The chart below shows how cups of lemonade Marcia sold each hour she had her lemonade stand set up.

Marcia charged 35 cents for each cup of lemonade, how much money did she make in the four hours? ​

Answer:

2 × 2 x 2 x 2 x 2 or 25

Answer:

2*2*2*2*2, which can be also written as [tex]2^5[/tex].

Answer:

23/24

Step-by-step explanation:

To find the total distance of Sunday and Saturday we add 5/8 + 1/3

= 5/8 + 1/3

= 5 × 3/8 × 3 + 1 × 8/3 × 8

= 15/24 + 8/24

= 15 + 8/ 24

= 23/24

Answer:

c

Step-by-step explanation:

Answer:

~c~

Step-by-step explanation:

Complete question is;

Researchers from the Educational Testing Service (ETS) found that providing immediate feedback to students answering openended questions can dramatically improve students’ future performance on exams (Educational and Psychological Measurement, Feb. 2010). The ETS researchers used questions from the Graduate Record Examination (GRE) in the experiment. After obtaining feedback, students could revise their answers. Consider one of these questions. Initially, 50% of the students answered the question correctly. After providing immediate feedback to students who answered incorrectly, 70% answered correctly. Consider a bank of 100 open-ended questions similar to those on the GRE. a. In a random sample of 20 students, what is the probability that more than half initially answer the question correctly? b. Refer to part a . After providing immediate feedback, what is the probability that more than half of the students answer the question correctly?

Answer:

A) 41.2%

B) 95.2%

Step-by-step explanation:

This is a binomial probability distribution problem, so we will use the formula;

P(k) = (n!/(k!(n - k)!) × p^(k) × (1 - p)^(n-k)

A) Initially, 50% of the students answered the question correctly.

Thus, p = 0.5

Also,n = 20

Now, the probability that more than half initially answer the question correctly would be:

P(k > 10)

This can be expressed as;

P(k > 10) = P(11) + P(12) + P(13) + P(14) + P(15) + P(16) + P(17) + P(18) + P(19) + P(20)

P(11) = (20!/(11!(20 - 11)!) × 0.5^(11) × (1 - 0.5)^(20-11) = 0.1602

Similarly,

P(12) = (20!/(12!(20 - 12)!) × 0.5^(12) × (1 - 0.5)^(20-12) = 0.1201

P(13) = (20!/(13!(20 - 13)!) × 0.5^(13) × (1 - 0.5)^(20-13) = 0.0739

Using online binomial probability calculator we can get the remaining values which are;

P(14) = 0.037

P(15) = 0.0148

P(16) = 0.0046

P(17) = 0.0011

P(18) = 0.0002

P(19) = 0.00002

P(20) = 0

Thus;

P(k > 10) = 0.1602 + 0.1201 + 0.0739 + 0.037 + 0.0148 + 0.0046 + 0.0011 + 0.0002 + 0.00002 + 0 ≈ 0.41192 = 41.2%

B) After providing immediate feedback, we are told that 70% answered correctly.

Thus; p = 70% = 0.7

Similar to A above and using online binomial probability calculator, we have;

P(11) = 0.0654

P(12) = 0.1144

P(13) = 0.1643

P(14) = 0.1916

P(15) = 0.1789

P(16) = 0.1304

P(17) = 0.0716

P(18) = 0.0278

P(19) = 0.0068

P(20) = 0.0008

Thus;

P(k > 10) = 0.0654 + 0.1144 + 0.1643 + 0.1916 + 0.1789 + 0.1304 + 0.0716 + 0.0278 + 0.0068 + 0.0008 = 0.952 = 95.2%

Answer:

31-32

Hyposis: SHe is the mother.

Conclusion: She's not.

Step-by-step explanation:

Solution:

Given:

Substitute the value of x into the expression.

[tex]5\sqrt{x - 1} + 9[/tex]

[tex]\rightarrow 5\sqrt{10 - 1} + 9[/tex]

Simplify the root:

[tex]\rightarrow5\sqrt{9} + 9[/tex]

[tex]\rightarrow(5 \times \sqrt{9}) + 9[/tex]

[tex]\rightarrow(5 \times 3) + 9[/tex]

Multiply 5 and 3:

[tex]\rightarrow15 + 9[/tex]

Add 15 and 9:

[tex]\rightarrow24[/tex]

Answer:

b = 3

Step-by-step explanation:

(2,5) is information! x = 2 and y = 5.

