Maplewood Furniture Store is having a sale on dining room furniture. When a customer purchases a set of dining chairs, a one-time discount of $55 is applied to the total. During the sale, Rhianna buys a set of 6 chairs that match the table she inherited from her grandmother. Rhianna pays $455 in all. Which equation can you use to find the regular cost, c, of each chair? ( ANSWERS 6c - 55 = 455, 55(c - 6) = 455, 55c - 6 = 455, 6(c - 55) = 455,) What is the regular cost of the chair

Answer:

∠ SPQ = 75°

Step-by-step explanation:

The sum of the 4 angles in a quadrilateral = 360°

Subtract the sum of the 3 angles from 360 for ∠ SPQ

∠ SPQ = 360° - (90 + 74 + 121)° = 360° - 285° = 75°

Answer:

[tex]\displaystyle \int {84} \, dx = 84x + C[/tex]

General Formulas and Concepts:

Calculus

Integration

Integration Rule [Reverse Power Rule]:                                                               [tex]\displaystyle \int {x^n} \, dx = \frac{x^{n + 1}}{n + 1} + C[/tex]

Integration Property [Multiplied Constant]:                                                         [tex]\displaystyle \int {cf(x)} \, dx = c \int {f(x)} \, dx[/tex]

Step-by-step explanation:

Step 1: Define

Identify

[tex]\displaystyle \int {84} \, dx[/tex]

Step 2: Integrate

Topic: AP Calculus AB/BC (Calculus I/I + II)

Unit:  Integrations

Answer:

11.2

Step-by-step explanation:

yz = 11.2

since the corresponding arc of yz and xy are same, their measures will ba same too

Answered by GAUTHMATH

Answer:

11.2

Step-by-step explanation:

good luck!

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Answer:

  y = 2x +4

Step-by-step explanation:

The slope can be found using the slope formula:

  m = (y2 -y1)/(x2 -x1)

  m = (12 -(-6))/(4 -(-5)) = 18/9 = 2

The y-intercept can be found from ...

  b = y -mx

  b = 12 -(2)(4) = 4

Then the slope-intercept equation for the line is ...

  y = mx +b

  y = 2x +4

Answer:

y=2x+4

Step-by-step explanation:

Hi there!

We want to find the equation of the line that passes through the points (-5, -6) and (4, 12)

The most common way to write the equation of the line is in slope-intercept form, which is y=mx+b, where m is the slope and b is the y intercept

First, let's find the slope of the line

The formula for the slope calculated from two points is [tex]\frac{y_2-y_1}{x_2-x_1}[/tex], where ([tex]x_1[/tex], [tex]y_1[/tex]) and ([tex]x_2[/tex], [tex]y_2[/tex]) are points

We have everything needed to calculate the slope, but let's label the values of the points to avoid any confusion

[tex]x_1[/tex]=-5

[tex]y_1[/tex]=-6

[tex]x_2[/tex]=4

[tex]y_2[/tex]=12

Now substitute into the formula (remember: the formula has SUBTRACTION in it)

m=[tex]\frac{y_2-y_1}{x_2-x_1}[/tex]

m=[tex]\frac{12--6}{4--5}[/tex]

Simplify

m=[tex]\frac{12+6}{4+5}[/tex]

Add

m=[tex]\frac{18}{9}[/tex]

Divide

m=2

So the slope of the line is 2

Here is the equation so far:

y=2x+b

We need to find b

As the line will pass through both (-5, -6) and (4, 12), we can use the values of either one to solve for b

Let's take (4, 12) for instance

Substitute 4 as x and 12 as y

12=2(4)+b

Multiply

12=8+b

Subtract 8 from both sides

4=b

Substitute 4 as b in the equation

y=2x+4

Hope this helps!

Answer:

Shawn earns $11 per hour.

Step-by-step explanation:

When looking at the x axis (hours), and find where 1 hour intersects with the y axis It intersects with the point labeled at $11. This means after working for 1 hour, Shawn earned $11.

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Answer:

  θ = 1.5 radians ≈ 85.9°

Step-by-step explanation:

The arc length in terms of central angle and radius is ...

  s = rθ

where θ is the central angle in radians. Here, we want to find θ, so we have ...

