Clare vwas solving an equation, but when she checked her answer she saw her solution was incorrect. She knows she made a mistake, but she can't find it. Where is Clare's mistake and what is the solution to the equation? 12(5 + 2y) = 4y- (5-9y) 72 + 24y = 4y -5-9y 72 + 24y = -5y -5 24y = -5y - 77 29y = -77 -77 y29​

Answer:

a wide divergence between two groups, typically producing tension or hostility.

Step-by-step explanation:

The area of triangle ABC with vertices is 22 square units

The vertices are given as:

A(4, -3) B(9,-3) , and C(10, −11)

The area of the triangle is calculated using

Area = 0.5 * |Ax(By - Cy) + Bx(Ay - Cy) + Cx(Ay - By)|

This gives

Area = 0.5 * |4 * (-3 + 11) + 9 * (-3 + 11) + 10 * (-3 - 3)|

Evaluate the sum of products

Area = 0.5 * |44|

Remove the absolute bracket

Area = 0.5 * 44

Evaluate

Area = 22

Hence, the area of ABC with vertices is 22 square units

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The volume of the prism is

The volume of the prism is solved by the formula

= area of triangle * depth

Area of the triangle

= 1/2 base * height

base = p = cos 51.34 * √41 = 4

height = q = sin 51.34 * √41 = 5

= 1/2 * 4 * 5

= 10

volume of the prism

= area of triangle * depth

= 10 * 7

= 70 cm³

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The dimensions of the fence that will maximize the area are-

Multiply the width by the height of a rectangle to find its area. If we know the lengths of two sides of a rectangle, we can calculate the height and width.

Now, as per the question;

Let 'L'  be the length and,

'W' width of the rectangular

Also, let the river is running along L.

Perimeter to be covered by fence:

P = L + 2W

2700 = L + 2W

Thus, L= 2700 - 2W

Substitute the value of L in the area

Area, A= LW

A = (2700 - 2W)W

A = 2700W - 2W²

This is a quadratic equation;

Now, the vertex of the rectangular with the greatest area will have the greatest width.

(W,A), where W= -b/2a where b = 2700 and a = -2

Solve for W,

W = -2700/2×(-2)

   = -2700/-4

W = 675 ft.

Substitute the value of W in L to find it.

L= 2700 - 2W

 = 2700 - 2×675

L = 1350 ft

Thus, the maximum area will become;

Maximum area A = 1350 × 675

Maximum area A = 911250 sq. ft

Therefore, the maximum area is found to be 911250 sq. ft

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The complete question is-

A farmer has 2700 feet of fencing available to enclose a rectangular area bordering a river. if no fencing is required along the​ river, find the dimensions of the fence that will maximize the area. what is the maximum​ area

Answer:

There are 2 solutions to square root x = 9

They are 3, and -3

Step-by-step explanation:

The square root of x=9 has 2 solutions,

The square root means, for a given number, (in our case 9) what number times itself equals the given number,

Or, squaring (i.e multiplying with itself) what number would give the given number,

so, we have to find the solutions to \(\sqrt{9}\)

since we know that,

\((3)(3) = 9\\and,\\(-3)(-3) = 9\)

hence if we square either 3 or -3, we get 9

Hence the solutions are 3, and -3

Answer:

x=2

Step-by-step explanation:

25/625 is 1/25

1/25 = 1/5^x

1/5 =sqrt 1/25 and that is 2

so x=2.

Hope this helps plz hit the crown :D

The weight of Christensen's family's kitten is 9 pounds 3 ounces.

The imperial unit of mass or weight measurement is the pound. The symbols for pounds are lb and lbm. A kilogram weighs 0.4535 pounds. The term "pound" has Germanic roots.

In the conventional system of measurement, a pound is a unit of weight. 16 ounces make up one pound.

Therefore,

We know that 1 pound = 16 ounces

16 ounces = 1 pound

Dividing each side by 16.

