KC
Apple
Juice
3 cm
7 cm
How many cubic cm of juice can fit into the juice box?
10 cm

Answer:

Alex:Chris 35:15

Step-by-step explanation:

7-3 (ratios)= 4

20 sweets= 4:1

20÷4= 5

5×7= 35 (how many sweets Alex got)

5×3= 15 (how many sweets Chris got)

Alex got 20 more sweets than Chris

(sorry if you didn't understand how I explained it)

By answering the presented question, we may conclude that As a result, the slope of  y3= -4(x - 5) is -4.

Here, we have,

The slope of a line indicates how steep it is. The term "gradient overflow" refers to a mathematical equation for the gradient (the change in y divided by the change in x).

The slope is defined as the ratio of the vertical change (rise) between two places to the horizontal change (run). The slope-intercept form of an equation is used to express a straight line's equation, which is written as y = mx + b.

The y-intercept is found where the slope of the line is m, b is b, and (0, b). For example, the slope and y-intercept of the equation y = 3x - 7 (0, 7). The slope of the line is m. b is b at the y-intercept, and (0, b).

The above equation is in point-slope form: y -y1 = m(x -x1 ), where (x1,y1 ) is a point on the line and m is the slope.

We can see by comparing the provided equation to the point-slope form that (x1,y1) = (5, 3) and m = -4.

As a result, the slope of y3 = -4(x - 5) is -4.

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complete question;

Linear Functions

Quiz Active

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What is the slope of the equation y-3 = -4(x - 5)?

If the distribution of the variable upon which the mean was derived is highly skewed to the right, it may be appropriate to use the t-test if the sample size is large enough.

When conducting research, the t-test is typically used to compare the means of two groups. One of the key assumptions of the t-test is that the population from which the sample was drawn follows a normal distribution.

However, if the distribution of the variable upon which the mean was derived is highly skewed to the right, it may not meet the normality assumption.

In this case, it is appropriate to use the t-test if the sample size is large enough. The t-test is based on the central limit theorem, which states that the sample mean tends to follow a normal distribution as the sample size increases, even if the population distribution is not normal. For large sample sizes (typically n > 30), the t-test is generally considered to be robust to violations of the normality assumption.

However, if the sample size is small, the t-test may not be appropriate, even if the sample mean follows a normal distribution. In this case, alternative statistical tests may be more appropriate. For example, the Wilcoxon rank-sum test can be used to compare the means of two groups when the normality assumption is not met.

In conclusion, if the sample size is small, alternative statistical tests may be more appropriate.

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We get the number of elements in the set B will be 62.

The universal set is A consists of the primary one hundred positive integers.

Set B is a subset of A.

One possibility is that B consists of the primary 62 positive integers.

Then only, the greatest quantity that may be shaped through the sum of any factors of set B is 123.

The number of elements in set B is equal to  62.

We also can selectively interchange one or more elements of B and and add them in complement of B

In most of these instances the number of elements in set B might be 62.

Therefore, we get the number of elements in the set B will be 62.

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The amount in the account after 20 years is $49530.32.

What is continuous compounding?

There is no cap on how frequently interest can compound thanks to continuous compounding. A balance can compound continuously an infinite number of times, which means interest is earned on it constantly.

Given:

Lira will not make any further investments in the withdrawals from the account until it is worth $10000.

Suppose that the interest rate for the account is 8.0% , compounded continuously.

We have to find the amount in the account after 20 years.

Consider, the compounded continuously formula

\(P(t)= P_0e^r^t\)

Where

P(t) = Value at time t.

\(P_0\) = Original principle sum = $10,000

r = Interest rate = 8.0% = 0.08

t = time in years = 20

Plug the values in the above formula

\(P(t) = 10000e^0^.^0^8^*^2^0\\P(t) = 49530.32\)

Hence, the amount in the account after 20 years is $49530.32.

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a) The magnitude of the resultant force exerted on the tree stump is 600N. b) The angle of the resultant force on the x-axis is approximately 36.87°.

a) To determine the magnitude of the resultant force exerted on the tree stump, we can use vector addition. The forces can be represented as vectors, where the first man's force is 360N in the northward direction (upward) and the second man's force is 480N in the eastward direction (rightward).

