Solve the two step equations
1. -3x - 4 = 23
2. x/2 - 12 = -4
3. 6a + ( -1) = 10
4. - ( x + 2 ) = 12
5. 7a + 12 = 10
6. -4 ( a + 2 ) = 12

Answer:

533.75

Step-by-step explanation:

Given the expression;

64.050÷0.12

Express first as a fraction

64.050 =  64050/1000

0.12 = 12/100

Divide both fractions

= 64050/1000÷12/100

= 64050/1000 *100/12

= 64050/10 * 1/12

= 64050/120

= 533.75

Hence the required answer is 533.75

Answer:

x=9

Step-by-step explanation:

Answer:

89.6 miles

Step-by-step explanation:

[tex]\frac{8}{5}[/tex] = [tex]\frac{x}{56}[/tex]

5x = 448

x=89.6

Step-by-step explanation:

if 8km=5

x =56km

5x=8×56

5x=448

x=89.6 miles

Answer:

(4, 2 )

Step-by-step explanation:

Given the 2 equations

3x + y = 14 → (1)

7x - 4y = 20 → (2)

Rearrange (1) making y the subject by subtracting 3x from both sides

y = 14 - 3x → (3)

Substitute y = 14 - 3x into (2)

7x - 4(14 - 3x) = 20 ← distribute parenthesis and simplify left side

7x - 56 + 12x = 20

19x - 56 = 20 ( add 56 to both sides )

19x = 76 ( divide both sides by 19 )

x = 4

Substitute x = 4 into (3) for corresponding value of y

y = 14 - 3(4) = 14 - 12 = 2

solution is (4, 2 )

Answer:

[tex]3x + y = 14 \\ y = 14 - 3x \\ substitute \: y \: into \: equation \: 2\\ 7x - 4(14 - 3x) = 20 \\ 7x - 56 + 12x = 20 \\ 19x = 76 \\ x = \frac{76}{19} =4 \\ y = 14 - 3( 4 ) = 2 \\ [/tex]

Answer:

12 x sin(85)

12x 0.99619

155.40

Solution:

12 x sin (85) = 11.95 (Since sin85 is 0.996194)

So, the answer is 11.95.

Answer:

μ = 6500

μx= 6500

σx= 76

σ= 450

n= 35

Step-by-step explanation:

Central Limit Theorem

The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

The average game is attended by 6,500 fans, with a standard deviation of 450 people.

This means that [tex]\mu = 6500, \sigma = 450[/tex]

35 games:

This means that [tex]n = 35[/tex]

Distribution of the sample mean:

By the Central Limit Theorem, we have [tex]\mu_x = \mu = 6500[/tex] and the standard deviation is:

[tex]\sigma_x = \frac{450}{\sqrt{35}} = 76[/tex]

Answer:

[tex]\lim_{(x,y) \to (0,0)} \frac{x^2 \sin^2y}{x^2+2y^2} = 0[/tex]

Step-by-step explanation:

Given

[tex]f(x,y) = \frac{x^2 \sin^2y}{x^2+2y^2}[/tex]

Required

[tex]\lim_{(x,y) \to (0,0)} f(x,y)[/tex]

[tex]\lim_{(x,y) \to (0,0)} f(x,y)[/tex] becomes

[tex]\lim_{(x,y) \to (0,0)} \frac{x^2 \sin^2y}{x^2+2y^2}[/tex]

Multiply by 1

[tex]\lim_{(x,y) \to (0,0)} \frac{x^2 \sin^2y}{x^2+2y^2}\cdot 1[/tex]

Express 1 as

[tex]\frac{y^2}{y^2} = 1[/tex]

So, the expression becomes:

[tex]\lim_{(x,y) \to (0,0)} \frac{x^2 \sin^2y}{x^2+2y^2} \cdot \frac{y^2}{y^2}[/tex]

Rewrite as:

[tex]\lim_{(x,y) \to (0,0)} \frac{x^2 y^2}{x^2+2y^2} \cdot \frac{\sin^2y}{y^2}[/tex]

