The area of triangle ABC is
square units.

Answer:

2x^2 +5x-3

Step-by-step explanation:

(x+3)(2x-1)

FOIL

first :(x*2x) = 2x^2

outer: x*-1 = -x

inner: 3*2x = 6x

last: -1 *3 = -3

Add together

2x^2 -x+6x-3

Combine like terms

2x^2 +5x-3

Answer:

The third option. 2x^2+5x-3.

Step-by-step explanation:

The product means to multiply them.

(x+3)(2x-1)

You don't multiply x to 2x and 3 and -1.

That is not the product and say it is 2x^2-3.

You have to multiply x to both 2x and -1.

You don't only multiply the terms that correspond with each other.

You have to do x times 2x and x times -1.

2x times x is 2x squared or 2x^2.

x times -1 is -x.

So you have 2x^2-x.

Leave that there for now.

Now, you have to multiply 3 with 2x and -1.

3 times 2x is 6x and 3 times -1 is -3.

Then you have 6x-3.

Bring back the 2x^2-x with the 6x-3.

Now you have 2x^2-x+6x-3.

You always have to simplify.

Combine like terms. -x plus 6x is 5x.

Therefore, you are left with 2x^2+5x-3.

That is the product of (x+3)(2x-1).

you can check by dividing the polynomials as well.

I hope this clarifies things!

The total account balance, including both the principal and interest, would amount to approximately $44 after 25 years of simple interest accumulation. To calculate the total account balance after 25 years, we can use the formula for simple interest: Total Balance = Principal + Interest

Given:

Principal (P) = $22

Interest Rate (r) = 4% = 0.04

Time (t) = 25 years

Using the formula for simple interest:

Interest = Principal * Interest Rate * Time

Substituting the given values:

Interest = $22 * 0.04 * 25 = $22 * 1 = $22

Therefore, the total account balance after 25 years would be:

Total Balance = Principal + Interest = $22 + $22 = $44 (rounded to the nearest dollar).

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1000 cubic centimeters would need to be placed in a tub of water to displace 1 Lter of water

Conversion of units simply refers to the method used in determining the equivalent of one unit in relation to another.

From the information given, we have that;

Number of cubic centimeters that would be placed in a tub of water to displace 1 L of water

So, we have that there is 1 liter of water in the tub

In order to displace, you need to put something in that is the same amount

Now, let's convert the units

1 liter = 1000 cubic cm

Hence, you need 1000 cubic cm to displace 1 liter

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Answer:

the question was not correctly solved

Step-by-step explanation:

A=½bh

23=½*b*h

²/1×23= bh

²/1×23=6h

46=6h

h=7.666666667 / h=23/3

I hope this is helpful

The area of a 2D form is the amount of space within its perimeter. The area of the school will be equal to 35/108 miles².

The area of a 2D form is the amount of space within its perimeter. It is measured in square units such as cm2, m2, and so on. To find the area of a square formula or another quadrilateral, multiply its length by its width.

The area of the school is the product of length and width. Given the length is 7/12 mile, while the width is 5/9 mile. Therefore, The area of the school campus will be,

Area = (7/12) × (5/9)

        = (35/108) miles²

Hence, the area of the school will be equal to 35/108 miles².

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Answer:

15% or 3/20

Step-by-step explanation:

25 in class and 10 are girls so probability of first choice being a girl is 10/25.

Then for the second pick there are 24 students and 9 are girls so the probability is 9/24. You multiply 10/25 by 9/24 to get your answer.

Answer:

Steps:

SA = 2LW + 2WH + 2LH

SA = 2(9×2) + 2(2×11/2) + 2(9×11/2)

SA = 2×18 + 2×22/2 + 2×99/2

SA = 36 + 22 + 99

SA = 157 in²

Answer:

0.60

Step-by-step explanation:

If you purchase 6 rolls, you pay $3.60

Each roll is $0.60.

