of a line can be represented in slope intercept form as follows;

y = mx + b

where

Therefore, the equation of the line 4x + 5y = -30 can be represented in slope intercept form as follows:

Using the format y = mx + b

4x + 5y = -30

subtract 4x from both sides of the equation

5y = -4x - 30

divide both sides of the equation by 5

y = - 4 / 5 x - 30 / 5

y = - 4 / 5 x - 6

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Using the concept of word problems and quadratic equation it will take 1 year until the sum of square of their ages be 45.

Word problems are mathematical problems that are delivered in ordinary words, instead of mathematical symbols.

Part of the problem with dealing with word problems that they first need to be translated into mathematical equations, and then the equations need to be solved.In this problem;

let x represent the number of years from now when the sum of square of their respective age will be

45.(x + 2)² + (x + 5)² = 45

Expanding the brackets;

x² + 4x + 4 + x² + 10x + 25 = 45

2x² + 14x + 29 = 45

2x² + 14x + 29 - 45 = 0

2x² + 14x - 16 = 0

Solving the quadratic equation for x;

x = 1, x = -8

Taking the positive value, the value of x is 1

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The mean of a data set is the sum of the data divided by the total number of data.

The median of a data set is the middle number in the set (after the numbers have been arranged from least to greatest, or, if there is an even number of data, the median is the average of the two middle numbers.

You have the next data set:

A total of 28 data.

The mean is equal to the sum of the 28 numbers and then divided into 28:

The simplified expression is  d/ c⁴.

To simplify the expression cd³ c⁻⁵ x d⁻², we can combine the variables with the same base (c and d) by adding their exponents:

Using the property of exponents as

When multiplying two exponential expressions with the same base, you can add the exponents. This can be expressed as follows:

aᵇ x aⁿ= aᵇ⁺ⁿ

When dividing two exponential expressions with the same base, you can subtract the exponents. This can be expressed as follows:

aᵇ / aⁿ= aᵇ⁻ⁿ

So, cd³ c⁻⁵ x d⁻²

= c¹⁻⁵ x d³⁻²

= c⁻⁴ x d¹

= dc⁻⁴

Again from the property of exponents

a⁻ᵇ = 1/aᵇ

So,  dc⁻⁴

= d/ c⁴

Therefore, the simplified expression is  d/ c⁴.

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Answer:

(2/3)r=30

r=45cm

Step-by-step explanation:

When trying to find a fraction of something, multiply to get your answer:

(2/3) of r = (2/3)r

The blue ribbon can be represented by both 30cm and (2/3)r cm:

(2/3)r=30

2r=90

r=45cm

Answer:

Step-by-step explanation:

it think it 23 becasue u add

1 divide it by 2

Given statement solution is :- The present value of R13,000 per year invested for 8 years at 10% compound interest is approximately R69,776.60.

To calculate the present value of an investment with compound interest, we can use the formula for the present value of an annuity:

PV = A *\((1 - (1 + r)^(-n)) / r\)

Where:

PV = Present value

A = Annual payment or cash flow

r = Interest rate per period

n = Number of periods

In this case, the annual payment (A) is R13,000, the interest rate (r) is 10% per year, and the investment is made for 8 years (n).

Using the formula and substituting the given values, we can calculate the present value:

PV = \(13000 * (1 - (1 + 0.10)^(-8)) / 0.10\)

Calculating this expression:

PV = \(13000 * (1 - 1.10^(-8)) / 0.10\)

= 13000 * (1 - 0.46318) / 0.10

= 13000 * 0.53682 / 0.10

= 6977.66 / 0.10

= 69776.6

Therefore, the present value of R13,000 per year invested for 8 years at 10% compound interest is approximately R69,776.60.

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Answer:

\(-2(-4)-2(0)=8\)

Step-by-step explanation:

Given

\(2x - 2y = 8\)

Required

Gaps: -2( )-2( )=8

Fill in in the gaps

The are numerous solutions to this.

One of them is:

Assume y = 0.

So, we have:

\(-2x - 2*0 = 8\)

\(-2x - 0 = 8\)

\(-2x = 8\)

Divide through by -2

\(\frac{-2x}{-2}= \frac{8}{-2}\)

\(x= -4\)

Fill in the gaps with these values of x and y respectively:

Hence; one solution is: \(-2(-4)-2(0)=8\)

Answer: the quotient of the given expression is, h5

Step-by-step explanation:

Use the exponent rule:

Given the expression:

⇒

Apply the exponent rules we have;

Simplify:

therefore, the quotient of the given expression is,

Answer:

C

Step-by-step explanation:

It is a negative slope because the y value decreases as the x value increases. It goes down 2 for every three that it goes across, so we can find, using rise over run, that the slope is -2/3

If Katie Pittman earns a $60,840 annual salary, her weekly gross salary is $1170.

What is  weekly gross salary?

The number of hours worked multiplied by the hourly wage of an employee is how gross wages are determined for hourly workers. For instance, an employee making $12 per hour and working 25 hours per week would earn a gross weekly salary of $300 (25 x 12 = 300).

What is annual salary?

