A scientist has two solutions, which she has labeled solution a and solution
b. each contains salt. she knows that solution a is 65% salt and solution b is 80% salt. she wants to obtain 150 ounces of a mixture that is 70% salt. how many ounces of each solution should she use?

Answer:

Step-by-step explanation:

(-2-3)-(4-5)+ (−1+6)−(−9+8)

-5-4+5-1+6+9-8

-9+4+15-8

-5+7

2

Answer:

Subtract the powers, 8-4.

When you simplify that equation itself, the answer is 10,000.

So when you do 10⁴, it's 10,000.

Answer:

B. 1

Step-by-step explanation:

Let's use the formula for finding the mean of a set of data:

mean = (sum of all data values) / (number of data values)

We know that the mean is 2.2, and we have all the other data values except for one. Let's call the missing value "x". The total number of data values is 10 (since there are 10 scores listed in the frequency table). So we can set up an equation:

2.2 = (sum of all 10 data values, including x) / 10

Multiplying both sides by 10, we get:

22 = sum of all 10 data values, including x

We can then subtract the sum of the known data values from both sides to find the missing value:

22 - (01 + 12 + 23 + 31 + 42 + 51) = x

22 - (0 + 2 + 6 + 3 + 8 + 5) = x

x = 22 - 24 = -2

However, a quiz score cannot be negative, so we made a mistake somewhere. Checking the frequency table, we see that there are no scores of 0 or 1, so the missing score must be 0 or 1. Let's try both possibilities:

If the missing score is 0:

2.2 = (01 + 12 + 23 + 31 + 42 + 51 + 0*1) / 10

2.2 = 18 / 10

2.2 = 1.8

This is not true, so the missing score cannot be 0.

If the missing score is 1:

2.2 = (01 + 12 + 23 + 31 + 42 + 51 + 1*?) / 10

2.2 = (18 + ?) / 10

22 = 18 + ?

? = 4

So the missing score is 1, and the answer is B.

Answer:

Answer is B

Total scores/total frequency =mean

54/24=2,25

If you added a score of 1

55/25=2,2

Step-by-step explanation:

hope that helps you

The equaltion for the line of best fit would be,

y = 0.67x + 4.05

The points on the scatter plot are: (1, 3.8), (2, 5.8), (3, 6.2) , (4, 7.5) , (5, 7.2), (6, 8.3), (7, 9.3), and (8, 8.5 )

First we find the mean of the x-values and mean of the y-values.

The mean of the x-values would be,

[tex]\bar{X}[/tex] = (1 + 2 + 3 + 4 + 5 + 6 + 7 + 8) / 8

[tex]\bar{X}[/tex] = 4.5

and the mean of the y-values would be,

[tex]\bar{Y}[/tex] = (3.8 + 5.8 + 6.2 + 7.5 + 7.2 + 8.3 + 9.3 + 8.5) / 8

[tex]\bar{Y}[/tex] = 7.075

The sum of squares (SSX) = 42

And the sum of products (SP) = 28.2

Regression Equation would be,

y = mx + c

m = SP/SSX

   = 28.2/42

   = 0.67143

And the y-intercept would be,

c =  4.05357

So, the equation for the line of best fit would be,

y = 0.67143x + 4.05357

Number of Households = 0.67143 (time) + 4.05357

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Find the complete question below.

The scatter plot shows the number of households, in millions, that have cable television over eight consecutive years.

Scatter plot with x axis labeled Time in Years and y axis labeled Number of Households with points at 1 comma 3 and 8 tenths, 2 comma 5 and 8 tenths, 3 comma 6 and 2 tenths, 4 comma 7 and 5 tenths, 5 comma 7 and 2 tenths, 6 comma 8 and 3 tenths, 7 comma 9 and 3 tenths, and 8 comma 8 and 5 tenths.

The equation which can be used to find the amount the admission tickets cost would be 4x + 25 = 175. The cost of the admission tickets would therefore be $ 37.50.

The total spent by Ms. Boi was $ 175.00 so this is what the entire equation would be equal to. The cost of admission tickets will be denoted as x because they are the unknown figure.

There are 4 tickets purchased so the equation would be:

4 x Cost of tickets - Parking cost = Total spent

4 x - 25 = 175

The cost of each admission ticket is:

4 x - 25 = 175

x = 150 / 4

x = $ 37.50

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Answer:

C is the correct answer.

