Ms. Takata has $480 to spend on redecorating her room. She bought 3 sets of curtains that cost $48. 25 each and a dresser that cost $234. 99. How much money does ms. Takata have left to spend?.

The actual value is 8.42 x 7.24 = 59.6576.

as an estimate she has rounded the values up to the nearest whole number ;

i.e. 8.42 ≅ 9 and 7.24 ≅ 8

to obtain 9 x 8 to get 72.

What is rounded value?

Making a number simpler while maintaining a value that is close to what it was is known as rounding.

Although less accurate, the outcome is simpler to utilize.

For instance, 73 equals 70 when rounded to the closest 10, since 70 is closer to 73 than 80 is. However, 76 rises to 80.

What is whole number?

Complete numbers the range of numbers that includes zero and natural numbers. not a decimal or fraction. {0, 2, 3, 4, 5 6, 7, 8, 9, 10, 11 …} Integer. a negative number, zero, or a counting number.

What is natural number?

Natural Numbers The numbers that we use when we are counting or ordering {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11 …} Whole Numbers The numbers that include natural numbers and zero. Not a fraction or decimal.

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Answer:

m = -3

b = 8

Step-by-step explanation:

y = -3x + 8 is in slope-intercept form, which is:

y = mx + b

so the slope is the m, the number right there beside the x. In your equation its -3. The b is the y-intercept, so its the last number tacked on the end of the equation there on the right. For your question, its the 8.

Slope is -3 and y-intercept is 8.

The probability that five cars will arrive during the next thirty minute interval is 0.0361

What is probability?

Probability is a way of calculating how likely something is to happen. Numerous things are difficult to forecast with absolute confidence.

Main Body:

Let X = number of cars arriving at Sami Schmitt's Scrub and Shine Car Wash.

The average number of cars arriving in 15 minutes is 6.

The average number of cars arriving in 1 minute is = 6/15 = 2/5

The average number of cars arriving in 5 minutes is, (2/5)*5 = 2

The random variable X follows a Poisson distribution with parameter λ = 2.

The probability mass function of X is:

P(X=[tex]x[/tex]) = [tex](e^{-2} 2^{x} )/x![/tex]  , x = 0,1 ,2 ,3...

Compute the probability that 5 cars will arrive in 5 minutes as follows:

P(X=5) =[tex](e^{-2} 2^{5} )/5![/tex]

P (X= 5) = 0.0361

Hence probability is 0.0361

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Haley’s Percentage Decrease from Test 1 to Test 2 to the nearest tenth is 7.5%

Nearest tenth can be defined as , Look at the hundredth number to round the decimal number to the nearest tenth. If it's more than 5, add one to the tenth value. Remove all the numbers that are present after the tenth place and leave the tenth place value alone if it is less than 5

Given that,

Haley’s Percent score in Test 1 = 93 %

Haley’s Percent score in Test 2 = 86%

Formula For calculating the Percentage Decrease is :

(Beginning Percentage – Final Percentage) / Beginning Percentage * 100

So, by using this formula we can calculate the percentage decrease of Haley’s Test

Percentage Decrease = (93% - 86%)/93% * 100

                 = 7.5%

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The system of inequalities and a possible solution is by working 2 hours removing wires and 6 hours tutoring.

What is Inequalities?

An inequality in mathematics is a relation that compares two numbers or other mathematical expressions in an unequal way. The most frequent application is to size-compare two numbers on a number line.

Here are the variables defined:

x is the quantity of tutoring hours worked.

Y = quantity of h

clearing cables is our job.

Since we know she can only work a maximum of 9 hours per week:

x + y ≤ 9

She also wants to earn at least $130 each week, so:

x*$22 + y*$10 ≥ $130

As a result, we have the inequality system listed below:

x + y ≤ 9

x*$22 + y*$10 ≥ $130

The graph of this system can be shown in the graphic below, where the intersection of the two shaded regions shows where the system's solutions are.

There are some solutions there, including:

y = 0, x = 8

y = 2, x = 6.