In limits:

[tex]\lim_{(x,y) \to (0,0)} \frac{\sin^2y}{y^2} \to 1[/tex]

So, we have:

[tex]\lim_{(x,y) \to (0,0)} \frac{x^2 y^2}{x^2+2y^2} *1[/tex]

[tex]\lim_{(x,y) \to (0,0)} \frac{x^2 y^2}{x^2+2y^2}[/tex]

Convert to polar coordinates; such that:

[tex]x = r\cos\theta;\ \ y = r\sin\theta;[/tex]

So, we have:

[tex]\lim_{(x,y) \to (0,0)} \frac{(r\cos\theta)^2 (r\sin\theta;)^2}{(r\cos\theta)^2+2(r\sin\theta;)^2}[/tex]

Expand

[tex]\lim_{(x,y) \to (0,0)} \frac{r^4\cos^2\theta\sin^2\theta}{r^2\cos^2\theta+2r^2\sin^2\theta}[/tex]

Factor out [tex]r^2[/tex]

[tex]\lim_{(x,y) \to (0,0)} \frac{r^4\cos^2\theta\sin^2\theta}{r^2(\cos^2\theta+2\sin^2\theta)}[/tex]

Cancel out [tex]r^2[/tex]

[tex]\lim_{(x,y) \to (0,0)} \frac{r^2\cos^2\theta\sin^2\theta}{\cos^2\theta+2\sin^2\theta}[/tex]

[tex]\lim_{(x,y) \to (0,0)} \frac{r^2\cos^2\theta\sin^2\theta}{\cos^2\theta+2\sin^2\theta}[/tex]

Express [tex]2\sin^2 \theta[/tex] as [tex]\sin^2\theta+\sin^2\theta[/tex]

So:

[tex]\lim_{(x,y) \to (0,0)} \frac{r^2\cos^2\theta\sin^2\theta}{\cos^2\theta+\sin^2\theta+\sin^2\theta}[/tex]

In trigonometry:

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

So, we have:

[tex]\lim_{(x,y) \to (0,0)} \frac{r^2\cos^2\theta\sin^2\theta}{1+\sin^2\theta}[/tex]

Evaluate the limits by substituting 0 for r

[tex]\frac{0^2 \cdot \cos^2\theta\sin^2\theta}{1+\sin^2\theta}[/tex]

[tex]\frac{0 \cdot \cos^2\theta\sin^2\theta}{1+\sin^2\theta}[/tex]

[tex]\frac{0}{1+\sin^2\theta}[/tex]

Since the denominator is non-zero; Then, the expression becomes 0 i.e.

[tex]\frac{0}{1+\sin^2\theta} = 0[/tex]

So,

[tex]\lim_{(x,y) \to (0,0)} \frac{x^2 \sin^2y}{x^2+2y^2} = 0[/tex]

Answer:

Random sample, [tex]np \geq 10[/tex] and [tex]n(1-p) \geq 10[/tex], so yes, both conditions were satisfied.

Step-by-step explanation:

60% of the people in a certain midwest city who are responsible for preparing the evening meal have no idea what they are going to prepare as late as 4PM in the afternoon.

This means that [tex]p = 0.6[/tex]

A recent survey was conducted from 1000 of these individuals.

This means that [tex]n = 1000[/tex]

Also, a random sample, so the first condition was satisfied.

The sample size must be large (so that at least 10 or more successes and failures).

[tex]np = 1000*0.6 = 600 \geq 10[/tex]

[tex]n(1-p) = 1000*0.4 = 400 \geq 10[/tex]

So yes, both conditions were met.

Answer:

(a) Increase the differences between the sample means this will increase the Numerator.

(b) Increase the sample variances will increase the denominator.

Step-by-step explanation:  

F Ratio = Variance between treatments/ Variance within treatments.  

Here,  

(a) Increase the differences between the sample means:  

  - Will increase the Numerator and  

  - Size of the F-ratio would increase  

(b) Increase the sample variances:  

 - Will increase the denominator and  

 - Size of the F Ratio would decrease.