Use these values in the equation:

y = x + b

5 = 2 + b

Subtract 2.

3 = b

The equation of the line is y = x + 3.

16 portions

explanation:

12 / 3/4

   = 12 * 4/3 

= 4*4 = 16

Answer:

If your question is set up like this [tex]\sqrt{6x^2-8}=-8x[/tex] then your answer is No solution.

If your question is set up like this[tex]\sqrt{6x^2}-8=-8x[/tex] then your answer is [tex]x=\frac{4(8-\sqrt{6}) }{29}[/tex] or x = 0.765

Hope this helps!

Answer:

I only

Step-by-step explanation:

dy/dx = x + 1 / y -3

(y - 3)dy = (x + 1) dx

integrate

1/2y^2 - 3x = 1/2x^2 + x

1/2y^2 = 1/2x^2 + 4x

y^2 = x^2 + 8x

y = (x^2 + 8x)^1/2

Answer:

220

Step-by-step explanation:

GIven:

Joyce paid $143.00 for an item at the store that was 35 percent off the original price.

To Find:

What was the original price?

Solution:

Since that was 35 percent off the original price

Thus, 100 - 35 = 65

Equation:

143 = 0.65x

DIvide both sides by 0.65

143/0.65 = 0.65x/0.65

x = 220

Check Answer:

220 x 65% = 143

~Lenvy~

Substitute y = tan(x) and dy = sec²(x) dx to transform the integral to

[tex]\displaystyle \int_0^{\frac\pi2} \cot(x) \ln(\sec(x)) \, dx = \frac12 \int_0^\infty \frac{\ln(1+y^2)}{y(1+y^2)} \, dy[/tex]

and we split the integral at y = 1.

Examining the one over [0, 1], expand into partial fractions :

[tex]\dfrac1{y(1+y^2)} = \dfrac1y - \dfrac y{1+y^2}[/tex]

Then

[tex]\displaystyle \int_0^1 \frac{\ln(1+y^2)}{y(1+y^2)} \, dy = \int_0^1 \frac{\ln(1+y^2)}y \, dy - \int_0^1 \frac{y \ln(1+y^2)}{1 + y^2} \, dy[/tex]

In the integral over [1, ∞), substitute y = 1/z :

[tex]\displaystyle \int_1^\infty \frac{\ln(1+y^2)}{y(1+y^2)} \, dy = \int_0^1 \frac{z \ln\left(1+\frac1{z^2}\right)}{1+z^2} \, dz \\\\ = \int_0^1 \frac{z \ln\left(1+z^2\right)}{1+z^2} \, dz - 2 \int_0^1 \frac{z \ln(z)}{1+z^2} \, dz[/tex]

Some terms cancel and we're left with

[tex]\displaystyle \int_0^\infty \frac{\ln(1+y^2)}{y(1+y^2)} \, dy = \frac12 \int_0^1 \frac{\ln(1+y^2)}y \, dy - \int_0^1 \frac{y \ln(y)}{1+y^2} \, dy[/tex]

Use the series expansions of ln(1 + y) and 1/(1 - y) - both are valid for |y| < 1.

[tex]\displaystyle \int_0^1 \frac{\ln(1+y^2)}y \, dy = - \sum_{n=1}^\infty \frac{(-1)^n}n \int_0^1 y^{2n-1} \, dy = -\frac12 \sum_{n=1}^\infty \frac{(-1)^n}{n^2} = \frac{\pi^2}{24}[/tex]

[tex]\displaystyle \int_0^1 \frac{y \ln(y)}{1+y^2} \, dy = \sum_{n=0}^\infty (-1)^n \int_0^1 y^{2n+1} \ln(y) \, dy = -\frac14 \sum_{n=0}^\infty \frac{(-1)^n}{(n+1)^2} = -\frac{\pi^2}{48}[/tex]

Putting everything together, we have

[tex]\displaystyle \int_0^{\frac\pi2} \cot(x) \ln(\sec(x)) \, dx = \frac12\times\frac{\pi^2}{24} - \left(- \frac{\pi^2}{48}\right) = \boxed{\frac{\pi^2}{24}}[/tex]