As a result, her situation might be resolved by working 2 hours removing wires and 6 hours tutoring.

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(1) The slope of the function is 11.99.

(2) The y-intercept of the function is 7.

(3) The slope indicates the per-month subscription fee.

(4) The y-intercept indicates the one-time subscription fee.

The slope-intercept form of a line is y = mx +c where m is the slope of the line and c is the y-intercept.

The given equation is c(m) = 11.99m+7.

Note that the equation is written in slope-intercept form.

The slope of the function is 11.99.

The y-intercept of the function is 7.

The slope indicates the value of the change in c(m) when there is a unit change in m.

Therefore, the slope of 11.99 indicates the per-month subscription fee.

The y-intercept indicates the value of c(m) when m is zero, therefore, the y-intercept to 7 represents that the one-time subscription is 7.

Hence,

(1) The slope of the function is 11.99.

(2) The y-intercept of the function is 7.

(3) The slope indicates the per-month subscription fee.

(4) The y-intercept indicates the one-time subscription fee.

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Answer:

C

Step-by-step explanation:

Answer:

8,333.312

Step-by-step explanation:

I did the test...

Option2 and 4 are the exponential decay from the equation.

Given that,

We have to find which one is exponential decay function.

Exponential decay function is in the form of y=abˣ where a is the initial value and b≠0,  0<b<1. power is x.

Now, Take the 1st option

y=0.25(2)ˣ

Here a is 0.25 and 2 is b

b>1

So, Option 1 is not an exponential decay.

Now, Take the 2nd option

y=2(0.20)ˣ

Here a is 2 and 0.20 is b

b<1

So, Option 2 is an exponential decay.

Now, Take the 3rd option

y=4.2(1.25)ˣ

Here a is 4.2 and 1.25 is b

b>1

So, Option 3 is not an exponential decay.

Now, Take the 4th option

y=0.55(0.91)ˣ

Here a is 0.55 and 0.91 is b

b<1

So, Option 4 is an exponential decay.

Therefore, Option2 and 4 are the exponential decay from the equation.

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Answer: Help my parents pay

bills and buy myself some shoes

By solving a linear inequation, it is obtained that

Victoria should get a minimum marks of 94 to get 'a' in science

What is linear inequation?

Inequation shows the comparision between two algebraic expressions by connecting the two algebraic expressions by >, <, [tex]\geq[/tex], [tex]\leq[/tex]

A one degree inequation is known as linear inequation.

Here, an inequation needs to be solved

Suppose the full marks of Victoria in each subject is 100

Marks obtained by Victoria in Science = 88, 86, 92

Let the fourth marks be x,

Average marks = [tex]\frac{88 + 86 + 92 + x}{4}[/tex]

                          = [tex]\frac{266 +x}{4}[/tex]

By the Problem,

                         [tex]\frac{266 + x}{4} \geq 90\\266 +x \geq 90\times 4\\266 +x \geq 360\\x \geq 360-266\\x\geq 94[/tex]

Victoria should get a minimum marks of 94 to get 'a' in science

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The common multiple of 60 and 1120 is 2³×3×7.

What is the least common multiple?

The least common multiple, lowest common multiple, or smallest common multiple of two integers a and b, denoted by lcm in arithmetic and number theory, is the smallest positive integer that is divisible by both a and b.

The least common multiple of 60 and 1120 is 3360.

2³×3×7 = 168

2²×3×5 = 60 -----(This is the common multiple)

27×3×5²×7 = 14175

2²x5 = 20

25×3×5×7 = 2625

2³×3×5²x7 = 4200

25×3×5×7² = 18375

25x5x7 = 875

Hence, the common multiple of 60 and 1120 is 2³×3×7.