If you purchase 13 individual rolls, you pay

13 x 0.6 = $7.80

But if you purchase the Baker's dozen, you pay only $7.20, so you save $0.60

7.80 - 7.20 = 0.60

Answer: 0.60

Step-by-step explanation:

If you purchase 6 rolls, you pay $3.60

Each roll is $0.60.

If you purchase 13 individual rolls, you pay

13 x 0.6 = $7.80

But if you purchase the Baker's dozen, you pay only $7.20, so you save $0.60

7.80 - 7.20 = 0.60

No, T cannot map R^n onto R^n if it has the property that T(u) = T(v) for some pair of distinct vectors u and v in R^n. This is because since T(u) = T(v), then the same vector in R^n will be mapped to two different vectors in R^n, which is not a valid mapping.

1. Suppose a linear transformation T: R^n → R^n has the property that T(u) = T(v) for some pair of distinct vectors u and v in R^n.

2. This means that the same vector in R^n will be mapped to two different vectors in R^n.

3. This is not a valid mapping and therefore T cannot map R^n onto R^n.

No, T cannot map R^n onto R^n if it has the property that T(u) = T(v) for some pair of distinct vectors u and v in R^n. This is because since T(u) = T(v), then the same vector in R^n will be mapped to two different vectors in R^n, which is not a valid mapping.

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The candy store will use 103 grams of sugar in 10 hours.

To find out how many grams of sugar the store will use in 10 hours, we can simply multiply the amount of sugar used in one hour (10.3 grams) by the number of hours (10).

To solve the problem, we use a simple multiplication formula: the amount used per hour (10.3 grams) multiplied by the number of hours (10) to find the total amount of sugar used in 10 hours.

We can interpret this problem using a rate equation: the rate of sugar usage is 10.3 grams/hour, and the time period is 10 hours. Multiplying the rate by the time gives the total amount of sugar used.

So the calculation would be:

10.3 grams/hour x 10 hours = 103 grams

Therefore, the candy store will use 103 grams of sugar in 10 hours.

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Answer:$2.40

Step-by-step explanation: divide the ounce with the cost

12 / 4.99 =2.40

I would say maybe 41 or 42 cents

a) The probability that at least one of them guesses correctly is $1-0.0625=0.9375$.

b) The probability that all four guess incorrectly is \(\$(0.5)^4\) = 0.0625$.

a) The probability that at least one of them guesses correctly is the complement of the probability that none of them guess correctly. Since each friend has a probability of 0.5 of guessing incorrectly, the probability that one friend guesses incorrectly is 0.5, and the probability that all four friends guess incorrectly is:

\(0.5 * 0.5 * 0.5 * 0.5 = 0.0625\) or 6.25%

Therefore, the probability that at least one friend guesses correctly is:

1 - 0.0625 = 0.9375

b) The probability that all of them guess incorrectly is the product of their individual probabilities of guessing incorrectly:

\(0.5 * 0.5 * 0.5 * 0.5 = 0.0625\)  or 6.25%

Therefore, the probability that all of them guess incorrectly is 0.0625.

It is a number between 0 and 1, with 0 indicating the event is impossible and 1 indicating it is certain.

By dividing the number of favourable outcomes by the total number of possible outcomes, one can determine the probability of an occurring.

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The complete question is:

Four friends are guessing answers to math questions. They believe that, independently of one another, each of them has a 0.5 chance of predicting the right response to any given question.

a) What is the probability that at least one of them guesses correctly?

b) What is the likelihood that every single guess is wrong?

\(answer = - 30 \\ let \: the \: number \: be \: x \\ 3x + 20 = x - 40 \\ or \: 3x - x = - 40 - 20 \\ or \: 2x = - 60 \\ or \: x = \frac{ - 60}{2} \\ x = - 30 \\ hope \: it \: helps \\ good \: luck \: on \: your \: assignment\)

Answer: I think is A

Step-by-step explanation:

The data set contains the variable height (giving a person's height) and the variable gender (coded O=female, 1=male). Then the y-intercept of the regression equation predicting height from gender is given by: option c) the average height of females in the data set.

