4. Celia is making biscuits. Her recipe calls for 1/3 cup of flour, but
she only has a 1/2 cup measure. About how full should she fill the
measuring cup?

Step-by-step explanation:

\( \frac{x - 9}{15} = \frac{2x - 9}{10} \\ \)

\( \frac{x - 9}{3} = \frac{2x - 9}{2} \\ \)

\(2( x - 9) = 3(2x - 9) \\ \)

\(2x - 18 = 6x - 27\)

\(27 - 18 = 6x - 2x\)

\(9 = 4x\)

\(x = \frac{9}{4} \\ \)

4500 people will stay in Sun City Hotel over a period of 3 years, assuming the monthly average of visitors remains constant throughout this period.

To calculate the number of people who will stay in Sun City Hotel over a period of 3 years, we need to know the total number of months in 3 years.

Since there are 12 months in a year, there are 12 x 3 = <<12*3=36>>36 months in 3 years.

So, if the monthly average of visitors is 125 people, then the total number of people who will stay in the hotel over a period of 3 years is:

125 x 36 = <<125*36=4500>>4500 people.

Therefore, 4500 people will stay in Sun City Hotel over a period of 3 years, assuming the monthly average of visitors remains constant throughout this period.

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Answer: Yes

Step-by-step explanation

Since the number being divided has a 0, it can be divided by 2

Answer:

x = 3

y = 2

Step-by-step explanation:

3x + 2y = 12

-2x + 3y = 5 to find the solution we will use elimination method and for that, multiply second equation with 3 and the first equation with 2

2 * 3x + 2y = 12

6x + 4y = 24

3 * -2x + 3y = 5

-6x + 9y = 15  now find the sum of both equation:

6x + 4y  -6x + 9y = 24 + 15 add like terms

13y = 39 divide both sides by 13

y = 3 now that we found the value of y we can use this to calculate the value of x

3x + 2y = 12 replace y with 3

3x + 2*2 = 12

3x + 4 = 12 subtract 4 from both sides

3x = 9 divide both sides by 3

x = 3

The Expansion of  (√2x + 2y - √3z)² is 2x + 4y + 3z - 2√6xy - 2√6xz - 4√3yz.

To expand the expression (√2x + 2y - √3z)², we can use the following identity:

(a + b + c)² = a² + b² + c² + 2ab + 2ac + 2bc

In this case, we can identify a = √2x, b = 2y, and c = -√3z. So we have:

(√2x + 2y - √3z)²

= (√2x)² + (2y)² + (-√3z)² + 2(√2x)(2y) + 2(√2x)(-√3z) + 2(2y)(-√3z)

Simplifying, we get:

(√2x + 2y - √3z)² = 2x + 4y + 3z - 2√6xy - 2√6xz - 4√3yz

Therefore, (√2x + 2y - √3z)² = 2x + 4y + 3z - 2√6xy - 2√6xz - 4√3yz.

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the volume in the first octant bounded by\(y^2=4−x\) and y=2z is pi/36 sqrt(3).

(1) To find the volume in the first octant bounded by the surfaces \(y^2 = 4 - x\) and y = 2z, we can set up a triple integral in cylindrical coordinates.

First, we need to determine the bounds for our variables. Since we are working in the first octant, we know that 0 <= z, 0 <= theta <= pi/2, and 0 <= r.

Next, we need to find the equation for the upper and lower bounds of z in terms of r and theta. We can start with the equation \(y^2 = 4 - x\) and substitute y = 2z to get:

\((2z)^2 = 4 - x\)

\(4z^2 = 4 - x\)

\(x = 4 - 4z^2\)

We can then use this equation along with the equation z = y/2 to get the bounds for z:

\(0 < = z < = (4 - x)^(1/2)/2 = (4 - 4z^2)^(1/2)/2\)

Squaring both sides, we get:

\(0 < = z^2 < = (1 - z^2)/2\)

\(0 < = 2z^2 < = 1 - z^2\)

\(z^2 < = 1/3\)

So the bounds for z are:

\(0 < = z < = (1/3)^(1/2)\)

Finally, we can set up the triple integral in cylindrical coordinates:

V = ∫∫∫ r dz dtheta dr

with bounds:

0 <= r

0 <= theta <= pi/2

\(0 < = z < = (1/3)^(1/2)\)

and integrand:

r

So the volume in the first octant bounded by y^2=4−x and y=2z is:

V = ∫∫∫ r dz dtheta dr

= ∫ from 0 to\((1/3)^(1/2) ∫ from 0 to pi/2 ∫ from 0 to r r dz dtheta dr\)

= ∫ from 0 to\((1/3)^(1/2) ∫ from 0 to pi/2 r^2/2 dtheta dr\)

= ∫ from 0 to\((1/3)^(1/2) r^2 pi/4 dr\)

\(= pi/12 (1/3)^(3/2)\)

= pi/36 sqrt(3)

Therefore, the volume in the first octant bounded by\(y^2=4−x\) and y=2z is pi/36 sqrt(3).

(2) To find the volume bounded by z = x^2 + y^2 and z = 4, we can use a triple integral in cylindrical coordinates.

First, we need to determine the bounds for our variables. Since we are working in the region where z is bounded by \(z = x^2 + y^2\) and z = 4, we know that 0 <= z <= 4.

Next, we can rewrite the equation \(z = x^2 + y^2\) in cylindrical coordinates as \(z = r^2.\)

So the bounds for r and theta are:

0 <= r <= 2

0 <= theta <= 2pi

And the bounds for z are:

\(r^2 < = z < = 4\)

Finally, we can set up the triple integral in cylindrical coordinates:

V = ∫∫∫ r dz dtheta dr

with bounds:

0 <= r <= 2

0 <= theta <= 2pi

\(r^2 < = z < = 4\)

and integrand: 1

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By solving for the number of employees, there were 70 employees at the party.

An equation is a mathematical statement that shows that two expressions are equal. An equation typically consists of two sides, with an equals sign (=) in between.

A linear equation is an equation in which the highest power of the variable is 1. In other words, a linear equation is an equation that can be written in the form:

ax + b = 0

where a and b are constants and x is the variable.

To find out how many employees attended the party, you can set up the following equation:

Number of employees * $30 per employee = $1000 for space + $850 for food + $250 for decorations

You can then solve for the number of employees by dividing both sides of the equation by $30 per employee:

Number of employees = ($1000 for space + $850 for food + $250 for decorations) / $30 per employee

= $2100 / $30

= 70 employees

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Answer: 1. 26

              2. 12.5

              3. 20%

Step-by-step explanation:

The equation of the line that passes through the point (-6,8) and has a slope of -5/3 is y=-5/3x-2.

Given that the line passes through the point (-6,8) and has a slope of -5/3.

We are required to find the equation of the line whose description is given.

Equation is basically the relationship between two or more variables that are expressed in equal to form. It may be linear equation, quadratic equation or cubic equation. Slope intercept form in the equation be y=mx+c.

We have been given slope be -5/3.

y=mx+c--------------1

Put m=-5/3 in equation 1.

y=-5/3x+c------------2

Put (-6,8) in equation 2.

8=-5/3 *(-6)+c

8=-5*(-2)+c

8=10+c

c=-2

Use the value of c in equation 2.

y=-5/3x-2

Hence the equation of the line that passes through the point (-6,8) and has a slope of -5/3 is y=-5/3x-2.

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\(\large\textsf{Hey there!}\)

\(\large\textsf{\# 1.}\)

\(\large\textsf{4x} \times\large\textsf{3x}\)

\(\large\text{COMBINE the LIKE TERMS}\)

\(\large\textsf{4x}\times\large\textsf{3x = \bf 12x}\mathsf{\bf ^2}\)

\(\boxed{\boxed{\large\textsf{Answer: \bf 12x}\bf ^2}}\huge\checkmark\)

\(\large\text{\# 2.}\)

\(\mathsf{\dfrac{2}{3}+\dfrac{1}{4}}\)

\(\mathsf{= \dfrac{2\times4+1\times3}{3\times4}}\)

\(\mathsf{2 \times 4 = \bf 8}\)

\(\mathsf{1 \times 3 = \bf 3}\)

\(\mathsf{3\times 4 = \bf 12}\)

