75% of the marbles in a bag are orange and the rest are blue. What fraction of the orange marbles must be removed from the bag so that 50% of the remaining marbles are orange?

Answer:

In both cases we get the same answer: the sum of the first 100 positive even numbers is 10,100.

Step-by-step explanation:

2 + 4 + 6 + 8 + ....+ 198 + 200 =

= (2 + 200) + (4 + 1998) + ... + (100 + 102) = 50*202 = 10,100

Part A

start by naming the variables you will be using in the system of equation

x= number of two-point baskets

y= number of three-point baskets

since she did 23 baskets the first equation representing the number of baskets she made will be

the second equation will be for the points, taking into account that x is 2 points and y is 3 points and she made 53 points.

Part B

Since the equations are not in the slope-intercept form they will be more complicated to graph, which using substitution it will be faster to find the solution of the system.

However both methods could be used.

Part C

Using the mathematical operation of division, Mrs. Doctor can fill 15 mugs using 10 cups.

The division operation is one of the basic mathematical operations.

The division operation involves using the divisor to divide the dividend, which results in a quotient.

For instance, since the pot holds 10 cups and the distribution is 2/3 cups for each mug, we can divide 10 cups by 2/3 cups to get 15 mugs.

The quantity of hot chocolate for each mug = 2/3 cups

The total number of cups that the pot holds = 10 cups

The number of mugs that can be filled from 10 cups = 15 (10 ÷ 2/3)

Thus, we can divide 10 cups by 2/3 cups to get the number of mugs Mrs. Doctor can fill.

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The power of each term in the expressions is D and E are positive integer. So, the expressions are a polynomial.

A polynomial is a type of algebraic expression in which the exponents of all variables should be a whole number. The exponents of the variables in any polynomial have to be a non-negative integer. A polynomial comprises constants and variables, but we cannot perform division operations by a variable in polynomials.

A) [tex]x^{-2}+15x-3[/tex]

Here, the exponent of x is -2. So, the expression is not a polynomial.

B) [tex]-x^3+5x^2+7\sqrt{x} -1[/tex]

Here, the power of one of the term is 1/2. So, the expression is not a polynomial.

C) [tex]\frac{3}{5}x^4-18x^2+5-\frac{10}{x^2}[/tex]

Here, the power of one of the term is -2. So, the expression is not a polynomial.

D) 5.3x²+3x-2

Here, the power of each term is positive integer. So, the expression is a polynomial.

E) [tex]4x^4-10[/tex]

Here, the power of each term is positive integer. So, the expression is a polynomial.

The power of each term in the expressions is D and E are positive integer. So, the expressions are a polynomial.

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Answer:

angle 4 and 5 are interior angles, and 3 and 6 as well

The problem states that "three increased by a quotient", this implies that the three is separated from the quotient, therefore, we need to create the equation in the following manner:

The correct answer is "b".

Answer:x>-11/2

search it for a better understanding of the understanding the question

Answer:

x > -11/2

Step-by-step explanation:

Given inequation,

→ 12(x + 3) > 4x - 8

Now the value of x will be,

→ 12(x + 3) > 4x - 8

→ 12x + 36 > 4x - 8

→ 12x - 4x > -8 - 36

→ 8x > -44

→ [ x > -11/2 ]

Hence, value of x is -11/2.

Step-by-step explanation:

You would start off with solving inside, the parenthesis, and you would get -8/27.

Then, your would solve the 1 1/4 - 3/4 and get 1/2.

You then have to multiply -8/27*1/2, which is -4/27.

Lastly, you divide by negative 4.

-4/27 divided by -4.

You have to flip it to multiply the reciprocal, and you get -4/27*-1/4.

Since negative times negative is positive, the answer would be 1/27.

Answer:

1/27

Hope this helped! :)

Answer:

A would be the correct answer because to find a function when you draw a line on the graph, the line cannot cross each other. Even if the line is verticle, it is still crossing each other.