  θ = s/r . . . . divide by r

For the given numbers, ...

  θ = (6 cm)/(4 cm) = 3/2 = 1.5 . . . radians

I radian is 180°/π, so 3/2 radians is ...

  (3/2)(180°/π) = 270°/π ≈ 85.9°

Answer:

The first three terms in the geometric sequence are 18, 24, 32.

Step-by-step explanation:

A number when added to [tex]x,y,z[/tex] that yields consecutive terms of a geometric sequence is an unknown number [tex]t\in \mathbb{Z}[/tex]

Given

[tex]x = 1, y = 7, z = 15[/tex]

We know

[tex]\alpha _1 = 1+t[/tex]

[tex]\alpha _2 = 7+t[/tex]

[tex]\alpha _3 = 15+t[/tex]

Recall that a geometric sequence is in the form

[tex]\boxed{a_n = a_1 \cdot r^{n-1}}[/tex]

Therefore, once  [tex]\alpha_1, \alpha_2, \alpha_1[/tex] are consecutive terms,

[tex]15+t = (1+t) r^{3-1} \implies 15+t = (1+t) r^2[/tex]

To find the ratio, for

[tex]\dots a_{k-1}, a_k, a_{k+1} \dots[/tex]

we know

[tex]\dfrac{a_k}{a_{k-1}} =\dfrac{a_k}{a_{k-1}} =r[/tex]

Therefore,

[tex]\dfrac{(7+t)}{(1+t)} =\dfrac{(15+t)}{(7+t)} \implies (7+t)^2 = (15+t)(1+t)[/tex]

[tex]\implies 49+14t+t^2=15+16t+t^2 \implies -2t=-34 \implies t=17[/tex]

The ratio is therefore

[tex]r=\dfrac{4}{3}[/tex]

Therefore, the first three terms in the geometric sequence are 18, 24, 32.

Answer:

7

Step-by-step explanation:

i had it

Answer:

A. Use the​ two-sample t-methods when a sample was taken from each of two populations​ (i.e. two groups being​ compared) and the population standard deviations are not known.

Step-by-step explanation:

T-distribution:

When the population standard deviation is not known, the t-distribution is used.

If a sample was taken from one population, we use the one-sample method, while if there is a comparison of two populations, the two-sample method is used, and thus, the correct answer is given by option A.

Answer:

the graph would cut the y-axis 11 units below y=f(x)

Answer:

the last two answers are the only correct ones

Answer:

The expected number of offspring is 2

Step-by-step explanation:

The given parameters can be represented as:

[tex]\begin{array}{cccccc}x & {0} & {1} & {2} & {3} & {4} \ \\ P(x) & {0.24} & {0.25} & {0.19} & {0.17} & {0.15} \ \end{array}[/tex]

Required

The expected number of offspring

This implies that we calculate the expected value of the function.

So, we have:

[tex]E(x) = \sum x * P(x)[/tex]

Substitute known values

[tex]E(x) = 0 * 0.24 + 1 * 0.25 + 2 * 0.19+ 3 * 0.17 + 4 * 0.15[/tex]

Using a calculator, we have:

[tex]E(x) = 1.74[/tex]

[tex]E(x) = 2[/tex] --- approximated

Answer:

Step-by-step explanation:

Answer:

q/N = g

Step-by-step explanation:

q = Ng

Divide each side by N

q/N = Ng/N

q/N = g

Answer:

3y=5x-4

Step-by-step explanation:

As the lines are parallel, the slope will be 5/3. The equation of line will be y=(5/3)*x-4/3. 3y=5x-4

Step-by-step explanation:

2 x y + x + 2 y is equal to 3 x y + 2 y final answer is 5xy

4. Percent increase

Because Original Value < New Value

5. Percent

6. Whole

Because it's asking what number that means total.

Thanks :)

Answer:

$1.85 = £1

Step-by-step explanation:

55680/72.50 = 786

55680/128 = 435

435x = (786 + 19.80)

x = 805.8/435

x = 1.85

Answer:

£1 = $1.72

Step-by-step explanation:

55680/72.50=768

55680/128=435

768.00 - 19.80 = 748.20

x = 748.20 / 435

x = $1.72

Answer:

0.0193 = 1.93% probability that there is equipment damage to the payload of at least one of five independently dropped parachutes.