The sine of the angle ANM is equal to 3/5 as the triangles are similar.

Given that the sine of angle ACB is equal to 3/5, line MN is parallel to BC and MN is midsegment of triangle ABC which implies that the triangles ABC and ANM are similar so;

sine ANM = 3/2 ÷ 5/2

sine ANM = 3/2 × 2/5

sine ANM = 3/5.

Therefore, the sine of the angle ANM is equal to 3/5 as the triangles are similar.

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The probability of choosing a red marble is 6/17.

The probability of an event occurring is the number of favorable outcomes divided by the total number of possible outcomes.

To calculate this probability, we can use the formula:

P(red marble) = number of red marbles / total number of marbles

In this case, we substitute the numbers we know:

P(red marble) = 6 / 17

So the probability of choosing a red marble is 6/17 or approximately 0.35.

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The smallest fraction is 8/12, which is equivalent to 2/3.

To compare fractions, it's best to convert them all to a common denominator.

3/4 is equivalent to 9/12

2/3 is equivalent to 8/12

10/12 is equivalent to 5/6

2/1 is equivalent to 24/12

So, the smallest fraction is 8/12, which is equivalent to 2/3.

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An expression to show how many books would be on each table is a/10

To find out how many books would be on each table, we need to divide the total number of books by the number of tables.

First, let's express the total number of books in terms of a and d. Since we are not given any specific numbers for a and d, we can simply use variables to represent them. Therefore, the total number of books is given by a.

Next, we need to divide a by 10, the number of tables. This gives us the expression:

a/10

So, the above expression shows how many books would be on each table if Mrs. Marcus combines her books and magazines and then divides them among 10 different tables.

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Complete question is:

Mrs. Marcus combines her atlases and dictionaries and then divides them among 10 different tables. If a represents the number of atlases and d represents the number of dictionaries Mrs. Marcus has, write an expression to show how many books would be on each table.

Answer: 3.6 is 5% of 72

Step-by-step explanation: If 3.6 is 5% then just multiply 3.6 by 95 to get 68.4 and add to get 72, Yw.

Where Rectangle ABCD and A’B’C’D’ are similar.

a. the scale factor from ABCD to A’B’C’D’ is 1/2

b. What is the scale factor from A’B’C’D’ to  ABCD is 2

In mathematics, a scale factor is the ratio of matching measurements of an item to a representation of that thing. The copy will be bigger if the scaling factor is a full number. The duplicate will be smaller if the scaling factor is a fraction.

When the scale factor is less than one, you are going from big to small. You are dilating negatively.

When you are going from small to big, you scale factor is reversed. In this case, we had 1/2 in a, in b it became 2/1 which = 2.

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Full Question:

Rectangle ABCD and A’B’C’D’ are similar.

a. What is the scale factor from ABCD to A’B’C’D’?

b. What is the scale factor from A’B’C’D’ to ABCD?

See attached image.

Answer:

2x^2 = (2 x 2) x (2 x 2)

= 4 x 4

= 16

I hope this helps you

Answer:

\( A=\frac{d^2}{2} \).

Step-by-step explanation:

Area of Square by Applying Formula for the Diagonal

We can use the relationship between diagonal length d and the side a length of a square to find its area A. So, the formula for area of square using diagonal is \( A=\frac{d^2}{2} \).

The True statements about the correlation are: (1), (2), (3), (5), (6) and (7)

1) We know that the adding, subtracting, multiplying or dividing a constant to all of the data points in one or both variables does not change the correlation coefficient.

So, the first statement is True.

2) We know that the correlation measures the strength of the pattern around a line of regression as well as the direction of the line. So, interchanging the variables would not change the correlation. The correlation between x and y is the same as the correlation between y and x.

Thus the second statement is True.

3) We know that the correlation coefficient does not have any units.

It is just a number between -1 to +1.

Thus the third statement is True.

4) We know that the outlier may weaken the correlation. It makes the data more scattered. So the correlation coefficient r gets closer to 0.

Thus the fourth statement is False.

5) We know that if the correlation coefficient r is close to 1 then it is a strong positive correlation and if r is close to -1 then it is a strong negative correlation.

Thus the fifth statement is True.

6) We know that the corrletaion coefficient values can range from -1 to 1.