The gross pay (before tax deductions) divided by the number of pay periods in a year yields the yearly salary. For instance, a worker making $1,500 each week would make $78,000 a year (1,500 multiplied by 52).

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Answer:

Point estimate of the corresponding population mean = $8,213

Step-by-step explanation:

Given:

Average cost of a wedding reception (x) = $8,213

Total number of sample (n) = 450

Standard deviation = $2185

Find:

Point estimate of the corresponding population mean

Computation:

Average cost of a wedding reception (x) = Point estimate of the corresponding population mean

Point estimate of the corresponding population mean = $8,213

The probability of randomly selecting socks that are not blue is 1/6.

A probability means the branch of math which deals with finding out the likelihood of the occurrence of an event. Its measures the chance of an event happening.

To get it, we will calculate number of favorable outcomes of socks that are not blue and divide by number of possible outcomes.

Out of 3 colors (purple, blue, orange), there are 2 colors (purple, orange) that are not blue. As we are selecting socks, there is only 1 option for the piece of clothing, so, number of favorable outcomes is 2.

The total number of possible outcomes is:

= 4 * 3

= 12.

Probability of selecting socks that are not blue is:

= Number of favorable outcomes / Total number of possible outcomes

= 2 / 12

= 1/6.

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Answer: p= 5 miles

Step-by-step explanation:

20/4 = 5

Answer:

P would equal 5 because all the sides are equal and since they are equal and the perimeter is 20 you would do 5+5+5+5=20

Answer:

A

Step-by-step explanation:

It is not B because 7x^2 means multiplying the equation by seven. It isn't C because that would move the graph DOWN seven units. And it's not D because when it is in parenthesis like that, it means that it is a horizontal shift, not vertical.

Answer:

A. G(x) = \(x^2+7\)

Step-by-step explanation:

→For the function to shift upwards 7 units, 7 must be added to the function, like so:

G(x) = \(x^2+7\)

→F(x) + c (in this case is 7), cases a vertical shift and the function is moved "c," units. The graph would shift downwards if 7 was being subtracted.

This means the correct answer is A.

Answer:

243 in^2

Step-by-step explanation:

9*9

Surface area of a side

81*3

The sides that are painted

You have to write the equation in "point-slope" form for a line that passes through point (11,16)

and is parallel to the line

If two lines are parallel, then their slopes are equal.

The slope of the given line is m=9 and this will be the sloe of the line you have to determine.

The point slope form is

m → slope

(x₁, y₁) → are the coordinates of a point of the line.

For m=9 and (11,16) the point slope form is

You can use the distributive property of multiplication to solve the term in parentheses:

A quadratic polynomial with integer coefficients is,
p(x) = x² + 6x + (17√21)/49.

A quadratic equation is an algebraic expression in the form of variables and constants.

A quadratic equation has two roots as its degree is two.

Given, The roots of the quadratic equation is x = 2/7, ± √21/7.

Let, p(x) = x² + bx + c.

p(x) = (x + 2/7 + √21/7)(x - 2/7 + √21/7).

p(x) = x² - (2/7)x + (√21/7)x + (2/7)x - (4/49) + 2√(21/49) + (√21/7)x - 2√21/49 + 21/49.

p(x) = x² + 2(√21/7)x + 21/49 - 4/49.

p(x) = x² + {(2√21)x}/7 + 17/49.

p(x) = x² + (42/7)x + (17√21)/49.

p(x) = x² + 6x + (17√21)/49.

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Answer:

What I would tell Charli is that his prediction is somewhat right because there is a 50/50 chance of landing the coin on each side because 325 is half of 650.

Step-by-step explanation:

The values of the expressions are;

z³³

d⁻¹⁶

Note that index forms are described as forms used in the representation of numbers or variables too large or small.

Some rules of index forms are;

Then, from the information given, we have that;

(z⁻⁴/z⁶  × z⁵/z⁻⁶)⁻¹¹

Subtract the exponents, we have;

(z⁻² × z⁻¹)⁻¹¹

expand the bracket

z²² ⁺ ¹¹

z³³

(d⁴)⁻³/(d⁶)⁻²  ÷  (d⁴/d⁶)⁻⁸

expand the brackets

d⁻¹²/d¹²  ÷    (d⁻²)⁻⁸

subtract the exponents

d⁰  ÷  d¹⁶

d⁻¹⁶

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The solution is, After decreasing £16870 by 3% we get, £16363.90.

Here, we have,

A percentage is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, "%".

First, find the percentage of £16870 by 3%

%value = 3% * 16870

           = (3 / 100) * 16870

           = 506.1

Now, just minus with actual value

New value = actual value - %value

We know, actual value = £16870 and %value = 506.1

so, New value = 16870 - 506.1

we get, New value = £16363.90

Therefore, After decreasing £16870 by 3% we get, £16363.90

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complete question:

Decrease £16870 by 3%

Give your answer rounded to 2 DP.

Answer:

a

Step-by-step explanation:

the data is represented in the dot plot

Answer:

answer is 77.67

Step-by-step explanation:

explain by the x axis is 68 to y axis is 84 so the median is 77.67