Answer:

y = 3

Step-by-step explanation:

Given that the shapes are similar then the ratios of corresponding sides are equal, that is

[tex]\frac{AB}{EF}[/tex] = [tex]\frac{CD}{GH}[/tex] , substitute values

[tex]\frac{3}{2}[/tex] = [tex]\frac{4.5}{y}[/tex] ( cross- multiply )

3y = 9 ( divide both sides by 3 )

y = 3

The answer is They left a 20% tip, so the service was probably above average.

A percentage is a number or ratio that can be expressed as a fraction of 100. A percentage is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, "%", although the abbreviations "pct.", "pct" and sometimes "pc" are also used. A percentage is a dimensionless number; it has no unit of measurement.

here, we have,

First step is to the amount of the sales tax.

If 100% is $73.89,

5.8% will be x (tax):

100% : $73.89 = 5.8% : x.

x = $73.89 * 5.8% : 100%.

x = $4.28.

Now, we have the price for meals, sales tax, and the total amount of money left, so we can calculate how much the tip is:

$93.00 - $73.89 - $4.28 = $14.83.

So, the tip is $14.83.

Let represent it as percent.

If $73.89 is 100%, $14.83 will be x.

$73.89 : 100% = $14.83 : x.

x = $14.83 * 100% : $73.89.

x = 20%.

So, they left a 20% tip, so the service was probably above average.

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Answer:

y=0

Step-by-step explanation:

1. Make variable y as subject for the first equation, which is y= -2x +10

2. substitute the first eq to the second one

3. x - (-2x+10) -5=0

4. solve x, which x = 5

5. substitute in eq 1 which is y= -2x +10

6. solve the eq, the possible solution is y=0

Answer:

729π ft³

Step-by-step explanation:

Applying,

Volume of a cone

V = πr²h/3.............. Equation 1

Where r = radius of the base, h = height, π = pie

From the question,

Given: r = 9 ft, h = 27 ft

Substitite these values into equation 1

V = π(9²)(27)/3

V = 729π ft³

Hence the volume of the figure in terms of π is 729π ft³

Answer:

Step-by-step explanation:

Answer:

0.4466 = 44.66% probability that, in exactly one of the two classes, all 8 students pass.

Step-by-step explanation:

For each student, there are only two possible outcomes. Either they pass, or they do not. The probability of an student passing is independent of other students, which means that the binomial probability distribution is used to solve this question.

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.

Probability that all students pass in a class:

Class of 8 students, which means that [tex]n = 8[/tex]

Each student has a 95% chance of passing their class independent of the other students, which means that [tex]p = 0.95[/tex]

This probability is P(X = 8). So

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

[tex]P(X = 8) = C_{8,8}.(0.95)^{8}.(0.05)^{0} = 0.6634[/tex]

Find the probability that, in exactly one of the two classes, all 8 students pass.

Two classes means that [tex]n = 2[/tex]

0.6634 probability all students pass in a class, which means that [tex]p = 0.6634[/tex].

This probability is P(X = 1). So

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

[tex]P(X = 2) = C_{2,1}.(0.6634)^{1}.(0.3366)^{1} = 0.4466[/tex]

0.4466 = 44.66% probability that, in exactly one of the two classes, all 8 students pass.

Answer:

A. (1, -5), (2, -1), (-1, 7)

Step-by-step explanation:

Reflecting a function over the x-axis:

When a function is reflected over the x-axis, the x-value stays the same, while y changes the signal, so the transformation rule is:

[tex](x,y) \rightarrow (x,-y)[/tex]

To find the range:

We apply the transformation to the points in the domain. Thus:

[tex](1,5) \rightarrow (1,-5)[/tex]

[tex](2,1) \rightarrow (2,-1)[/tex]

[tex](-1,-7) \rightarrow (-1,-(-7)) = (-1, 7)[/tex]

Thus the correct answer is given by option a.

