After 8 examinations, Kacey's average was 55. Her next result increased her average to 60. What was the next score?

Step-by-step explanation:

-3 = -3/1

7.3 = 73/10

8 1/3 = 24/3 + 1/3 = (24+1)/3 = 25/3

Answer:  b

Step-by-step explanation:

I think

After considering the given data we conclude that the value of \(x^2 dV\) in cylindrical coordinates is \((16/5) \pi.\)

To evaluate \(x^2 dV\) in cylindrical coordinates, where E is the solid that lies within the cylinder
\(x^2 + y^2 = 9,\)
above the plane z = 0, and below the cone \(z^2 = 9x^2 + 9y^2,\) we can use the following steps:
Express the solid E in cylindrical coordinates. Since the cylinder \(x^2 + y^2 = 9\) is symmetric about the z-axis, we can use cylindrical coordinates (r, \(\theta\), z) to describe the solid.
The cylinder has a radius of 3 in the xy-plane, so we have 0 <= r <= 3. The cone \(z^2 = 9x^2 + 9y^2\) can be expressed in cylindrical coordinates as \(r^2 = 9\), or r = 3. Therefore, the solid E can be described as \(0 < = r < = 3, 0 < = \theta < = 2\pi, and 0 < = z < = \sqrt(9 - r^2).\)
Express \(x^2\) in terms of cylindrical coordinates. Since \(x = r cos(\theta)\), we have \(x^2 = r^2 cos^2(\theta).\)
Express dV in terms of cylindrical coordinates. In cylindrical coordinates, we have \(dV = r dz dr d\theta.\)
Evaluate the integral \(x^2\) dV over the solid E. Substituting the expressions for \(x^2\) and dV, we get:
\(x^2 dV = r^4 cos^2(\theta) dz dr d\theta\)
Integrating over the limits of z, r, and\(\theta\), we get:
\(\int\int\int x^2 dV = \int 0^3 \int 0^2\pi \int 0^{\sqrt(9 - r^2) r^4} cos^2(\theta) dz dr d\theta\)
Integrating with respect to z, we get:
\(\int \int \int x^2 dV = \int 0^3 \int 0^2\pi r^4 cos^2(\theta) \sqrt(9 - r^2) dr d\theta\)
Integrating with respect to r, we can use the substitution \(u = 9 - r^2\), du = -2r dr, to get:
\(\int \int \int x^2 dV = \int 0^3 \int 0^2\pi (9 - u)^{(3/2)} cos^2(\theta) du d\theta\)
Integrating with respect to u, we can use the substitution v = 9 - u, dv = -du, to get:
\(\int \int \int x^2 dV = \int 0^3 \int 0^2\pi v^{(3/2)} cos^2(\theta) dv d\theta\)
Integrating with respect to \theta, we get:
\(\int \int \int x^2 dV = 2\pi \int 0^3 v^{(3/2)} cos^2(\theta) dv\)
Integrating with respect to v, we get:
\(\int \int \int x^2 dV = (16/5) \pi\)
Therefore, the value of \(x^2 dV\)in cylindrical coordinates is \((16/5) \pi.\)
To learn more about cylindrical coordinates,
https://brainly.com/question/31397074
#SPJ4

Answer:

$2,610.37

Step-by-step explanation:

The computation of the amount that should be earn in 15 years is shown below:

As we know that

Future value = Present value × (1 + rate of interest)^number of years

= $1,000 × (1 + 6.5% ÷ 2)^15 × 2

= $1,000 × (1 + 3.25%)^30

= $1,000 × 2.610368439

= $2,610.37

Answer:

B. MT = CA

Step-by-step explanation:

MW should be equal to CD

AD should be equal to TW

MT should be equal to CA

Therefore B is the correct answer

The missing values are derived from the graph as follows:

3 ) 7, 14, 21, 28, 35

4) 3, 7, 10, 14, 17

5) 1, 21, 10, 49, 19

In mathematics, a graph is defined as a graphical representation or diagram that organizes facts or values. The graph's points frequently reflect the relationship between two or more objects.

In order to solve for the above values, the best way is to spot the function that exists in the graph which is given as:

F(y) = 3.5x

In the first table, where x = 2

y= 3.5 *2

= 7

This iteration goes on and on and is consistent for all the values.

In the second table,

Where F(y) is known, for example 10.5, then x is derived as:

10.5 = 3.5x (divide both sides by 3.5)

x = 3

This iteration goes on and on and is consistent for all the values.

In the third table, we simply swap the values back and forth using the function F(y) = 3.5x to derive all values.

Learn more about graphs:

https://brainly.com/question/16608196
#SPJ1

we have AD = CB and AE = EC, which implies that ABCD is a parallelogram. Moreover, since angle A = 90 degrees, we have angle B = angle D = 90 degrees. Therefore, ABCD is a rectangle.