The y- intercept of a direct retrogression relationship represents the value of one variable when the value of the other is zero. Non-linear retrogression models also live, but are far more complex. Retrogression analysis is a important tool for uncovering the associations between variables observed in data, but can not fluently indicate occasion. The data set contains the variable height (giving a person's height) and the variable gender (enciphered O = womanish, 1 = manly). also the y- intercept of the retrogression equation prognosticating height from gender is given by option c) the average height of ladies in the data set.

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Answer:

Step-by-step explanation:

Sadie bought 8 hotdogs and 6 tacos.  (8,6) is intersect point

y=-3/4x+12 & y=x-2, graph it , it'll help graph on delta more accurately

Therefore,

Answer:

2.)4n>(n/2)^2

3. (The problem isn't clear)

4.)n^2+2n-3=129

5.)n-5=171

Step-by-step explanation:

2.)

4n(four times the number) >(larger than) (n/2)^2 (half the number squared)

4.)

Sum=addition

n^2 (number squared) +2n (twice the number)-3=129

5.)

N(unknown number of pages) -5(amount of pages already read)= 171(the number of pages it took her to finish)

Answer:

she will need 5 more 3 cups of apple juice

Step-by-step explanation:

15÷3=5

3×3×3×3×3=15

ABC. No image attached btw

Answer:in triangle def, the measure of def

Step-by-step explanation:

Just go 3 letters down

we know that the weights of tomatoes in August follow a normal distribution with a mean of 0.52 lb and a standard deviation of 0.15 lb. This means that most of the tomatoes will weigh somewhere close to the mean, and the weights will be spread out in a way that follows a bell curve.

Additionally, we can use this information to calculate the probability of certain weight ranges or outcomes. For example, we can use the z-score formula to find the probability of a tomato weighing less than or more than a certain amount. The z-score is calculated as the difference between the observed value and the mean, divided by the standard deviation.

For instance, if we want to know the probability of a tomato weighing between 0.3 lb and 0.6 lb, we can first calculate the z-score for both values. For 0.3 lb, the z-score would be (0.3 - 0.52) / 0.15 = -1.47. For 0.6 lb, the z-score would be (0.6 - 0.52) / 0.15 = 0.53.

Once we have these z-scores, we can use a standard normal distribution table or calculator to find the probabilities associated with each z-score. For example, the probability of a tomato weighing less than 0.3 lb would be the same as the probability of a z-score less than -1.47, which is 0.0708 or about 7.08%. The probability of a tomato weighing between 0.3 lb and 0.6 lb would be the probability of a z-score between -1.47 and 0.53, which is 0.6411 or about 64.11%.

I hope this helps! Let me know if you have any further questions.

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The explicit formula to represent the given  situation is

Explicit: pn = 14 + 9*n

Here we want to express the number of pizza delivered. Lets try to understand the case.

If we buy one pizza (p1) the cost is 14 because of the delivery plus 9 for the cost of the pizza. So:

p1 = 14 + 9 = 23

If we buy 2 pizzas (p2) we have to pay 14 for the delivery and 9 for each pizza:

p2 = 14 + 9 + 9 = 14 + 2*9 = 32

If 3 pizzas are bought (p3) the reasoning is the same, 14 for the delivery and 9 for each pizza:

p3 = 14 + 9 + 9 + 9 = 14 + 3*9 = 41

Here we can see a pattern: for any amount of pizzas n the cost will be 14 plus n-times 9, the price of a pizza. It is:

pn = 14 + 9*n

But we can separate the last equation in such a way:

pn = 14 + 9*(n-1) + 9 , as 9*(n-1) + 9 = 9*n

But if our general formula it true, the first to terms on the right are the vost of buying n-1 pizzas, so:

pn = pn-1 + 9

We can keep on separating terms as we did to arrive to this form, this is, separating the 9n in  9*(n-2) + 9*2,  9*(n-3) + 9*3, ...,  9*(n-m) + 9*m for any m < n . Here I will keep pn = pn-1 + 9 as the Recursive Formula, but you could use other formulation with, e.g., pn-2, pn-3, etc, using the above recursion.