Thus the sixth statement is True.

7) We know that the y-intercept is nothing but the point at which the regression line intercepts the y-axis. The y-intercept of the regression line and the correlation coefficient have the same sign.

Thus the seventh statement is True.

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Answer: The answer is actually 12 pieces of vanilla cake.

Answer:

87 I think.

Step-by-step explanation:

29 x 3 = 87

Answer:

[tex]30d^2[/tex]

Step-by-step explanation:

Answer: To work out 2.1/0.7 without a calculator, you can use long division as follows:

0.7 | 2.1

    1.4   (3 times 0.7 is 2.1)

   -----

    0.7

    0.0   (there is no remainder)

Therefore, 2.1/0.7 = 3, which means that 2.1 is equal to 3 times 0.7.

Answer:

see below

Step-by-step explanation:

2.1

-----

.7

Multiply the top and bottom by 10 to get rid of the decimals.

2.1 *10 = 21

.7 * 10 = 7

21/7 = 3

Step-by-step explanation:

x = -2 or x = 2

x + 2 = 0 or x - 2 = 0

(x + 2) (x - 2) = 0

x² - 4 = 0

The value of proᵥᵥv is (-30/37)i + (42/37)j and the decomposed vector v into v₁ and v₂ are  6 + 6j and -5i + j - 6 respectively.

a. To find the projection of w onto v (proᵥᵥw), we can use the formula,

proᵥᵥw = (w · ȳ)ȳ where ȳ is the unit vector in the direction of v.

First, let's find the unit vector in the direction of v,

|v| = √((-5)² + 7²) = √(74)

ȳ = v/|v| = (-5/√(74))i + (7/√(74))j

Next, let's find the dot product of w and ȳ,

w · ȳ = (-1)(-5/√(74)) + (-1)(7/√(74))

w · ȳ  = 12/√(74)

Finally, we can find the projection of w onto v,

proᵥᵥw = (w · ȳ)ȳ = (12/√(74))((-5/√(74))i + (7/√(74))j)

(w · ȳ)ȳ = (-60/74)i + (84/74)j

(w · ȳ)ȳ = (-30/37)i + (42/37)j

Therefore, the projection of w onto v is (-30/37)i + (42/37)j.

b. v₁ = ((v · w)/|w|²)w

v₂ = v - v₁ where |w| is the magnitude of w. First, let's find |w|,

|w| = √((-1)² + (-1)²)

|w| = √(2)

Next, let's find v · w,

v · w = (-5)(-1) + (7)(-1)

v · w = -12

Using the formula, we can find v₁,

v₁ = ((v · w)/|w|²)w = (-12/2)(-1 - j)

v₁ = 6 + 6j

Now, finding v₂,

v₂ = v - v₁

v₂ = (-5i + 7j) - (6 + 6j)

v₂ = -5i + (7 - 6)j - 6

v₂ = -5i + j - 6

As a result, the vector v can be divided into two parts: v₁ = 6 + 6j and v₂ = -5i + j - 6, where v₁ is parallel to w and v₂ is orthogonal to w.

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Complete question - Given v = - 5i + 7j and w = - 1 - j.

a. Find proᵥᵥv

b. Decompose v into two vectors v₁ and v₂ where v₁ is parallel to w and v₂ is orthogonal to w.

The shortest path from vertex A to vertex L is ACFIL. The total distance of the path is 27 units.

To find the shortest path from vertex A to vertex L, we can use Dijkstra's algorithm. We start by marking the distance of each vertex from A as infinite except for A, which is 0. Then, we choose the vertex with the smallest marked distance and update the distances of its neighbors. We repeat this process until we reach L.

In this case, we would start at A and update the distances of B and D to 2 and 19, respectively. We would then choose B and update the distances of C, F, and E to 11, 10, and 18, respectively.

Next, we would choose F and update the distances of I and L to 27 and 30, respectively. Finally, we would choose L and have found the shortest path from A to L: ACFIL with a total distance of 27.

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Answer: Yes, y = 9(-5)^x represents an exponential function.

An exponential function is a function in the form y = ab^x, where a and b are constants and b is a positive real number not equal to 1. The base, b, is raised to the power of x, and the resulting value is multiplied by the constant a.