Given that in quadrilateral ABCD, angle A = 90 degrees = angle C, and diagonal AC bisects diagonal BD.

To prove that ABCD is a rectangle, we need to show that its opposite sides are parallel and equal in length.

Let E be the point where diagonal AC intersects BD. Since AC bisects BD, we have BE = ED.

Now, in triangles ADE and CBE, we have:

AD = CB (opposite sides of a rectangle are equal)

Angle ADE = Angle CBE (each is equal to half of angle BCD)

Angle DAE = Angle BCE (vertical angles are equal)

Therefore, by the angle-angle-side congruence theorem, triangles ADE and CBE are congruent. Hence, AE = EC.

To learn more about rectangle visit:

brainly.com/question/29123947

#SPJ11

H(x) is not equal to K(x) and functions H and K are not equal.

Functions H and K are defined from R to R by the formulas:For all x ∈ R, H (x) = (x –2)2 and K (x) = (x – 1)(x – 3) + 1.

Explain.Solution:For all x ∈ R,H (x) = (x –2)2......(1)and K (x) = (x – 1)(x – 3) + 1......(2)To check whether H = K, we will have to verify whether H(x) = K(x) for all x ∈ R.Therefore, we will equate equations (1) and (2) as:H(x) = K(x)(x –2)2 = (x – 1)(x – 3) + 1x2 – 4x + 4 = x2 – 4x + 4 – 3x + 1x2 – 4x + 4 = x2 – 3x + 5x = –1If we analyze the equation x = –1, we can conclude that it is not a member of R (the domain of the functions).Thus, there is no such x ∈ R that satisfies H(x) = K(x).

Therefore, we can say that H(x) is not equal to K(x) and functions H and K are not equal.

A function is a correspondence between two sets that assigns to each element of one set (the domain) exactly one element of the other set (the range).Functions are widely used in mathematics because they allow us to model real-life situations. The input value of a function is called the independent variable, and the output value is called the dependent variable.

Know more about functions here,

https://brainly.com/question/31062578

#SPJ11

Answer:

D, X^2 -18 + 81 = -45 + 81

Step-by-step explanation:

it is complating squer method that used for solving x in a quadratic equetion . in this step you will add

(y/2)^2 if y is the cofitient of x .

the equation (\(x^2 + 3x - 10 = 0\)) has both 2 and -5 as solutions. Therefore the correct option is a.

To determine which equation(s) have both 2 and -5 as solutions, substitute these values into each equation and see if they satisfy the equation. Let's check each option:

a. \(x^2 + 3x - 10 = 0\)

Substituting x = 2:

\((2)^2 + 3(2) - 10 = 4 + 6 - 10 = 0\)

Substituting x = -5:

\((-5)^2 + 3(-5) - 10 = 25 - 15 - 10 = 0\)

Both 2 and -5 satisfy the equation, so option a has both 2 and -5 as solutions.

b. \(x^2 - 3x - 10 = 0\)

Substituting x = 2:

\((2)^2 - 3(2) - 10 = 4 - 6 - 10 = -12\)

Substituting x = -5:

\((-5)^2 - 3(-5) - 10 = 25 + 15 - 10 = 30\)

Neither 2 nor -5 satisfy the equation, so option b does not have both 2 and -5 as solutions.

c. \(x^2 + 7x + 10 = 0\)

Substituting x = 2:

\((2)^2 + 7(2) + 10 = 4 + 14 + 10 = 28\)

Substituting x = -5:

\((-5)^2 + 7(-5) + 10 = 25 - 35 + 10 = 0\)

Only -5 satisfies the equation, so option c does not have both 2 and -5 as solutions.

d. \(x^2 - 7x + 10 = 0\)

Substituting x = 2:

\((2)^2 - 7(2) + 10 = 4 - 14 + 10 = 0\)

Substituting x = -5:

\((-5)^2 - 7(-5) + 10 = 25 + 35 + 10 = 70\)

Only 2 satisfies the equation, so option d does not have both 2 and -5 as solutions.

In conclusion, the equation in option a (\(x^2 + 3x - 10 = 0\)) has both 2 and -5 as solutions.

To learn more about equation

https://brainly.com/question/17482667

#SPJ11

Answer:

1) X = 0

2) X = 0 or X = 1

Step-by-step explanation:

1)

\( \sqrt{6x} + 9 + 2 = 11 \)

6x = 0 since root can only be = 0 if radicand is 0

X = 0

2)

\( \sqrt{x} - 3 + 3 = x\)

\( \sqrt{x} = x\)

X = x^2 ( We are squaring both sides to simplify)

x-x^2 = 0

x (1-x) = 0 (Factor the expression)

X = 0 or

1 -x = 0

X = 1

Answered by Gauthmath

Answer:

-3 and 8

Step-by-step explanation:

take a look at the picture. Hope it helps! Mark Brainliest pleaseee :)

The x intercepts occur where x = 8 and x= -3

A quadratic equation is an algebraic equation of the second degree in x. The quadratic equation in its standard form is \(ax^{2}+bx+c=0\).