Step-by-step explanation:

For each parachute, there are only two possible outcomes. Either there is damage, or there is not. The probability of there being damage on a parachute is independent of any other parachute, which means that the binomial probability distribution is used to solve this question.

To find the probability of damage on a parachute, the normal distribution is used.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

And p is the probability of X happening.

Normal Probability Distribution

Problems of normal distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

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 p-value, we get the probability that the value of the measure is greater than X.

Probability of a parachute having damage.

The opening altitude actually has a normal distribution with mean value 185 and standard deviation 32 m, which means that [tex]\mu = 185, \sigma = 32[/tex]

Equipment damage will occur if the parachute opens at an altitude of less than 100 m, which means that the probability of damage is the p-value of  Z when X = 100. So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{100 - 185}{32}[/tex]

[tex]Z = -2.66[/tex]

[tex]Z = -2.66[/tex] has a p-value of 0.0039.

What is the probability that there is equipment damage to the payload of at least one of five independently dropped parachutes?

0.0039 probability of a parachute having damage, which means that [tex]p = 0.0039[/tex]

5 parachutes, which means that [tex]n = 5[/tex]

This probability is:

[tex]P(X \geq 1) = 1 - P(X = 0)[/tex]

In which

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 0) = C_{5,0}.(0.0039)^{0}.(0.9961)^{5} = 0.9807[/tex]

Then

[tex]P(X \geq 1) = 1 - P(X = 0) = 1 - 0.9807 = 0.0193[/tex]

0.0193 = 1.93% probability that there is equipment damage to the payload of at least one of five independently dropped parachutes.

Answer:

5

Step-by-step explanation:

4.5*10^-8/ 9*10^-9

1) Reduce the fraction, express 9 as a product of multiplying 4.5*2

4.5*10^-8/4.5*2*10^-9

2) Then notice the common factor of numerator and denominator( 4.5) , get rid of it in both numerator and dnominator

3) 10^-8/ 2*10^-9= 1/2*(10^-8/10^-9)= 0.5* (10^-8/10^-9)

10^-8/10^-9= 10^(-8-(-9))= 10^1=10.

so 0.5*10=5 (it is the answer written in scientific form)

Let W be the random variable representing your winnings from playing the game. Then

[tex]P(W=w)=\begin{cases}\text{prob. of rolling an even number}=\frac12&\text{if }w=\$0.50-\$1=-\$0.50\\\text{prob. of rolling a 1}=\frac16&\text{if }w=\$2-\$1=\$1\\\text{prob. of rolling 3 or 5}=\frac13&\text{if }w=\$1-\$1=\$0\\0&\text{otherwise}\end{cases}[/tex]

In short, you have a 1/6 chance of profiting from the game, and a 5/6 chance of losing money. So the odds of winning are (1/6)/(5/6) = 1/5 or 1 to 5.

Answer:

Hey there!!

The total number of cents - 20

Cost for each pencil - 3 cents

Number of pencils bought - ' x '

y = number of pennies left

What is the domain ?

Show how y is dependent on x ..

Let's get this into an equation :

... The total cost for x pencils bought = 3x

... Number of pennies left = 20 - 3x

... y = number of pennies left

... y = 20 - 3x

Notice : If the x value changes, the y value changes too

... If x = 1 , then , y = 17; If x = 2 , then , y = 14

Hence, we could say y is dependent upon x

Domain = ?

... Remember - The total number of pennies = 20 ; hence, the total cost cannot go above 20 cents.

Hence, we will have to work with inequalities

The equation :

... 20 ≥ 3x

Divide 3 on both sides

20 / 3 ≥ x

x ≥ 6.667

Let's take this as 6

Hence , the domain will be :

D : { 1 , 2 , 3 , 4 , 5 , 6 }

Hope my answer helps!