3x⁴ = 3x³ • x, and

3x³ (x - 2) = 3x⁴ - 6x³

Subtract this from the numerator to get a remainder of

(3x⁴ - 8x³ - x² + 9x + 5) - (3x⁴ - 6x³) = -2x³ - x² + 9x + 5

-2x³ = -2x² • x, and

-2x² (x - 2) = -2x³ + 4x²

Subtract this from the previous remainder to get a new remainder of

(-2x³ - x² + 9x + 5) - (-2x³ + 4x²) = -5x² + 9x + 5

-5x² = -5x • x, and

-5x (x - 2) = -5x² + 10x

Subtract this from the last remainder to get a new one of

(-5x² + 9x + 5) - (-5x² + 10x) = -x + 5

-x = -1 • x, and

-1 (x - 2) = -x + 2

This gives a new remainder of

(-x + 5) - (-x + 2) = 3

3 does not divide x, so we're done.

So, we have

(3x⁴ - 8x³ - x² + 9x + 5) / (x - 2) = 3x³ - 2x² - 5x - 1 + 3/(x - 2)

Answer:

Plug the x values into the equation and the answers are the y values

Answer:

Options A & C are False while Options B & D are true.

Step-by-step explanation:

The definition of least squares regression line is given as;

The Least Squares Regression Line is a line that normally causes the vertical distance from the data points to the regression line to be as small as possible.

The term “least squares” is derived from the fact that the best line of fit is one that minimizes the the sum of squares of the errors which is also called the variance.

From this definition above, we can see that options A and C are false while option B is the perfect definition for the least line of squares.

Now, the point (x-bar,y-bar ) is known as the mean.

However, every least squares must pass through the middle point of the given data. The mean is the middle point of data in regression analysis. Thus, we can infer that the least-squares regression line always passes through the mean which is point (x-bar,y-bar ). Thus, option D is true.

Answer:

[tex]x \: intercept = ( \frac{5}{2} ,0) \\ y \: intercept = (0, \frac{5}{3} )[/tex]

Step-by-step explanation:

STEP 1: Define x and y intercepts

The x-intercept is where a line crosses the x-axis, and the y-intercept is the point where the line crosses the y-axis.

Step 2: We plot the graph of the given function

The graph can be seen in the graph image I sent. The x and y intercepts are also identified.

Answer:

A) 3

Step-by-step explanation:

Ques: 30/(4√3 + 3√2) = 4√3 - a√2

Rationalise the denominator.

→ 30/(4√3 + 3√2) × (4√3 - 3√2)/(4√3 - 3√2) = 4√3 - a√2

→ (120√3 - 90√2)/(48 - 18) = 4√3 - a√2

→ (120√3 - 90√2)/30 = 4√3 - a√2

→ 120√3 - 90√2 = 120√3 - 30a√2

→ 90√2 = 30a√2

On solving we get,

→ a = 3

Ques: 30/(4√3 + 3√2) = 4√3 - a√2

→ 30 = 4√3(4√3) + 4√3(-a√2) + 3√2(4√3) + 3√2(-a√2)

Solve the brackets,

→ 30 = 48 - 4a√6 + 12√6 - 6a

→ - 18 = - 4a√6 - 12√6 - 6a

Put like terms on one side,

→ - 18 + 6a = - 4√6 (a + 3)

Take the common,

→ 3(a - 3) = - 2√6 (a + 3)

→ 3 (a - 3) = 2√6 (-a - 3)

→ [3(a - 3)]/2√6 = - a - 3

Rationalise the denominator,

→ 2√6(3a - 9)/24 = - a - 3

→ (3a√6 - 9√6)/12 = - a - 3

→ √6(a - 3) = - 4a - 12

Do squaring on both sides,

→ [√6(a - 3)]² = - (4a + 12)²

→ 6(a² + 9 - 6a) = - (16a² + 144 + 96a)

Solve the brackets,

→ 6a² + 54 - 36a =  - 16a² - 144 - 96a

→ 22a² - 132a + 198 = 0

→ 11a² - 66a + 99 = 0

→ a² - 6a + 9 = 0

Split the middle term,

→ a² - 3a - 3a + 9 = 0

→ a(a - 3) -3(a - 3) = 0

→ (a - 3)(a - 3) = 0

On comparing we get,

→ a = 3 (key to solve this and similar questions is rationalisation of the denominator)

Hence, the correct option is option A) 3.