( 16 / 16) ounces = ( 1/16 ) pound

1 ounce = ( 1/16 ) pound

Multiplying each side by 147,

1 ounce × 147 = ( 1/16 ) × 147 pound

147 ounces = ( 147 / 16 ) pounds

147 ounces = 9.1875 pounds

147 ounces = 9 + 0.1875 pounds

147 ounces = 9 pounds 3 ounces

The weight of the kitten is 9 pounds 3 ounces.

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Answer:

question 3 = 9x^2 -81

question 4 = 36x^4-84x^2y^3+49y^6

question 5 = 64x^8 +90x^4y^3+25y^6

Step-by-step explanation:

see photo

The equation holds true, confirming that our solution for v is correct.

The unknown vector v is (6, -3).

To solve for the unknown vector v in the equation c - v = b, we can rearrange the equation to isolate v.

First, let's substitute the given values:

c - v = b

(2, 0) - v = (-4, 3)

Next, we can subtract c from both sides of the equation:

-v = (-4, 3) - (2, 0)

-v = (-4 - 2, 3 - 0)

-v = (-6, 3)

To solve for v, we multiply both components of -v by -1:

v = (6, -3)

The unknown vector v is (6, -3).

To verify our solution, we can substitute the value of v back into the original equation:

c - v = b

(2, 0) - (6, -3) = (-4, 3)

(2 - 6, 0 - (-3)) = (-4, 3)

(-4, 3) = (-4, 3)

The equation holds true, confirming that our solution for v is correct.

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Answer:

x <-2

Step-by-step explanation:

-3x+6>12

Subtract 6 from each side

-3x+6-6>12-6

-3x> 6

Divide each side by -3, remembering to flip the inequality

-3x/-3 < 6/-3

x <-2

The simplified expression is 2cos²(x) + sinx - 1 = 0

The expression we will be simplifying is

=> 1/sinx+cosx + 1/sinx-cosx = 2sinx/sin⁴x-cos⁴x.

To begin, let us look at the left-hand side of the expression. We can combine the two fractions using a common denominator, which gives us:

(1/sinx+cosx)(sinx-cosx)/(sinx+cosx)(sinx-cosx) + (1/sinx-cosx)(sinx+cosx)/(sinx-cosx)(sinx+cosx)

Simplifying this expression using the distributive property, we get:

(1 - cosx/sinx)/(sin²ˣ - cos²ˣ) + (1 + cosx/sinx)/(sin²ˣ - cos²ˣ)

Next, we can simplify each fraction separately. For the first fraction, we can use the identity sin²ˣ - cos²ˣ = sinx+cosx x sinx-cosx to obtain:

1 - cosx/sinx = (sinx+cosx - cosx)/sinx = sinx/sinx = 1

Similarly, for the second fraction, we can use the same identity to obtain:

1 + cosx/sinx = (sinx-cosx + cosx)/sinx = sinx/sinx = 1

Substituting these values back into the original expression, we get:

1 + 1 = 2sinx/(sin⁴x - cos⁴x)

Now, we can simplify the denominator using the identity sin²ˣ + cos²ˣ = 1 and the difference of squares formula:

sin⁴x - cos⁴x = (sin²ˣ)² - (cos²ˣ)² = (sin²ˣ + cos²ˣ)(sin²ˣ - cos²ˣ) = sin²ˣ - cos²ˣ

Substituting this back into the expression, we get:

2 = 2sinx/(sin²ˣ - cos²ˣ)

Finally, we can simplify the denominator using the identity sin²ˣ - cos²ˣ = -cos(2x):

2 = -2sinx/cos(2x)

Multiplying both sides by -cos(2x), we get:

-2cos(2x) = 2sinx

Dividing both sides by 2, we get:

-cos(2x) = sinx

Using the double-angle formula for cosine, we get:

-2cos²(x) + 1 = sinx

Simplifying this expression, we get:

2cos²(x) + sinx - 1 = 0

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Answer: About 0.2 gallons

Step-by-step explanation: 4/18=0.2 repeating, so each person gets about 0.2 gallons.

Each of her friend will get 4 and a half gallons of juice.