\(\mathsf{= \dfrac{8 + 3}{12}}\)

\(\mathsf{8 + 3 = \bf 11}\)

\(\mathsf{= \dfrac{11}{12}}\)

\(\boxed{\boxed{\large\textsf{Answer: }\mathsf{\bf \dfrac{11}{12}}}}\huge\checkmark\)

\(\large\textsf{Good luck on your assignment \& enjoy your day!}\)

~\(\frak{Amphitrite1040:)}\)

Answer:

x° = 50°

y° = 70°

z°  = 60°

p° = 50°

(p + 10)° = 60°

(p + 20)° =70°

Step-by-step explanation:

Angles with measurements (p + 20), p and (p + 10) degrees are all on the same line. Therefore these three angles are supplementary angles. In other words the sum of these angles = 180°

Plugging in the expressions for these angles we get

(p + 20 ) + p + (p + 10) = 180°

3p + 30 = 180

Subtracting 150 from both sides,
3p = 180 - 30  = 150

p = 150/3 = 50

x is a vertically opposite angle to p.

Therefor x = p = 50°

y is vertically opposite and equal to p + 20
y = p + 20 = 50 + 20 = 70°

z is vertically opposite and equal to p + 10
z = p + 10 = 50 + 10 = 60°

Answer:

19.05 knots average per hour

Step-by-step explanation:

Distance traveled = 200 nautical miles

Time taken = \(10\frac{1}{2}\)  hours = \(\frac{10\times2+1}2=\frac{21}{2}\) hours

To find:

How many knots did the ship average each hour ?

Solution:

Here, we are given the distance traveled and total time taken to travel the distance.

As per question statement, we have to find the average speed of the ship.

Formula for average speed is given as:

\(\text{Average Speed = }\dfrac{\text{Total Distance traveled}}{\text{Total Time Taken}}\)

Putting the values in the formula:

\(\Rightarrow \text{Average Speed = }\dfrac{200}{\frac{21}{2}}\\\Rightarrow \text{Average Speed = }\dfrac{200\times 2}{21}\\\Rightarrow \text{Average Speed = }\dfrac{400}{21}\\\Rightarrow \text{\bold{Average Speed = 19.05 nautical miles per hour}}\)

It is also given that 1 nautical mile per hours is equal to one know.

Therefore, the average speed can be written as:

19.05 knots average per hour

To find 100,000 less than five hundred sixty thousand, three hundred thirteen, we subtract 100,000 from the given number. The resulting value is four hundred sixty thousand, three hundred thirteen.

To subtract 100,000 from five hundred sixty thousand, three hundred thirteen, we can use the place value chart and place value disks to visualize the operation.

Place Value Chart:

Hundred Thousands Ten Thousands Thousands Hundreds Tens Ones

Given 5 6 0 3 1 3

-100,000 - - - - - -

Result 4 6 0 3 1 3

By subtracting 100,000 from the ten thousands place, we get no change in the value. The result is four hundred sixty thousand, three hundred thirteen. In standard form, the answer is 460,313.

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The time needed for light to travel 42000 Km is 0.14 second.  

Given that,

The speed of the light is = 3 × 10⁸ m/s

Distance travelled by light is = 42000 km = 42 × 10⁶ m [since 1 km = 10³ m]

We have to find the time needed to travel the distance 42000 km by the light.

We know that from the velocity formula,

Speed = Distance/Time

Time = Distance/Speed

Time = (42 × 10⁶)/(3 × 10⁸) = 14 × 10⁻² = 0.14 second.

Hence the time needed for light to travel 42000 Km is given by 0.14 second.  

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Answer:

x > 6

Step-by-step explanation:

2x + 26 + 11 > 49

2x + 37 > 49

2x > 49 - 37

2x > 12

The solution of the expression will be 3, -2, and -22 respectively.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that the expressions are:-

2x²−3x−2 if x is less than or equal to -1

E = 2x²−3x−2

E = 2 (-1) ² - 3 x -1 -2

E = 2 + 3 - 2

E = 3

E = −x²+2x+1 if -1

E = -(-1)² + 2 x -1 + 1

E = -1 - 2 + 1

E = -2

E = −2x²−x−1

E = -2 ( 3 )² - 3 - 1

E = -18 - 3 - 1

E = -22

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Answer:

Step-by-step explanation:

Answer:4/3

Answer:

The tangent of the larger acute angle in a right triangle with side lengths 10, 24, and 26 is 12/5.