Answer:

It is letter A and please give me brainliest

Step-by-step explanation:

Explanation:

30 years = 30*12 = 360 months

If the monthly payment is $2,223.17 for 360 months, then you'll pay back a total of 2223.17*360 = 800,341.20 dollars overall.

Subtract off the amount financed, or amount loaned, to get the total interest.

800,341.20 - 275,000 = 525,341.20 is the amount of interest paid (in dollars).

This works because effectively, the total amount paid back consists of principal + interest. The principal is the amount the bank loans you.

So we could rephrase that last equation into saying

principal + interest = 275,000 + 525,341.20 = 800,341.20 = total amount paid back.

Answer:

(3 × 3) - (3 ÷ 3) = 8

Step-by-step explanation:

We want to find an expression that when solved will be equal to 8.

But we are restricted to using only the number "3" four times with any Maths operation.

Thus let's try;

(3 × 3) - (3 ÷ 3) = 9 - 1 = 8

Answer:

[tex](a)\ m = \frac{4}{3}[/tex] --- slope of OA

[tex](b)\ y = \frac{4}{3}x[/tex] --- the equation

Step-by-step explanation:

Given

The attached graph

Solving (a): Slope of OA

First, we identify two points on OA

[tex](x_1,y_1) = (0,0)[/tex]

[tex](x_2,y_2) = (3,4)[/tex]

So, the slope (m) is:

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

This gives:

[tex]m = \frac{4-0}{3-0}[/tex]

[tex]m = \frac{4}{3}[/tex]

Solving (b): The equation

This is calculated as:

[tex]y = m(x - x_1) + y_1[/tex]

Recall that:

[tex](x_1,y_1) = (0,0)[/tex]

[tex]m = \frac{4}{3}[/tex]

So, we have:

[tex]y = \frac{4}{3}(x - 0) + 0[/tex]

[tex]y = \frac{4}{3}(x)[/tex]

[tex]y = \frac{4}{3}x[/tex]

Answer:

32P6  

Step-by-step explanation:

nPr

n=32

r=6

Answer:

[tex](a)\ Area = 13.0695[/tex]

[tex](b)\ Area = 26.139[/tex]

Step-by-step explanation:

Given

The attached image

Solving (a): The area (one side up)

This is calculated as:

Area= Area of semicircle + Area of rectangle

So, we have:

[tex]Area = \pi r^2 + l *w[/tex]

Where:

[tex]l,w =2,3[/tex] --- the rectangle dimension

[tex]d = 3[/tex] --- the diameter of the semicircle

So, we have:

[tex]Area = \pi * (3/2)^2 + 2 * 3[/tex]

[tex]Area = \pi * 2.25 + 6[/tex]

[tex]Area = 2.25\pi + 6[/tex]

[tex]Area = 2.25*3.142 + 6[/tex]

[tex]Area = 13.0695[/tex]

Solving (b): Area when both leaves are up.

Simply multiply the area in (a) by 2

[tex]Area = 2 * 13.0695[/tex]

[tex]Area = 26.139[/tex]

Answer:

[tex]Drink = 354.882\ mL[/tex]

Step-by-step explanation:

Given

[tex]Drink = 12oz[/tex]

Required

Equivalent in mL

We have:

[tex]1\ oz = 29.5735\ mL[/tex]

So:

[tex]Drink = 12 * 29.5735mL[/tex]

[tex]Drink = 354.882\ mL[/tex]

Answer:

30 minutes

Step-by-step explanation:

that problem description is imprecise.

I think what is meant here : they each keep jogging at their own same speed.

Diane's speed is 1/3 miles / 10 min.

Jack's speed is 2/3 miles / 10 min.

now, to bring this to regular miles/hour format, we need to find the factor between 10 minutes and an hour (60 minutes) and multiply numerator and denominator (top and bottom of the ratio) by it.

60/10 = 6.

so, we need to multiply both speeds up there by 6/6 to get the miles/hour speeds.