Division is one of the four main arithmetical operations by which we find the equal distribution of something.

Given that, At Lara's party, 4 gallon of fruit punch are shared equally among 18 friend.

To find how much each of them got, we will divide total amount of punch  by total number friends

Amount of juice each of them gets, = 18/4 = 4.5

Hence,  Each of her friend will get 4 and a half gallons of juice.

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Answer:

b= 29/11

Step-by-step explanation:

2b+8-5b+3=-13+8b-5

8-5b+3=-13+8b-5-2b

8-5b+3=-13+6b-5

8+3=-13+6b-5+5b

8+3=-13+11b-5

8+3=-18+11b

11=-18+11b

29=11b

b=2.63

Answer: 38.35%

Step-by-step explanation:

59%=59/100=0.59

0.59-0.35(0.59)=

0.59-0.2065=

0.5900-0.2065=

0.3835=38.35%

Answer:

  D.  (y +4)² = -4(x -2)

Step-by-step explanation:

The directrix is a vertical line, and the focus is to the left of it. The parabola will open to the left.

The vertex is halfway between the focus and directrix, so is located on the same horizontal line as the focus, at ...

  x = (1 +3)/2 = 2

The focus to vertex distance is the difference in x-coordinates: 1 -2 = -1. This is the value of p in the form ...

  (y -k)² = 4p(x -h) . . . . . . . parabola with vertex (h, k)

The equation is ...

  (y +4)² = -4(x -2)

_____

Additional comment

Once you determine that the directrix is a vertical line, you know the equation will have a y² term. The only answer choice that has that is D.

Answer:

radius: 8.4   Area: 221.5

Step-by-step explanation:

16.8 divided by 2 = 8.4

The Formula for finding the area of circle= R₂ (radius squared: radius times itself) Multiplied by pi. pi = 3.14

8.4₂ multiplied by 3.14

The probability that a visitor did not make a purchase and did not visit MSN (visited Yahoo) is 43.75%. The probability the visitor visited Yahoo if the visitor did not make a purchase is 0.4. The probability that a visitor makes a purchase or visits MSN is 48%.

Given Information: Number of visitors = 120

Probability of making a purchase = 0.25

Probability of visiting Yahoo = 0.4

Probability of visiting MSN = 0.3

Formula: Probability of an event = Number of ways that event can occur / Total number of possible outcomes

Answer 1: To find the probability that a visitor did not make a purchase and did not visit MSN (visited Yahoo),

First, we need to find the probability of not making a purchase and not visiting MSN.

P(not purchase and not MSN) = 1 - P(purchase or MSN) [Using De Morgan's law]

P(purchase or MSN) = P(purchase) + P(MSN) - P(purchase and MSN) [Using the Addition Rule]

P(purchase or MSN) = 0.25 + 0.3 - (0.25 * 0.3) = 0.475

P(not purchase and not MSN) = 1 - 0.475 = 0.525

Now, we can use the formula to find the probability.

Probability of a visitor did not make a purchase and did not visit MSN (visited Yahoo) = 0.525/120 = 0.004375 ≈ 0.4375 ≈ 43.75%

Answer 2: If the visitor did not make a purchase, the probability the visitor visited Yahoo,

P(Yahoo | Not purchase) = P(Yahoo and Not purchase) / P(Not purchase) = (0.4*0.75)/0.75 = 0.4

Now, we can use the formula to find the probability.

P(Yahoo | Not purchase) = 0.4

Answer 3: To find the probability that a visitor makes a purchase or visits MSN,

P(purchase or MSN) = P(purchase) + P(MSN) - P(purchase and MSN) [Using the Addition Rule]

P(purchase or MSN) = 0.25 + 0.3 - (0.25 * 0.3) = 0.475

Now, we can use the formula to find the probability.

P(purchase or MSN) = 0.475 ≈ 0.48 ≈ 48%

Therefore, The probability that a visitor did not make a purchase and did not visit MSN (visited Yahoo) is 43.75%. The probability the visitor visited Yahoo if the visitor did not make a purchase is 0.4. The probability that a visitor makes a purchase or visits MSN is 48%.