Step-by-step explanation:

In a right triangle, the hypotenuse (the side opposite the right angle) is the longest side.

Therefore, in a right triangle with side lengths 10, 24, and 26, the hypotenuse measures 26 units and the legs measure 10 and 24 units.

In a right triangle:

Therefore, the largest acute angle is between the hypotenuse and the shortest leg, which means the side opposite the angle is the longest leg.

The tangent ratio is the ratio of the side opposite the angle to the side adjacent the angle.

Therefore the tangent of the largest acute angle is:

\(\implies \sf \dfrac{O}{A}=\dfrac{24}{10}=\dfrac{12}{5}\)

Answer

It is the first answer.

Step-by-step explanation:

Parallel lines are lines that will never cross each other.

Perpendicular lines are lines that cross each other at 90 degree angles (represented by the box in the corner).

A set of parallel lines and a set of perpendicular lines in this image are; AB║CD, CD ⊥ EF and AB ⊥ EF

Parallel lines have the same slope since the slope is like a measure of steepness and since parallel lines are of the same steepness, thus, are of the same slope.

Since Parallel lines are lines that will never cross each other.

We know that Perpendicular lines are lines that cross each other at 90 degree angles.

The parallel lines are AB and CD, the perpendicular are AB and EF because the first sets are side by side and the second sets cross each other at a certain point.

Therefore the  set of parallel lines and a set of perpendicular lines in this image are; AB║CD, CD ⊥ EF and AB ⊥ EF

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The next three letters in the sequence J F M A M J J A are S, O, N.

To find the next three letters in the sequence J F M A M J J A, we need to identify the pattern or rule that governs the sequence. In this case, the sequence follows the pattern of the first letter of each month in the year.

The sequence starts with 'J' for January, followed by 'F' for February, 'M' for March, 'A' for April, 'M' for May, 'J' for June, 'J' for July, and 'A' for August. The pattern repeats itself every 12 months.

Therefore, the next three letters in the sequence would be 'S' for September, 'O' for October, and 'N' for November.

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The next three letters in the sequence "J F M A M J J A" are "S O N", indicating the months of September, October, and November.

The given sequence "J F M A M J J A" represents the first letters of the months in a year, starting from January (J) and ending with August (A). To find the next three letters in the sequence, we need to continue the pattern by considering the remaining months.

The next month after August is September, so the next letter in the sequence is "S". After September comes October, represented by the letter "O". Finally, the month following October is November, which can be represented by the letter "N".

Therefore, the next three letters in the sequence "J F M A M J J A" are "S O N", indicating the months of September, October, and November.

It is important to note that the given sequence follows the pattern of the months in the Gregorian calendar. However, different cultures and calendars may have different sequences or names for the months.

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Write an example from daily life that uses rational numbers .

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The critical number of the function g(y) is -1/8.

The given function is g(y) = y - 4y^2 - 2y + 8To find the critical points of the given function g(y), we need to follow the below steps:

Step 1: Find the first derivative of the given function g(y) with respect to y.

Step 2: Set the first derivative of g(y) equal to zero.

Step 3: Solve for y to get the critical points of the given function g(y).

Step 1:First, we need to find the first derivative of the given function g(y) with respect to

y.g(y) = y - 4y^2 - 2y + 8

Differentiating with respect to y, we get:g'(y) = 1 - 8y - 2

Step 2:Next, we need to set the first derivative of g(y) equal to zero and solve for y to get the critical points of the given function g(y).g'(y) = 0⇒ 1 - 8y - 2 = 0⇒ -8y - 1 = 0⇒ -8y = 1⇒ y = -1/8

Hence, the critical number of the function g(y) is -1/8.

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50 quarts of sparking water and 25 quarts of grape juice are needed for 75 quarts of punch.