Diane : (1/3 × 6) / hour = 2 miles / hour

Jack : (2/3 × 6) / hour = 4 miles / hour

since Jack is running twice as fast as Diane, she will finish one length in the same time he finishes a round trip (back and forth).

Diane running 1 mile going 2 miles/hour takes her 30 minutes.

Jack running 2 miles (back and forth) going 4 miles/hour will take him also 30 minutes.

so, they will meet at his starting point after 30 minutes.

Answer:

[tex]\displaystyle V = \frac{176 \pi}{15}[/tex]

General Formulas and Concepts:

Pre-Algebra

Algebra I

Calculus

Integrals

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

Integration Rule [Fundamental Theorem of Calculus 1]:                                        [tex]\displaystyle \int\limits^b_a {f(x)} \, dx = F(b) - F(a)[/tex]

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

Integration Property [Addition/Subtraction]:                                                           [tex]\displaystyle \int {[f(x) \pm g(x)]} \, dx = \int {f(x)} \, dx \pm \int {g(x)} \, dx[/tex]

Shell Method:

[tex]\displaystyle V = 2\pi \int\limits^b_a {xf(x)} \, dx[/tex]

Step-by-step explanation:

Step 1: Define

Identify

Graph of region

y = x²

x = 2

y = 4

Axis of Revolution: y = -1

Step 2: Sort

We are revolving around a horizontal line.

Step 3: Find Volume Pt. 1

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

Unit: Applications of Integration

Book: College Calculus 10e

Explanation:

There are 8 different flavors and 3 types of cones. This means there are 8*3 = 24 different combos possible.

Imagine a table with 8 rows and 3 columns. Each row is a different flavor and each column is a different cone type. The table formed has 24 inner cells to represent a different combination of flavor + cone type. So that's why we multiplied those values earlier.

Note: This only works if you're only able to select one type of flavor.

Answer:

-73, -71, -69

Step-by-step explanation:

Suppose the middle of the 3 integers is x.

(x-2)+(x)+(x+2)=-213

x-2+x+x+2=-213

3x=-213

x=-71

The integers are -69, -71, and -73

Answer:

-73,-71,-69

Step-by-step explanation:

Let x represent an odd interger

Odd intergers are serpated by the value of 2 so let the three consective intergers be represented by

[tex](x )+ (x + 2) +( x + 4)[/tex]

Set that equation equal to 213.

[tex]x + x + 2 + x + 4 = - 213[/tex]

[tex]3x + 6 = - 213[/tex]

[tex]3x = - 219[/tex]

[tex]x = - 73[/tex]

Plug -73 in the consective intergers expression.

[tex] - 73 + ( - 73 + 2) + ( - 73 + 4)[/tex]

So our three intergers are

[tex] - 73[/tex]

[tex] - 71[/tex]

[tex] - 69[/tex]

Answer:

C

Step-by-step explanation:

200 x 5 = 1,000

100 x 10 = 1,000

C - 5 to 10 days

Answer:

C. 5 to 10 days

Step-by-step explanation:

If she drove 100 miles per day, then

1000/100 = 10

it took her 10 days.

If she drove 200 miles per day, then

1000/200 = 5

it took her 5 days.

Since she drove between 100 miles and 200 miles per days,

it took her from 5 to 10 days.

Answer: C. 5 to 10 days

Answer:

- A corresponds to A’

- A’AC’ corresponds to B

- CB corresponds to C’A

- ABC ~ A’AC’

Step-by-step explanation:

The equivalent of the products given = 3√7

A perfect square root is said to be a number that gives rise to an integer when it's square root is carried out. Examples are √16, √9 which is 4 and 3 respectively.

√3 × √21

But √a ×√b = √ a×b

Find the prime factors which when multiplied would give 21 = 3 and 7.

Therefore,

[tex] \sqrt{3 \times 3 \times 7} [/tex]

[tex] \sqrt{9 \times 7} [/tex]

[tex] 3 \sqrt{7} [/tex]

Therefore, the equivalent of the products of √3 × √21 =

3√7

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