The x-intercept is where a line crosses the x-axis

Given,

\(-x^{2} +5x+24=0\)

Factor the expression,

\(-x^{2} +5x+24=0\\-(x^{2} -5x-24)=0\\x^{2} -5x-24=0\\(x-8)(x+3)=0\\\)

Therefore,

x= 8 and x = -3

Hence, the x intercepts occurs where x= 8  and x= -3

Learn more about Quadratic equation and x intercept here

https://brainly.com/question/24177704

#SPJ2

Using One way ANOVA and Randomized block design, the sum of squares between groups (ssb) is equal to the sum of sum of sum of explantary variable A's sum of squares and errors sum of square.

Statistics uses one-way ANOVA to compare the means of three or more independent groups to determine if there is a statistically significant difference between the corresponding population means. It is constructed using the sum of squares measure of total variability used in the numerator of the standard deviation, subtracting the mean, squaring the difference, and adding all observations to obtain the total variability Generate a scale. For multiple groups, we focus on decomposing this total variability (total sum of squares) into the variability between means (the sum of squares of the explanatory variable A) and the variability of the residuals or errors (the error sum of squares).

SSTotal = sum of squares = ∑( yᵢ - Y )²

Total variation is assessed by the total mean (the estimated mean of all observations, available from mean-only models).

SSA = Sum of Squares of Explanatory Variable A

Also called treatment, regression, or model sum of squares. ∑∑(yᵢⱼ - Y' )²

SSE = error (residual) sum of squares

Variation of response around group mean.

Also called the sum of squared residuals.

SSE = ∑∑( Y - Y')²

The total sum of squares is always equal to the sum of the sum of the squares of the explanatory variable A and the sum of the squared errors, SST (total) = SSA + SSE. This equation means that if SSA increases, SSE must decrease if SSTotal remains the same. This result is called the sum of squares decomposition formula.

To learn more about One-way ANOVA test, refer:

https://brainly.com/question/15084465

#SPJ4

Answer:

23

Step-by-step explanation:

Hope this helps! Pls give brainliest!

Answer:

the answer is 23 because this very easy math

Step-by-step explanation:

hope this helps and brainlest

Answer:

If the model is made using a 1:25 scale, then every inch on the model corresponds to 25 inches on the actual house. Therefore, if a part of the model measures 7 inches, the corresponding measurement on the actual house would be 7 * 25 = <<7*25=175>>175 inches.

Step-by-step explanation:

Answer:

5.6

Step-by-step explanation:

11*7=77

11.8*7= 82.6

82.6-77=5.6

Using the Ratio Test the series ∑(n³ / \(4^n\)) converges. Option A is the correct answer.

To determine the convergence or divergence of the series ∑(n³ / \(4^n\)), we can apply the Ratio Test.

The Ratio Test states that if the limit of the absolute value of the ratio of consecutive terms in a series is less than 1, then the series converges. If the limit is greater than 1 or it does not exist, the series diverges.

Let's apply the Ratio Test to the given series:

lim n → ∞ |(\(a_n\) + 1) / \(a_n\)| = lim n → ∞ |((n + 1)³ / \(4^{(n + 1)\)) / (n³ / \(4^n\))|

We simplify the expression by multiplying by the reciprocal:

lim n → ∞ |((n + 1)³ / \(4^{(n + 1)\)) × (\(4^n\) / n³)|

Next, we simplify the expression inside the absolute value:

lim n → ∞ |((n + 1)³ × \(4^n\)) / (\(4^{(n + 1)\) × n³)|

Now, we can cancel out the common factors:

lim n → ∞ |(n + 1)³ / (4 × n³)|

Simplifying further:

lim n → ∞ |(n + 1) / (4n)|³

Taking the limit as n approaches infinity:

lim n → ∞ |(1 + 1/n) / 4|³

Since the limit of the absolute value of the ratio is less than 1 (as n approaches infinity), the series converges.

Therefore, the answer is:

A. Converges

Learn more about Ratio Tests at

https://brainly.com/question/20876952

#SPJ4

The question is -

Use the Ratio Test to determine the convergence or divergence of the series. If the Ratio Test is inconclusive, determine the convergence or divergence of the series using other methods.