We can draw a vector diagram to represent the forces. Let's designate the northward direction as the positive y-axis and the eastward direction as the positive x-axis. The vectors can be represented as follows:

First man's force (360N): 360N in the +y direction

Second man's force (480N): 480N in the +x direction

To find the resultant force, we can add these vectors using vector addition. The magnitude of the resultant force can be found using the Pythagorean theorem:

Resultant force (F) = √\((360^2 + 480^2)\)

= √(129,600 + 230,400)

= √360,000

= 600N

b) To find the angle of the resultant force on the x-axis, we can use trigonometry. We can calculate the angle (θ) using the tangent function:

tan(θ) = opposite/adjacent

= 360N/480N

θ = tan⁻¹(360/480)

= tan⁻¹(3/4)

Using a calculator or reference table, we can find that the angle θ is approximately 36.87°.

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Answer: angleAOB = 40°

Step-by-step explanation: Drawing these angles, we see that angle AOC is the sum of angle AOB and angle BOC, so:

angleAOC = angleAOB + angleBOC

108 = 3x + 4 + 8x - 28

108 + 24 = 11x

11x = 132

x = 12

Knowing x, to find angleAOB, just substitute and calculate:

angleAOB = 3x+4

angleAOB = 3.12 + 4

angleAOB = 40°

The angle AOB is 40°.

The value of chi-square statistic (\(X^{2}\)) is 11.26

As per the given question

the sample space of all the four cases are 30

the proportions that land upright are the same when the dropping height is 3, 5, 10, and 20 cm.

the formula of chi-squared test is

\(X^2=\sum\frac{(O_i-E_i)^2}{E}\)

where

\(X^{2}\) is chi-square

\(O_i\) is the observed value

\(E_i\) is the expected value

the upright observed value are 20,23,27,29

the upright expected values are 24.75

now

the chi-square at 3cm height is

\(X^2=\(\frac{(20-24.75)^2}{24.75}\)

=> \(X^2=0.91\)

the chi- square at 5cm height is

\(X^2=\(\frac{(23-24.75)^2}{24.75}\)

=> \(X^2=0.12\)

the value of chi-square at 10cm is

\(X^2=\(\frac{(27-24.75)^2}{24.75}\)

=>\(X^2=0.20\)

the value of chi-square at 20cm is

\(X^2=\(\frac{(29-24.75)^2}{24.75}\)

=> \(X^2=1.97\)

the not upright observed values are

10,7,3,1

the not upright expected values are 5.25

the chi-square test at 3cm height is

\(X^2=\(\frac{(10-5.25)^2}{5.25}\)

=> \(X^2=4.30\)

the chi-square test at 5cm height is

\(X^2=\(\frac{(7-5.25)^2}{5.25}\)

=> \(X^2=0.58\)

the chi-square test at  10cm height is

\(X^2=\(\frac{(3-5.25)^2}{5.25}\)

=> \(X^2=0.96\)

the chi-square test at 20 cm is

\(X^2=\(\frac{(1-5.25)^2}{5.25}\)

=> \(X^2=3.44\)

now,

the total

chi-square value at 3cm height is

=>X^2=0.91+4.30

=> \(X^{2}\)= 5.21

chi-square at 5cm height is

=> \(X^{2}=0.12+0.58\)

=> \(X^2=0.71\)

chi-square at 10cm is

=> \(X^{2}=0.20+096\)

=> \(X^2=1.16\)

chi-square at 20 cm is

=> \(X^{2}=0.73+3.44\)

=> \(X^{2}=4.17\)

now ,

the total chi-square statistic is

=>\(X^{2}=\)5.21+0.71+1.17+4.17

=>\(X^{2}=\) 11.26

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Question 3: True

Question 4: False

Question 5: True

If the derivative of a function, f'(x), is positive for values of x less than c and negative for values of x greater than c, then it indicates a change in the slope of the function. This change from positive slope to negative slope suggests that the function has a maximum value at x = c.

This is because the function is increasing before x = c and decreasing after x = c, indicating a peak or maximum at x = c.

Question 3: If f'(c) < 0 then f(x) is decreasing and the graph of f(x) is concave down when x = c.

True

When the derivative of a function, f'(x), is negative at a point c, it indicates that the function is decreasing at that point. Additionally, if the second derivative, f''(x), exists and is negative at x = c, it implies that the graph of f(x) is concave down at that point.

Question 4: A local extreme point of a polynomial function f(x) can only occur when f'(x) = 0.

False

A local extreme point of a polynomial function can occur when f'(x) = 0, but it is not the only condition. A local extreme point can also occur when f'(x) does not exist (such as at a sharp corner or cusp) or when f'(x) is undefined. Therefore, f'(x) being equal to zero is not the sole requirement for a local extreme point to exist.

Question 5: If f'(x) > 0 when x < c and f'(x) < 0 when x > c, then f(x) has a maximum value when x = c.