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(A) If Two independent events, A and B, are such that P(A) = 0. 2 P(A U B) = 0. 8, then probability P(B) =  5/8.

The possibility of the result of any random event is referred to as probability. This term refers to determining how likely an event is to occur. What are the chances of getting a head when we toss a coin in the air, for instance? The quantity of outcomes depends on the response to this question. Here, the outcome could be either head or tail. Thus, there is a 50% chance that the result will be a head.

The probability serves as a gauge for the likelihood that an event will occur. It gauges how likely an event is to occur. The probability equation is given by;

P(E) = Number of Favourable Outcomes/Number of total outcomes

We know that

P(A∪B) = P(A) + P(B) - P(A∩B)

P(A∪B) = P(A) + P(B) - P(A).P(B)

0.8 = 0.2 + P(B) - 0.2.P(B)

0.5 = P(B)  - 0.2.P(B)

0.5 = 0.8.P(B)

P(B) = 0.5/0.8

P(B) = 5/8

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Therefore, the length of segment ST is 8/3 cm, assuming that triangles PTQ and RTS are similar.

Triangles are used in various applications, such as in the construction of buildings, bridges, and other structures, as well as in navigation and surveying. They are also important in various fields of mathematics, including trigonometry and geometry.

Here,

Let's denote the length of segment ST as x, and the corresponding sides in triangle PTQ and RTS as y and z, respectively. We can set up the following proportion:

y / PR = z / RT

Substituting the given values, we get:

y / 12 = z / 14

Now, we can use the fact that triangles PTQ and RTS are similar to set up another proportion involving the length of segment ST:

y / x = z / 16

Substituting the value of y / 12 = z / 14 from the first proportion, we get:

(z / 14) / 12 = z / 16 / x

Simplifying this equation, we get:

z = (14 / 12) * (16 / x) * z

z cancels out on both sides, and we are left with:

x = (16 * RT) / (14 * PR)

Substituting the given values, we get:

x = (16 * 14) / (14 * 12)

= 8/3

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A hypothesis is a testable guess about how a commodity works. It may be an idea, proposition, a possible medium of commerce, or a statement about an effect. A null hypothesis is a vaticination that there's no difference between groups or conditions or a statement or idea that can be falsified or proved wrong.

What's meant by a hypothesis in statistics?

In Statistics, a thesis is defined as a formal statement, which explains the relationship between the two or further variables of the specified population. It helps the experimenter to restate the given problem into a clear explanation for the outgrowth of the study.

Characteristics of hypothesis

The important characteristics of the hypothesis are

• The hypothesis should be short and precise

• It should be specific

• A hypothesis must be related to the being body of knowledge

• It should be able to verification

What's the Null hypothesis?

The null hypothesis is a kind of hypothesis that explains the population parameter whose purpose is to test the validity of the given experimental data. This thesis is either rejected or not rejected grounded on the viability of the given population or sample. In other words, the null hypothesis is a hypothesis in which the sample compliances effect by chance. It's said to be a statement in which the surveyors want to examine the data. It's denoted by H₀.

Hence a hypothesis is a testable guess about how a commodity works. It may be an idea, proposition, a possible medium of commerce, or a statement about an effect. A null hypothesis is a vaticination that there's no difference between groups or conditions or a statement or idea that can be falsified or proved wrong

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Answer:

x^2 + 2x

Step-by-step explanation:

x (x+2)

Distribute the x to each term inside the parentheses

x *x + x*2

x^2 + 2x

Answer:

step 1

use x to multiple the bracket

x(x+2)

x^2+2x

Hello!

surface area

= 2(6*2) + 2(4*2) + 4*6

= 2*12 + 2*8 + 24

= 24 + 16 + 24

= 64 square inches

Jamie multiplied 3x and 7 by -5 to eliminate the parentheses.

This procedure is justified by the distributive property.

This property states that multiplying the total of two or more addends by a number will provide the same outcome as multiplying each addend by the number separately and then adding the results together.