Step-by-step explanation:

Answer:

Step-by-step explanation:

Let the green graph be G and the blue graph, be B:

1) Be cognate of the fact that the function in blue is completely negative, while the upper green graph is positive

Note: First, we should note that the blue function must therefore be a transformation of the Green function.

This means B takes the form:

y = (s)*a*|X+b|

We are required to find a, b, and s, where s is the sign.

2) From (1), we can deduce that, if graph G was transformed into B, then the first transformation begins by reflecting G along the X-axis (multiplying by -1).

Therefore, s = -1

3) From (2), it follows that the first transformation produces the following effect:

y = |X| transformed to y = -|X|

and B now takes the form y = -a*|X+b|

4) We notice again that the apexes of both functions do not touch. This means G was not only reflected along the X-axis but was also shifted or translated along the X-axis.

5) Building from (4), we notice that the Blue function takes a value of 0 when x is 1. If we put this in the general equation for B;

y = -a*|X+b| implies;

0= -a*|1+b|      

|1+b| = 0/-a

|1+b| = 0

1+b = 0

and y becomes:

Notice also that when the x is 5, the Blue function now takes a value of -1. If we put this in a general equation for B;

y = -a*|X-1|

-1 = -a*|5-1|

-1 = -a*|4|

-4a = -1

Blaise M.

The advantage and disadvantages are sampling.

We have to find the advantages and disadvantages of sampling.

The advantage is:

It provides an opportunity to do data analysis with a lower likelihood of carrying an error.

Researchers can analyze the data that is collected with a smaller margin of error thanks to random sampling. This is permitted since the sampling procedure is governed by predetermined boundaries. The fact that the entire procedure is random ensures that the random sample accurately represents the complete population, which enables the data to offer precise insights into particular topic matters.

The disadvantage is:

No extra information is taken into account.

Although unconscious bias is eliminated by random sampling, deliberate bias remains in the process. Researchers can select areas for random sampling in which they think particular outcomes can be attained to confirm their own bias. The random sampling does not take into account any other information, however sometimes the data collector's supplementary information is retained.

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given the proportion :

we will find x as follows:

So, the answer is: x = 32

The factors of the quadratic equation 5x^2 + 44x - 9 are (5x - 1) and (x + 9)

In Mathematics, factorization or factoring is defined as the breaking or decomposition of an entity (for example a number, a matrix, or a polynomial) into a product of another entity, or factors, which when multiplied together give the original number or a matrix, etc.

In the given question, we can factorize 5x^2 + 44x - 9 by finding two factors that when they multiply will give us the original polynomial.

The factor for this polynomial or quadratic equation are (5x - 1)(x + 9).

This can be summarized as the factorization of 5x^2 + 44x - 9 is (5x -1)((x+ 9)

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The given statement can be written algebraically as follow:

3(7 - x)

3 means '3 is multipled by' and the factor (7-x) means 'the difference of seven and a number'

s is 4/15 of the equation one sixth plus s equals 21 over 30.

Two or more expressions with an Equal sign is called as Equation.

The given equation is

one sixth plus s equals 21 over 30

This can be written as

one sixth can be written as 1/6.

21 over 30 can be written as 21/30.

so the equation is 1/6+s=21/30.

Let us separate the variable s to find the value of s.

s=21/30-1/6

The LCM of 30 and 6 is 30

s=21-5/30

s=16/30=4/15

Hence s is 4/15 of the equation one sixth plus s equals 21 over 30.

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The solution of system of equation is x = 2 and y = 7. We should multiply first equation with 2 so that when we add the two equations, we csystem of equation an eliminate the variable y.

What is system of equation?

Two or more equations that share variables are said to be .