True

If the derivative of a function, f'(x), is positive for values of x less than c and negative for values of x greater than c, then it indicates a change in the slope of the function. This change from positive slope to negative slope suggests that the function has a maximum value at x = c. This is because the function is increasing before x = c and decreasing after x = c, indicating a peak or maximum at x = c.

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Answer: 64juu5

Step-by-step explanation:

your gay

Answer: it’s C

Step-by-step explanation: I took the test :)

Answer:

C

Step-by-step explanation:

mark the other guy

:)

Answer:

A rational number

Step-by-step explanation:

If "a" and "b" are integers, then a/b must be rational since it can be written as a fraction.

1. When using completing the square, 2 solution are obtained (option B)

2. if x^2 has a coefficient has then, we divide both sides by the coefficient ( option A)

3. The value of b is 5 ( optionB)

4. All options are quadratic equation

5. The expression ax²+bx+c= 0 is a quadratic equation ( option C)

A quadratic equation is an algebraic equation in which the highest power of it's variable is 2. A quadratic equation is given as ax²+bx+c = 0

for example the equation 2x²= -5x+7 is an example of quadratic equation but should be properly arranged as 2x²+ 5x-7=0. Therefore a= 2, b= 5 and c = -7.

the values of the variable of a quadratic equation always have 2 solutions.

Quadratic equation can be solved by factorization, completing the square and using formula.

When using completing the square method , we make the coefficient of x² to be 1. therefore if it is not 1, we divide both sides by the coefficient of x².

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The volume of the round metal washer is  94.25 cm cube.

As inferred from the question, the shape of the round metal washer is that of a hollow cylinder with:

outer radius=  8 cm

inner radius =2 cm

thickness = 0.5 cm

we know that the formula for calculating the volume of a hollow  cylinder is as follows:

V = π ( \(R^{2}\)-\(r^{2}\))h cubic units

[ where R = outer radius, r= inner radius]

Putting the values in the above formula gives:

V=  π ( 8 - 2) X 0.5

-> V=  π (64-4) X 0.5 = 94.25 cm cube

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The Practice Operations with radical expressions is simplified using the basic of the Algebra:

Algebraic expressions incorporating radicals are known as radical expressions. The root of an algebraic expression makes up the radical expressions (number, variables, or combination of both). The root might be an nth root, a square root, or a cube root. Radical expressions can be made simpler by taking them down to their most basic form and, if feasible, getting rid of all of the radicals.

Radical expressions are simplified by taking them down to their most basic form and, if feasible, altogether deleting the radical. An algebraic expression's numerator and denominator are multiplied by the appropriate radical expression if the denominator contains a radical expression.

Practice Operations with radical expressions are:

1) \(\sqrt{540}\) = \(\sqrt{36 * 15 }\)

= 6√15

2) \(\sqrt[3]{432}\) = \(\sqrt[3]{216*2}\)

= \(6\sqrt[3]{2}\)

3) \(\sqrt[3]{128}\) = \(\sqrt[3]{64*2}\)

= \(4\sqrt[3]{2}\)

4) \(-\sqrt[4]{405}\) = \(-\sqrt[4]{81*5}\)

= \(-3\sqrt[4]{5}\)

5) \(\sqrt[3]{-5000}\) = \(-\sqrt[3]{1000*5}\)

= \(-10\sqrt[3]{5}\)

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The mean height of the boys will be 1.73m.

Mean is defined as the ratio of the sum of the number of the data sets to the total number of the data.

Given that:-

If the mean height of 15 girls is 1.65m, the sum of the girls’ heights is 15×1.65 = 24.75m.

If the mean height of 10 boys is x meters, the sum of the boys’ heights is 10x m. The sum of all 25 students’ heights is

25×1.682=42.05m.

The mean height of the boys.

24.75+10x=42.05,

x =(42.05-24.75)/10

x =1.73m,

Therefore the mean height of the boys will be 1.73m.

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Answer:

$13.44

Step-by-step explanation:

$4.00 x 12 (comic books) = $48

$48 x 28% = 13.44

It is not of exponential order for h(t) = et2. F is of exponential order and has order. F is piecewise continuous. No function's Laplace transform is possible. g(t) = eat, where t [0,.

Non-exponential form:

To represent a scientifically notated number as a non-exponential quantity: • Remove the exponential component of the number by moving the decimal point the same number of places as the exponent's value. The decimal is moved to the right by the same number if the exponent is positive.

Here are a few instances of functions other than exponential ones. y = 3 1 x as a result. n = 0 3 p as a result. Because y = ( 4) x. Since b = 1, y = 6 0 x.