When we need to multiply a number by the sum of two numbers, the distributive property of multiplication over addition comes into play. Let's multiply 7 by the sum of 20 plus 3 as an illustration. This can be expressed mathematically as 7(20 + 3).

The distributive rule of multiplication over addition and subtraction is another name for the distributive property. By its very name, the procedure implies that something will be divided or distributed. Both addition and subtraction are under the scope of the distributive law.

Jamie multiplied 3x and 7 by -5 to eliminate the parentheses.

This procedure is justified by the distributive property.

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(a) The 99% confidence interval for the mean reduction in time to find Waldo is (34.03, 39.97) minutes.

(b) The given statement " the population mean reduction µ lies within your region with probability 0.99" is True.

(a) The 99% confidence interval for the mean reduction in time to find Waldo can be calculated using the formula:

mean ± (Z * σ / √n), where mean is the sample mean reduction (37 minutes), Z is the critical value corresponding to a 99% confidence level, σ is the population standard deviation (4 minutes), and n is the sample size (13).

(b)The 99% confidence interval means that if we were to take repeated samples and construct confidence intervals in the same way, 99% of those intervals would contain the true population mean reduction.

It does not mean that there is a 99% probability that the population mean reduction lies within this specific interval. The interval provides a range of plausible values for the population mean reduction, and we can be 99% confident that the true population mean reduction falls within this range.

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The 95% tolerance limits that contain 95% of the diameters is 2.262

Diameter:

In math, the straight line passing through the center of a circle or sphere and meeting the circumference or surface at each end is known as diameter.

Given,

Here we need to find the 95% tolerance limits that contain 95% of the diameters estimation of the mean diameter, while important, is not nearly as important as trying to pin down the location of the majority of the distribution of diameters.

According to the given question we have identified the following values,

Tolerance percentage = 95%

Diameter percentage = 95%

x = 61,492

n = 10

s = 3035

c = 95% = 0.95

Now, the value of t is determine by looking in the row starting with degrees of freedom 

=> df = n−1 = 10−1 = 9 and in the column with 

=> α/2 = (1−c)/2

=>0.025 

Then as per the table of the Student’s T distribution:

=> tα​=2.262

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The zeros of the polynomial are: x = 1/2 (with multiplicity 1), x = 3 (with multiplicity 1), and x = 5/2 (with multiplicity 1).We have found all three real zeros of the polynomial, which confirms that there are no complex zeros.

f(x) = 2x³ - 112x² + 27x - 41x + 15

To find the zeros and their multiplicities of this polynomial, we can begin by using Descartes' Rule of Signs. Let's consider the sign changes in the coefficients:

There are 2 sign changes in the coefficients (from 2x³ to -112x² and then to 27x, and finally to -41x and 15), which means there are either 2 or 0 positive real zeros.

There are no sign changes when we replace x with -x, which means there are either 0 or 2 negative real zeros.

Thus, there can be either 0, 2, or 4 real zeros, but we cannot determine their exact number or location with Descartes' Rule of Signs alone.

Next, we can use the Upper and Lower Bound Theorem to limit our search for rational zeros. According to this theorem, any rational zero of the polynomial must be of the form p/q, where p is a factor of the constant term (15 in this case) and q is a factor of the leading coefficient (2 in this case). Therefore, the possible rational zeros of the polynomial are:

±1/2, ±1, ±3/2, ±5, ±15/2, ±30

We can use synthetic division or long division to check these possible rational zeros and see which ones are actually zeros of the polynomial. Doing so, we find that the rational zeros of the polynomial are:

x = 1/2 (with multiplicity 1), x = 3 (with multiplicity 1), and x = 5/2 (with multiplicity 1).

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180-110 = 70

base angles theorem makes all the base angles of the triangle equal

110 - 70 = x

x = 40 degrees

Answer:

9

Step-by-step explanation:

(5x-4)+(6x-5)=90 degrees, because complementary angles add up to 90 degrees. So, 11x-9=90, 11x=99, then x=9.