For instance, consider two equations where x and y are shared:

x + y = 6

3x + y = 2

We might be able to solve equations that have the same number of variables. Where the lines intersect in this case is the answer (1,5)

Given system of equation:

5x + 3y = 41,

3x - 6y = 9

Lets multiply the first equation with 2, we get

10x + 6y = 82

Adding these equation with second given equation we get,

10x +6y +(3x - 6y) = 82 + 9

13x = 91

x = 91/13

x = 7

putting the value of x in any one equation

3(7) -6y = 9

y = 2

Therefore, the x and y in the given system of equation are 7 and 2 respectively.

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Given that the backyard is rectangular and the length is 56 feet while the area is 1400 square feet. Recall that the area A of a rectangle is the product of the length L and the width B.

A = L * B

Hence the width B may be found from

1400 = 56 * B

B = 1400/56

B = 25 feet

b. If the fencing cost $10 per foot then because a rectangle has two lengths and two widths,

the total cost to fence the backyard will be

= $10 * 2(56 + 25)

= $1,620

A) To find the length AC, we must use the trigonometric ratio

adjacent = 5cm

hypothenuse = AC

B) To find the length AB, we will use the value of AC just obtained to get it

since triangle ABC is a right-angled triangle, we will use Pythagoras theorem

so that

|AC|^2 = |AB|^2 +|BC|^2

AC = 5.8332cm

BC = 4cm

|AB|^2 = |AC|^2 - |BC|^2

C) The perimeter of the quadrilateral can be found by adding the length of all the sides around its edges.

Perimeter = AD +CD + BC + AB

We do not have CD and we must find CD

Perimeter of ABCD = 5 + 3.004366195 + 4 +4.245729883 = 16.25009708cm

D) To find the area of the quadrilateral we must find the area of triangle ADC and triangle ABC.

Area of triangle ADC = 1/2 x base x height= 1/2 x 3.004366195 x 5 = 7.510915488 square centimeter

Area of triangle ABC = 1/2 X base x height = 1/2 x 4 x 4.245729883 =8.491459766 square centimeter

Area of quadrilateral ABCD = 7.510915488 + 8.491459766 = 16.00237525 square centimeter

SOLUTION

From the question

Cross multiplying you have that

Hence, the answer is 70

EXPLANATION

Since the initial amount of money was of $29,820, and the account earns interest rate by a reason of 7% per year, we can use the simple interest rate equation as shown as follows:

Where P=Principal= 29,820, r=rate in decimal form=7/100=0.07 , t=time in years=4,

Plugging in the numbers into the expression:

Multiplying numbers:

Adding the Interest to the Initial Capital: 29,820+8,349 = 38,169

In conclusion, Colin will have $38,169 after 4 years

Answer:

7/6 feet

Step-by-step explanation:

The board is 3 and 1/2 feet long, so it is 3+(1/2) feet long.

3 + 1/2 = ?

3/1 + 1/2 = ?

6/2 + 1/2 = ?

(6 + 1)/2 = ?

= 7/2

3 + 1/2 = 7/2

In other words, the board is 7/2 feet long.

Now we have to divide by 3 since Andrea is cutting the board in three pieces.

So:

(7/2)/3       or        (7/2) ÷ 3       or        [tex]\frac{\frac{7}{2}}{3}[/tex]        or     (7/2) × (1/3)

= 7/(2×3)

= 7/6

So we found that each piece (after cutting the board into three pieces) is 7/6 feet long.

The reasonable domain and range are 0 ≤ x ≤ 15 and 0 ≤ y ≤ 360 and the domain is continuous

From the question, we have

Gallon gas tank = 15 gallons

This means that the domain is from 0 to 15

This can be represented as 0 ≤ x ≤ 15

For the range, we have

0 * 24 ≤ y ≤ 15 * 24

Evaluate

0 ≤ y ≤ 360

This means that

Range: 0 ≤ y ≤ 360

Lastly, the domain of the situation is continuous

This is so because the gas in the tank can take decimal values

Take for instance, the gas tank can be 13.79 gallons full

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Yes, conditions of randomness and normality of the population met for this test.