In the given function, we have a = 9 and b = -5. Although b is negative, it is still a real number not equal to 1, so the function is still considered exponential. Furthermore, the exponent x is a variable, which is raised to a constant base -5, meeting the definition of an exponential function.

Therefore, y = 9(-5)^x is an exponential function.

Step-by-step explanation:

To explain why A + B is irrational, we need to show that it cannot be expressed as a ratio of two integers.

Suppose that A + B is rational, which means we can write it as the ratio of two integers p and q (where q is not zero):

A + B = p/q

Now, we can substitute the values of A and B and simplify:

√363 + √27 = p/q

We can then rearrange the terms to isolate one of the square roots:

√363 = p/q - √27

We can square both sides of this equation to eliminate the square roots:

363 = p^2/q^2 + 27 - 2(p/q)√27

Notice that the right-hand side of this equation has a term with a square root. This means that if we assume that A + B is rational, we arrive at a contradiction: we have shown that √363 (which is equal to A) is irrational, which means that p^2/q^2 + 27 must also be irrational. However, the left-hand side of the equation is rational. Therefore, our assumption that A + B is rational must be false, and we conclude that A + B is irrational.

To explain why AB is rational, we can use the fact that the product of two rational numbers is rational.

We can rewrite A and B as follows:

A = √(363) = √(121 x 3) = √(11^2 x 3) = 11√3

B = √(27) = √(9 x 3) = √(3^2 x 3) = 3√3

Therefore, AB = 11√3 x 3√3 = 33 x 3 = 99.

Since 99 is a rational number (which can be expressed as the ratio of the integers 99 and 1), we conclude that AB is rational.

A passenger can travel 6.875 miles for $20 using the given taxi fare function.

To determine how many miles a passenger can travel for $20 using the taxi fare function f(x) = 2.56x + 2.40, we need to set up an equation and solve for x.

The equation we need to solve is:

2.56x + 2.40 = 20

To solve for x, we can start by subtracting 2.40 from both sides of the equation:

2.56x = 17.60

Next, we can divide both sides by 2.56:

x = 6.875

This calculation assumes that the fare is based solely on distance and that there are no additional fees or charges.

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Answer:

34

Step-by-step explanation:

This is sequnce has an easy pattern with adding 1 to the difference every time and goes +4, +5, +6 , so the next should be +7

Answer: think it’s a5=34

Step-by-step explanation:

Anna has $165 left in the jar. The solution has been obtained by using the arithmetic operations.

All real numbers are supposed to be explained by the four fundamental operations, often known as "arithmetic operations." In mathematics, operations like quotient, product, sum, and difference occur after operations like division, multiplication, addition, and subtraction.

We are given that Anna saved $20 in a jar each month for 2 complete years and for 9 months of next year.

So, total months = 9 + 12 + 12 = 33

Now, using the multiplication operation, we get

⇒ Total money saved = 33 * 20

⇒ Total money saved = $660

It is given that she spent 75% of her savings on computer.

So, using the subtraction operation, we get

⇒ Amount left = 660 - 75%

⇒ Amount left = $165

Hence, Anna has $165 left in the jar.

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The expressions are written as;

h(t)+k(t) = 10t - 1

h(t)−k(t) = -2t + 1

Note that algebraic expressions are described as expressions that are made up of coefficients, variables, terms, constants and factors.

These expressions are made up of arithmetic operations, which includes;

From the information given, we have that;

h(t)=4t

k(t)=t+5t−1

To determine the value of h(t) + k(t), we have;

4t + t + 5t - 1

add the like terms, we get;

10t - 1

To determine h(t) = k(t)

4t- t - 5t + 1

add like terms

-2t + 1

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Note that in order to map A onto B, Kyle would have to dilate the given figure by a scale factor or 3.

A dilation is a function f from a metric space M into itself that fulfills the identity d=rd for all locations x, y in M, where d is the distance between x and y and r is some positive real integer. Such a dilatation is a resemblance of space in Euclidean space.

The original point of figure A which has 4 points are


(0,02)
(-1, 2)
(0, 1)
(1, 2)

Multiply all th e points by 3, and you get,

(0,02) x 3 = (0, -6) =
(-1, 2) x 3 = (-3, 6)
(0, 1) x 3 = (0, 3)
(1, 2) x3 = (3, 6)

Plotting the new values will give us the transformation (dilation) required. See the attached image.

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