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The intervals where the graph is decreasing are given as follows:

The behavior of the function regarding increase or decrease depends on the orientation of the graph, as follows:

Hence the intervals describing the behavior of the function are given as follows:

The decreasing interval can be divided into two intervals, as follows:

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Answer: w= -18

Step-by-step explanation:

1.) 3(6t2+5t+-4)

2.) 12(-2)power of 2+15(-2)-12

3.) 24-30-12

4.) -6-12

5.) -18

The location of the solutions of the inequality are quadrant in I, III, and IV

An inequality is a non-equal comparison between quantities, variables or mathematical expressions.

The specified inequality is; [tex]y \leq\dfrac{2}{3} \cdot x-4[/tex]

The line of the inequality is a straight line that has a positive slope.

The y-intercept is at (0, -4)

The x-intercept is found as follows;

[tex]y=\dfrac{2}{3} \cdot x-4[/tex]

[tex]0 =\dfrac{2}{3} \cdot x-4[/tex]

[tex]4 =\dfrac{2}{3} \cdot x[/tex]

x = 6

The x-intercept = (0, 6)

The graph therefore from quadrant III enters quadrant IV at (0, -4), then enters into quadrant I at the x-intercept (0, 6)

The solution of the inequality, found by the coordinates of the intercepts and the path through of  the line of the inequality are in I, III, and IV

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Answer:

yes

Step-by-step explanation:

Given that [tex]\cos x\sin x\tan x+\cos^2x=1[/tex]

Substitute [tex]\tan x=\frac{\sin x}{\cos x}[/tex], we obtain:

[tex]\cos x\sin x\frac{\sin x}{\cos x}+\cos^2 x=1[/tex]

Simplifying this, we get:

[tex]\sin x\sin x+\cos^2x=1[/tex]

This is equivalent to:

[tex]\sin^2x+\cos^2x=1[/tex]

The acute angles in a right triangle have measures of 30 degrees and 60 degrees if the ratio of these angles is 1:2.

The hypotenuse, along with the two legs, make up a right triangle. The hypotenuse, the longest side of the right triangle and the side opposite the right angle, is where the two legs of a right triangle come together at a 90° angle. There are a few unique varieties of right triangles, including the 45°-45° and the 30°-60° varieties.

The ratio of the angular dimensions of the acute angles of a right triangle is 1:2.

Consider x

Sum of three angles is 180 degrees.

Now,

180=90 + x + 2x

180 - 90=3x

3x = 90

x = 30

here, x and 2x, are two angles  30 and 60 degrees.

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Answer:

4x^2+6x-49

Step-by-step explanation:

(3x-8)(2x+13)-(X+11)(2x-5)

(6x^2+39x-16x-104)-(2x^2-5x+22x-55)

(6x^2+23x-104)-2x^2-17x+55

4x^2+6x-49

Hopes this helps please mark brainliest

Answer:

The triangles are congruent.

Step-by-step explanation:

The pair of triangles shown on the image are congruent triangles by ASA postulate.

ASA postulate is the postulate where two triangles are congruent by two Angles and a Side length.

The two triangles are congruent by RHS congruency property.

We know two similar planer figures are congruent when we have sides or angles or both that are the same as the corresponding sides or angles or both.

Given are two right-angle triangles.

Also given the height of both the triangles are similar and the two angles are also congruent therefore sides opposite to the similar angles are also similar hence these two right-angled triangles are congruent

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The required group of software packages that can be selected is 28.

In arithmetic, combination and permutation are two different ways of grouping elements of a set into subsets. In a combination, the components of the subset can be recorded in any order. In a permutation, the components of the subset are listed in a distinctive order.

Examples of permutation and combination, Organizing people, numbers, numerals, alphabets, notes, and colors are examples of permutations. Choosing of menu, foodstuffs, dresses, matters, and the group are examples of combinations.

Here,

Choice of six free software packages. there are 8 different software packages from which to select.

n = 8,  r = 6

Groups of software packages can be selected= 8C6

8C6 = n!/r!(n - r)!

8C6 = 8! / 4! 2!

8C6 = 8 * 7 / 2 / 1

8C6 = 28

Thus, the required group of software packages that can be selected is 28.