The textbook committee made a histogram of the sample data, and it was single peaked with no outliers. The conditions of randomness and normality of the population met for this test, the reason is that it was a random sample, and the plot of the sample data has no outliers.

So, yes, conditions of randomness and normality of the population met for this test.

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The function; g(x)=f(x+ 2)+2, it follows that the vertex of the function is;

(5, 3+2) +2 = (5, 5) + 2

Given,

A quadratic function y=f(x)y=f(x) is plotted on a graph and the vertex of the resulting parabola is (5, 3)(5,3).

To find the what is the vertex of the function defined as g(x)=f(x+2)+2g(x)=f(x+2)+2

Now,

What is the equation of the parabola?

Let the point (h, k) be the vertex of the parabola and a be the leading coefficient.

Then the equation of the parabola will be given as,

y = a(x - h)² + k

A quadratic function y = f(x) is plotted on a graph and the vertex of the resulting parabola is (5, 3).

Hence, if the function; g(x)=f(x+ 2)+2, it follows that the vertex of the function is; (5, 3+2) +2 = (5, 5) + 2.

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‘B’ had a better college entrance exam score due to the higher value of Z-Score.

The Z-score of an observation is the number of standard deviations it falls above or below the mean. Standard deviation is a statistic that is used to measure the dispersion of a dataset relative to its mean and is calculated by doing the square root of the variance.

[tex]Z=\frac{(observation-mean)}{standard deviation}[/tex]

By putting the values as given in the question,We get,

A's score is (600 - 500) / 200 = 0.5 standard deviation i.e. above the mean.

B's score is (25 - 20) / 5 = 1 standard deviations i.e. above the mean.

Thus ‘B’ had a better score.

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If two lines are perpendicular, it means that the slope of one line is equal to the negative reciprocal of the slope of the other line. Given a value, a/b, the negative reciprocal of a/b is - b/a.

From the information given, the slope of the red line is 2/5. This means that the slope of the green line which is perpendicular to the red line is - 5/2

Option D is correct

The correct option regarding the error in the proportional relationship is given as follows:

Row 2 should show 6 feet is equivalent to 182.88 centimeters.

A direct proportional relationship is a function in which the output variable y is calculated by the multiplication of the input variable x and the constant of proportionality k, as follows:

y = kx.

In the context of this problem, the input and the output are given as follows:

The constant is calculated dividing the output by the input of each of the lengths, hence:

Due to the different ratio, the mistake is in Row 2, and the correct value should be of:

6 x 30.48 =182.88 centimeters.

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ANSWER

EXPLANATION

Given;

Recall;

Therefore, the time taken is 3.2hours.

Answer:

32x – 72

OR

–72 + 32x

Step-by-step explanation:

To use the Distributive Property, just simply follow my steps:

Write the equation:

–8(9 – 4x)

To distribute, multiply the numbers inside the parenthesis by the number outside of the parenthesis SEPARATELY. It should look like this:

(–8 • 9)(–8 • –4x)

(–72)(32x)

Since the 32 is positive, the equation could be written either way:

–72 + 32x

OR

32x – 72

If you want the equation to be fully solved...

Set the equation equal to zero:

32x – 72 = 0

Isolate the variable. Subtract 72 from both sides:

32x – 72 + 72 = 0 + 72

32x = 0 + 72

32x = 72

Divide:

32x/32 = 72/32

x = 9/4 (Improper Fraction Form)

OR

x = 2 (and) 1/4 (Mixed Number Form)

Convert 9/4 to a decimal:

x = 9/4

x = 2.25

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answer to the question that you have

2,048.0

2050 because

1-9 = ones place

10-99 = tenth place

100-999 = hundrends place

1000 - 999999 - thousands place

and you round to the nearest 0 if it is 5 or up and if it is 1 to 4 it stays the same