∑ n = 1 to ∞ (n³ / 4^n)

lim n → ∞ |(a_n + 1) / a_n| = _______

A. Converges

B. Diverges

Answer:

-9, -8.2, -4, 6, 1 3/4

Step-by-step explanation:

The larger the number is if it's a negative, the lower it is (if that makes sense). For example, -9 is lower than -7.

1 3/4 = 1.75

Answer:

it going be b 65.75

Step-by-step explanation:

just did test

The total amount of money put down by Xi-ling monthly  is mathematically given as

y=65.75

Question Parameters:

Xi-ling has a net income that is 5% of her monthly salary of $2,315. Xi-ling would like to keep a net income of $50

Generally,  5% of her monthly salary   is mathematically given as

x=0.05*2315

x=115.75

Therefore, if she has a net income equal to 115.75

y=115.75-50

y=65.75

Xi-ling puts y=65.75 towards paying down debt each month.

For more information on Arithmetic

https://brainly.com/question/22568180

The "True" or "False" for each of the statements are

Given that

Faces = 12

We have the following statements:

Since there are six even numbers (2, 4, 6, 8, 10, 12) and six odd numbers (1, 3, 5, 7, 9, 11) on the dice, the probability of rolling an even number is the same as the probability of rolling an odd number, which is 1/2.

There is only one face on the dice with the number 11, so the probability of rolling an 11 is 1/12, which is relatively low.

As mentioned above, there are six odd numbers and six even numbers on the dice, so the probability of rolling an odd number is the same as the probability of rolling an even number, which is 1/2.

There are five faces on the dice with numbers less than 6 (1, 2, 3, 4, 5) and seven faces with numbers greater than or equal to 6 (6, 7, 8, 9, 10, 11, 12), so the probability of rolling a number less than 6 is actually lower than the probability of rolling a number greater than or equal to 6.

Read more about probability at

https://brainly.com/question/251701

#SPJ1

Answer:

x = 39.1

Step-by-step explanation:

To find the mean, add up all the data points and then divide by the number of data points

(31.7+ 42.8+ 26.4+ x)/4 = 35

Multiply each side by 4

(31.7+ 42.8+ 26.4+ x)/4*4 = 35*4

(31.7+ 42.8+ 26.4+ x) = 140

Combine like terms

100.9+x = 140

Subtract 100.9 from each side

x = 140-100.9

x = 39.1

The Multiplication property of equality refers to a mathematical concept that states that if two quantities are equal, then multiplying both sides of an equation by the same number will still result in an equal equation.


To understand and apply the multiplication property of equality, you can follow these steps:

1. Identify the given equation or problem that involves multiplication.
2. Determine the desired outcome or solve for a specific variable.
3. Use the multiplication property of equality to simplify or solve the equation.
  - If you multiply both sides of the equation by the same number, the equation will still hold true.
4. Simplify both sides of the equation by performing the multiplication.
5. Continue solving or simplifying the equation until you obtain the desired solution or value.

Remember, it's important to work through the problem step by step and show your work. This will help you understand the concept and ensure accuracy in your answers. If you're having trouble with a specific problem, feel free to ask for assistance by providing the equation or problem details.

Learn more about the multiplication property of equality here: https://brainly.com/question/22088663

#SPJ11

Based on the given clues, we can determine the person, drink, and price paid for each individual:

Calvin: Root Beer, $4.99

Dean: Lemonade, $7.99

Kelli: Water, $6.99

Lee: Iced Tea, $5.99

From clue 1, we know that either Calvin or the person who got the Root Beer paid $4.99. Since Calvin paid more than Lee according to clue 4, Calvin cannot be the one who got the Root Beer. Therefore, Calvin paid $4.99.

From clue 2, Kelli paid $6.99.

From clue 3, the person who got the water paid $1 less than Dean. Since Dean paid the highest price, the person who got the water paid $1 less, which means Lee paid $5.99.

From clue 5, the person who got the Root Beer paid $1 less than the person who got the Iced Tea. Since Calvin got the Root Beer, Lee must have gotten the Iced Tea.

Therefore, the final assignments are:

Calvin: Root Beer, $4.99

Dean: Lemonade, $7.99

Kelli: Water, $6.99

Lee: Iced Tea, $5.99

Learn more about word problems at https://brainly.com/question/21405634

#SPJ1

Answer:  A. $970

Step-by-step explanation:

An individual earning $60,000 would pay 10% on the first $9,700 they earned then pay for remaining amount earned depending on which tax brackets the amount falls within.

Answer:

x =< 2

Step-by-step explanation:

5x - 6 =< 2 + (3x - 4)

5x - 6 =< 2 + 3x - 4

5x - 3x =< 2 - 4 + 6

2x =< 4

x =< 2

Answer:

349.02 / 42 = answer

Step-by-step explanation:

method used is dividing total cost by number of goods used gives the exact cost of each plant