Answer: A

Step-by-step explanation: x=-2, y=3, z=-3

Answer:

A. -2, 3, -3

Step-by-step explanation:

x = 7 - 2y + z

y = 21 + 6x + 2z = 21 + 6×(7 - 2y + z) + 2z =

= 21 + 42 - 12y + 6z + 2z = 63 - 12y + 8z

13y = 63 + 8z

y = (63 + 8z)/13

2x + 2y - 3z = 11

2×(7 - 2y + z) + 2×(63 + 8z)/13 - 3z = 11

2×(7 - 2×(63 + 8z)/13 + z) + 2×(63 + 8z)/13 - 3z = 11

14 - 4×(63 + 8z)/13 + 2z + 2×(63 + 8z)/13 - 3z = 11

-2×(63 + 8z)/13 - z = -3

-2×(63 + 8z) - 13z = -39

-126 - 16z - 13z = -39

-29z = 87

z = -3

y = (63 + 8×-3)/13 = (63 - 24)/13 = 39/13 = 3

x = 7 - 2×3 + -3 = 7 - 6 - 3 = -2

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Answer:

  D, C

Step-by-step explanation:

The only two rational expressions that have appropriate denominators are ...

  1/(x² +6x) . . . contributes a factor of x to the denominator

  (x+2)/(x² -36) . . . contributes a factor of (x -6) to the denominator

The proper order in the expression is ...

  [tex]\displaystyle\dfrac{x+2}{x^2-36}-\dfrac{1}{x^2+6x}=\dfrac{x^2+x+6}{x(x-6)(x+6)}[/tex]

Answer:

(x+2/x^2-36) - (1/x^2+6x) = (x^2+x+6/x(x-6)(x+6))

Step-by-step explanation:

I hope that helps

Answer:

the number is 788......

Answer:

y =6

Step-by-step explanation:

We can write a ratio to solve

3           y

----- = ----------

4            8

Using cross products

3*8 = 4y

24 = 4y

Divide by 4

24/4 = 4y/4

6 = y

Answer:

4% and 5% respectively

Step-by-step explanation:

Let the intrest rate be x in the first account at x% and (x+1)% in the second account.

ATQ, 100=(x)*1500/100+(x+1)*800/100

x=4.

Answer:

$54

Step-by-step explanation:

10% of $60 is $6

$60-$6=$54

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Answer:

  (x, y) = (0, -2)

Step-by-step explanation:

When solving by substitution, you usually want to find an expression for one of the variables in terms of the other. So, the first thing you look for is an equation that has a coefficient of 1 or -1 on one of the variables. Recognizing that the second equation's terms all have a common factor of 3, you basically have two choices.

Using equation 1, you can write an expression for y:

  y = 5x -2 . . . . . . add 5x to both sides

Then substituting this into the original equation 2, you have ...

  -3x +6(5x -2) = -12

  27x -12 = -12 . . . . . . . simplify

  27x = 0 . . . . . . . . . add 12

  x = 0 . . . . . . . . .  divide by 27

  y = 5(0) -2 = -2 . . . . find y using the expression for substitution

The solution is (x, y) = (0, -2).

__

If you decide you'd rather substitute for x, you can solve the second equation easily for x.

  -3x +6y = -12

  x -2y = 4 . . . . . . divide by -3

  x = 2y +4 . . . . . . add 2y

Substituting for x in the first equation gives ...

  -5(2y +4) +y = -2 . . . . substitute for x

  -9y -20 = -2 . . . . . . . simplify

  -9y = 18 . . . . . . . . .  add 20

  y = -2 . . . . . . . . . . . divide by -9

  x = 2(-2) +4 = 0 . . . . find x using the expression for substitution

The solution is (x, y) = (0, -2).

_____

Additional comment

In some cases, there are no variables that have a coefficient of ±1, so you just need to "bite the bullet" and deal with the resulting fractions.

Example:

  solve for y: -5x +2y = -2

     2y = 5x -2

     y = 5/2x -1 . . . . expression used to substitute for y

Of course, you can multiply the equation after substitution by 2 to eliminate fractions, or just work the problem as is. The point of looking for coefficients of ±1 is to avoid having to do arithmetic with fractions. It can help avoid errors to work with integers, but ultimately the method is the same regardless of the form of the numbers.

__

You don't always have to substitute for the "bare" variable. Sometimes it can save steps to substitute for expressions instead of variables. If our system of equations were ...

You can substitute into the second equation for (2y). In that case, the second equation becomes ...

  -3x +3(2y) = -12

  -3x +3(5x-2) = -12 . . . . . . where 2y = 5x -2