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Julia's estimation for the expression 183 + (76 - 15) + 29, when Rounding each number to the nearest ten, is 270.

To determine Julia's estimation, we need to round each number to the nearest ten and perform the calculation.

Rounding each number to the nearest ten:

183 rounds to 180

76 rounds to 80

15 rounds to 20

29 rounds to 30

Now, let's perform the calculation using the rounded numbers:

183 + (76 - 15) + 29

= 180 + (80 - 20) + 30

= 180 + 60 + 30

= 240 + 30

= 270

Therefore, Julia's estimation for the expression 183 + (76 - 15) + 29, when rounding each number to the nearest ten, is 270.

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The pooled mean standard error is a measure of the variability associated with the difference between two group means in a statistical hypothesis test with equal variances.

The pooled mean standard error is a measure of the variability or uncertainty associated with the difference between two group means in a statistical hypothesis test, where the two groups have equal variances. Specifically, it is the standard error of the difference between the means of two independent samples, calculated by combining the standard errors of the two sample means into a single estimate.

The formula for the pooled mean standard error is:

SEp = \(\sqrt{ [ (s1^2/n1) + (s2^2/n2) ]}\)

where SEp is the pooled mean standard error, s1 and s2 are the standard deviations of the two samples, n1 and n2 are the sample sizes, and sqrt represents the square root function.

The pooled mean standard error is used in the calculation of the t-statistic in a two-sample t-test, which is used to test the hypothesis that there is a significant difference between the means of the two groups. By accounting for the variability of both groups, the pooled mean standard error provides a more accurate estimate of the standard error of the difference between the means, which in turn allows for more precise hypothesis testing.

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Answer:

-2

Step-by-step explanation:

1. reduce the numbers by taking out the greatest common factor which is 9.

2. taking out 9 leaves you with \(-8\) multipied by 1/4

Answer:

-2

Step-by-step explanation:

\((-\frac{8}{9} )\) ÷\((\frac{4}{9})\)

changing division sign to multiplication and doing reciprocal

\(-\frac{8}{9}*\frac{9}{4}\)

9 and 9 gets cancel so,

\(-\frac{8}{4}\)

4 divides 8 exactly by 2 and keep minus sign as it is

-2

Answer:

girl = 7

boy = 5

Step-by-step explanation:

Answer:

boy = 5

girl = 7

The cost of the wall paper per square feet is 0.72 dollars.

The wall paper is rectangular in shape. The dimension of the wall paper is 42 feet by 25.5 feet.

The total cost of the wall paper is 771.12 dollars. Therefore, let's find the cost per square ft.

Hence,

area of the wall paper = 42 × 25.5

area of the wall paper = 1071 ft²

Therefore,

1071 ft² =  771.12 dollars

1 ft² = ?

Hence,

cost per square feet = 771.12  / 1071

cost per square feet = 0.72 dollors

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Answer: y=3x-8, y=5x-8, and y=2x-8

Step-by-step explanation:

These equations are all lines in slope-intercept form (y=mx+b where b is the y-intercept). y=3x-8, y=5x-8, and y=2x-8 all have -8 as the b value. Therefore, these equations have the same y-intercept.

Answer:

m∠A 60°, m∠B= 120°, m∠C =60°, m∠D=120°

Step-by-step explanation:

\( In\: ||^{gm} \: ABCD, \: BK\perp AD... (given) \\

\therefore \angle BKA = 90\degree \\

In\:\triangle BKA, \\\\

\cos \angle A = \frac{AK}{AB}\\\\

\cos \angle A = \frac{3}{6}\\\\

\cos \angle A = \frac{1}{2}\\\\

\cos \angle A = \cos 60\degree.. (\because \cos 60\degree = \frac{1}{2}) \\\\

\huge \red {\boxed {\therefore \angle A = 60\degree}} \\\)

Since, adjacent angles of a parallelogram are Supplementary.

\( \therefore \angle A + \angle B = 180\degree \\

\therefore 60\degree + \angle B = 180\degree \\

\therefore \angle B = 180\degree - 60\degree\\

\huge \purple {\boxed {\therefore \angle B = 120\degree}} \\\)

Since, opposite angles of a parallelogram are congruent.

\( \therefore \angle C = \angle A

\\

\huge \red{\boxed {\therefore \angle C = 60\degree}} \\\\

\therefore \angle D = \angle B

\\

\huge \purple {\boxed {\therefore \angle D = 120\degree}} \\\)

Answer:

12 cups

Step-by-step explanation:

1 quart is 4 cups, so 4 x 3= 12 and 1 x 3 = 3.. Good Luck!