Solution:

the percent markdown of the iPad is 17.86%

Given:

Original Price = $700

Final price = $575

The markdown is gotten by;

[tex]Markdown=original~price-final~price[/tex]

[tex]Markdown=700-575[/tex]

Markdown = $125

Thus, the percent markdown is gotten by;

[tex]percent~markdown=\frac{markdown}{original~price}~x~ 100[/tex]

percent markdown = [tex]\frac{125}{700}[/tex] × 100%

percent markdown =[tex]\frac{12500}{700}[/tex]

percent markdown = 17.857 %

percent markdown  ≈ 17.86%

Therefore, the percent markdown of the iPad is 17.86%

Hope this helps!!

If you have any questions please ask.

Explanation:

Any parallelogram has two pairs of opposite sides that are parallel.

A rectangle is a parallelogram, but not the other way around.

Choices A and B are trapezoids with exactly one pair of parallel sides.

Answer:

[tex]\sf\fbox\red{Answer:-}[/tex]

gud noon!

dopamine is responsible for how we feel pleasure

[tex]\small\fbox{\blue{\underline{mαrk \; mє \; вrαínlíєѕt \; plєαѕє ♥}}}[/tex]

Answer:− -19s

Step-by-step explanation:

Move  

Answer:

he Formula h = -16t^2 + vt + s; where

h = height after t seconds

t = time in seconds

v = upward velocity

s = initial height (t=0)

also note that

-16t^2 represents the downward force of gravity for t seconds

+vt = the upward force for t seconds

:

the height when he hits the water = 0 therefore:

0 = -16t^2 + 8t + 24

usually written

-16t^2 + 8t + 24 = 0

we can simplify this, divide by -8, then we have

2t^2 - t - 3 = 0

this will factor to

(2t - 3)(t + 1) = 0

the positive solution

2t = 3

t = 3/2

t = 1.5 seconds to hit the water

-

Form the actual equation

Find vertex as vertex is maximum

x coordinate

y coordinate

Max height is 25m

Time to reach is 0.25s

Answer: A

Step-by-step explanation:

Answer:

The answer is A;
✔ m∠2 + m∠3

Step-by-step explanation:

1)

Take 12x as a common factor

12x(3x-2)

12 since both 36 and 24 are divisible by 12

2)

Take 12x as a common factor again

12x(x-2)

3)

Take 15x as a common factor

15x(3x²-2)

3x²-2 can be written as the difference of 2 squares

15x(√3 x+√2)(√3 x-√2)

Answer:

[tex]12x(3x-2); 12x(x-2); 15x(3x^2-2)[/tex]

Step-by-step explanation:

Look at the coefficients of the first espression. 36 and 24 are both multiples of 12. We can collect 12x from both and we get

[tex]36x^2-24x=12x(3x-2)[/tex]

Second, 12 and 24 are obviously one twice the other, the common factor is again 12x:

[tex]12x^2-24x = 12x(x^2-2)[/tex]

Third polynomial: this time the greatest common divisor of 45 and 30 is 15. Let's collect 15x from either

[tex]45x^3-30x=15x(3x^2-2)[/tex]

Answer:

You would use lbs.

Step-by-step explanation:

mm is a unit of distance.

Oz is too small of a unit for weight.

lbs are just right!

Answer: X minus 1 over 2

Step-by-step explanation:

Use an inverse function calculator

Answer:

18.98°

Step-by-step explanation:

1) p=arcsin(13/40);

2) p=arcsin0.325≈18.98°.

A real-world situation to model the number line is: It was colder on Friday night than Saturday morning because 0 is greater than -1

See attachment for the number line

From the figure, we have the following points

0 and -1

The number line can be modelled by temperature where a colder temperature is represented by 0, while the other temperature is -1 degrees Celsius

Hence, a complete scenario is:

On a Friday night, the measure of the temperature is 0 degrees Celsius. On Saturday morning, the temperature is -1 degree Celsius. It was colder on Friday night than Saturday morning because 0 is greater than -1

Read more about number lines at:

https://brainly.com/question/10851163

The value '0' is between the points above sea level and points below sea level. '0' being neither negative nor positive means it cannot be below or above sea level, rather '0' meters represents sea level.

Hope that helps!