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The coordinates of triangle PQR under the translation (x,y) → (x+2,y-4) are P'(-1,-6), Q'(1,0), R'(4,-6).

Translation of coordinates is done by adding the horizontal translation at each vertex of the triangle. It is the process of shifting the location of the figure without changing the size and dimensions of the figure.

The coordinates of the triangle PQR are given as P(-3,-2), Q(-1,4), R(2,-2). The property under translation is given as (x,y) → (x+2,y-4). Now, let us apply this for all vertices.

P(-3,-2) → P'(-3+2,-2-4) → P'(-1,-6)

Q(-1,4) → Q'(-1+2,4-4) → Q'(1,0)

R(2,-2) → R'(2+2,-2-4) → R'(4,-6)

Thus, the vertices after translation are P'(-1,-6), Q'(1,0), R'(4,-6).

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By using the concept of confidence interval, it is obtained that the sample needed  in order to be 95% confident that the sample proportion will not differ from the true proportion by more than 4% = 601

What is confidence interval?

Let the quantity which is to be estimated is [tex]\theta[/tex] .  A confidence interval for the parameter θ, with confidence level  is the interval (a, b), where

P(a < [tex]\theta[/tex] < b) = , P is the probability

Here,

the formula for sample size n = [tex]\frac{p(1-p)z^2}{e^2}[/tex]

p is the sample proportion,

z is the z score associated with the level of confidence

e is the margin of error

Now,

e = 0.04

p = [tex]\frac{1}{2}[/tex]

z = 1.96

n = [tex]\frac{0.5(1-0.5) \times 1.96^2}{0.04^2}[/tex]

n = 600.25

Sample size needed = 601

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Answer:

  (a) in 2001: 150.4 thousand

  (b) in 2018: 467.5 thousand

Step-by-step explanation:

You want the value of the expression modeling the number of students abroad for different values of x. That expression is 123.1(1.069^x).

The value of x is the difference between the year (2001) and the reference year (1998). In the attachment, we let the calculator find that difference. It tells us, for x = 2001 -1998 = 3, the number of students is about ...

  y = 123.1(1.069^3) ≈ 150.4 . . . . thousand

In 2018, the value of x is 2008 -1998 = 10, and the number of students studying abroad is ...

  y = 123.1(1.069^10) ≈ 467.4 . . . . thousand

The cake slice with 15m due west and 15m due north is closer

Here , the slice of cake is 20m due east and then 10 m due south.

consider it as triangle ABC.

Required Displacement can be calculated by Pythagoras theorem -

AC = √ ( AB )² + ( BC )²

By substitution,

⇒ AC = √ ( 20 )² + ( 10 )²

⇒ AC = √ ( 400 + 100 )

Simplifying this equation, we get

⇒ AC = √500

⇒ AC = 10 √5

⇒ AC = 22.56

Thus , The cake slice is 22.56 m far away.

Here another slice of cake is 15m due west and 15m due north.

consider it as a triangle DEF.

Therefore,

⇒ DF = √ ( DE )² + ( EF )²

By substitution,

⇒ DF =  √ ( 15 )² + ( 15 )²

Simplifying this equation, we get

⇒ DF = √ ( 225 + 225 )

⇒ DF = √ 450

⇒ DF = 15 √2

⇒ DF = 21.21

Thus the cake slice is 21.21 m far away.

Therefore this slice is closer.

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The consumption of minutes should be less than or equal to 500 for each month.

A linear equation is a first-order (linear) term and a constant in an algebraic equation of the form y=mx+b.

The telephone bill of Chris can be written in the form of linear equation.

C(x)=$26.00+$0.12x

Here x is the number of minutes, for every one minute there is a charge of $0.12.

Chris can afford monthly bill of $86 or less not more. The linear inequality can be written as,

$26.00+$0.12x<=$86

$0.12x<=$86-$26.00

$0.12x<=$60

x<=$60/$0.12

x<=500.

The number of minutes that Chris should use should be less than or equal tp 500.

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