An ordered pair of numbers a and b, represented as a / b, is a ratio if b is not equal to 0. A proportion is an equation that sets two ratios at the same value. The numerical relationship between two values demonstrates how frequently one value contains or is contained within another.

Given that a punch recipe calls for 1(¹/₂) quart of sparkling water and 3/4 of a quart of grape juice.

The ratio of sparkling water to grape juice is,

1(¹/₂) : (3/4 quarts) = (3/2) : (3/4) =  2 : 1

The amount sparkling water in the total volume is 2 : (2+1) = 2/3 of the total volume. For a volume of 100 quarts, the sparkling water content is

2/3 · 75quarts = 50 quarts

Then the grape juice content is,

1/3 · 75 quarts = 25 quarts

Therefore, 50 quarts of sparking water and 25 quarts of grape juice are needed for 75 quarts of punch.

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The time taken for the trip if the return trip was 9 hours is 17 hours.

The outward journey used 432 mph. The return journey was 480 mph and this was for 9 hours.

Let the time taken for the initial trip be x. This will be:

x/9 = 432 / 48

Cross multiply

480x = 432 × 9

x = (432 × 9) / 480

x = 8

Therefore, the initial trip was 8 hours.

The time taken for the whole trip will be:

= Outward trip + Return trip

= 8 hours + 9 hours

= 17 hours.

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The test for an association in this case is a chi-square test of independence.

This is because the chi-square test of independence is used to test for relationships between two categorical variables. For example, if we had two variables, A and B, with two possible outcomes for each (e.g. A: yes/no and B: yes/no), then we could use the chi-square test of independence to determine whether there is an association between the two variables. We could calculate the chi-square statistic using the following formula:

\(χ2= ∑(O-E)2/ E\)

Where O is the observed frequency, and E is the expected frequency. The p-value obtained from the chi-square test can then be used to determine whether the association between the two variables is statistically significant or not.

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False. The expected cell frequency in statistical analysis, specifically in the context of contingency tables and chi-square tests, is not based on the researcher's opinion. Instead, it is determined through mathematical calculations and statistical assumptions.

In contingency tables, the expected cell frequency refers to the expected number of observations that would fall into a particular cell if the null hypothesis of independence is true (i.e., if there is no relationship between the variables being studied). The expected cell frequency is calculated based on the marginal totals (row totals and column totals) and the overall sample size.

The expected cell frequency is computed using statistical formulas and is not influenced by the researcher's opinion or subjective judgment. It is a crucial component in determining whether the observed frequencies in the cells significantly deviate from what would be expected under the null hypothesis.

By comparing the observed cell frequencies with the expected cell frequencies, statistical tests like the chi-square test can assess the association or independence between categorical variables in a data set.

Thus, the statement "the expected cell frequency is based on the researcher's opinion" is false. The expected cell frequency is derived through statistical calculations and is not subject to the researcher's subjective input.

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Answer:

6/7

Step-by-step explanation:

Answer: 6/7

Step-by-step explanation:

Answer:

20

Step-by-step explanation:

\(4 \times 5 = 20\)

Answer:

x=4

Step-by-step explanation:

Step 1: Simplify both sides of the equation.

0.75x+3=6(x−3)

0.75x+3=(6)(x)+(6)(−3)(Distribute)

0.75x+3=6x+−18

0.75x+3=6x−18

Step 2: Subtract 6x from both sides.

0.75x+3−6x=6x−18−6x

−5.25x+3=−18

Step 3: Subtract 3 from both sides.

−5.25x+3−3=−18−3

−5.25x=−21

Step 4: Divide both sides by -5.25.

−5.25x/-5.25    =    -21/-5.25

Answer: x=4

The value of x from the given equation is 4.

The given equation is 0.75x + 3 = 6 (x - 3).

In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

The given equation can be solve for x as follows:

0.75x + 3 = 6x - 18

⇒ 6x-0.75x = 3+18

⇒ 5.25x=21

⇒ x=21/5.25

⇒ x=4

Therefore, the value of x from the given equation is 4.

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Answer:

y=1 1/2x

Step-by-step explanation:

y= mx+c

1st point : (2,3)

2nd point : (4,6)

m= 3-6/2-4

= -3/-2

= 1 1/2

y=1 1/2x