Now, the explicit formula is such that gives as the value of any amount, finding all the terms of the sequence with those not depending on previous terms (contrary to the recursive). This formula was showed above and is: pn = 14 + 9*n. This is, given any number of pizzas we can find the cost without knowing the cost of previous values.

So, we have:

Recursive: pn = pn-1 + 9

Explicit: pn = 14 + 9*n

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Answer:

Where's the chart?

Step-by-step explanation:

The expression becomes:

∫[0 to 1] (t)(t²)(\(e^{t^{3} }\)) dy

To evaluate the expression `[₂ C xy ez dy C: x = t, y = t², z = t³, 0 ≤ t ≤ 1]`, let's break it down step by step.

1. Start with the integral sign `[₂ C ... dy C]`, which indicates that we're evaluating a definite integral.

2. Next, we have `xyez dy` as the integrand. Since `x = t`, `y = t²`, and `z = t³`, we can substitute these values into the integrand: `(t)(t²)(\(e^{t^{3} }\))dy`.

3. The limits of integration are given as `0 ≤ t ≤ 1`.

Putting it all together, the expression becomes:

∫[0 to 1] (t)(t²)(\(e^{t^{3} }\)) dy

To solve this integral, we need to determine if `y` is an independent variable or a function of `t`. If `y` is an independent variable, then we can't perform the integration with respect to `y`. However, if `y` is a function of `t`, we can proceed with the integration.

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The correct answer is B. The statement is true.

The statement claims that if the equation Ax = 0 has a nontrivial solution, then A has fewer than n pivot positions. In other words, if there exists a nontrivial solution to the homogeneous system of equations Ax = 0, then the matrix A cannot have n pivot positions.

The Invertible Matrix Theorem states that a square matrix A is invertible if and only if the equation Ax = 0 has only the trivial solution x = 0. Therefore, if Ax = 0 has a nontrivial solution, it implies that A is not invertible.

In the context of row operations and Gaussian elimination, the pivot positions correspond to the leading entries in the row-echelon form of the matrix. If a matrix A is invertible, it will have n pivot positions, where n is the dimension of the matrix (n × n). However, if A is not invertible, it means that there must be at least one row without a leading entry or a row of zeros in the row-echelon form. This implies that A has fewer than n pivot positions.

Therefore, the statement is true, and option B is the correct answer.

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Given:

A regular pentagon with side 8 cm and apothem 6 cm.

To find:

The area of the given regular pentagon.

Solution:

The area of a regular polygon is:

\(A=\dfrac{n\times s\times a}{2}\)

Where, n is the number of sides of the regular polygon, s is the side length and a is the apothem.

In a regular pentagon the number of sides is 5.

Substituting \(n=5,s=8,a=6\) in the above formula, we get

\(A=\dfrac{5\times 8\times 6}{2}\)

\(A=\dfrac{240}{2}\)

\(A=120\)

The area of the regular pentagon is 120 cm². Therefore, the correct option is C.

The solutions for x, y, z, and w in terms of a, b, c, d, e, and f are: x y = - (a b c d)^-1 (e f z w), z w = - (a b c d)^-1 (e f x y)

To solve for x, y, z, and w in terms of a, b, c, d, e, and f given the equality a b c d x y i 0 = e f z w,

we can rearrange the equation as follows: x y i 0 = - (a b c d)^-1 (e f z w).

Then we can solve for x and y by multiplying both sides by the matrix

(1 0 0 0; 0 1 0 0; 0 0 0 1; 0 0 0 1)

to obtain x y = - (a b c d)^-1 (e f z w).

Finally, we can solve for z and w by multiplying both sides by the matrix (

0 0 1 0; 0 0 0 1; 1 0 0 0; 0 1 0 0) to obtain z w = - (a b c d)^-1 (e f x y).

Thus, the solutions for x, y, z, and w in terms of a, b, c, d, e, and f are:

x y = - (a b c d)^-1 (e f z w)

z w = - (a b c d)^-1 (e f x y)

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Carolyn made an error in her work because she did not correctly distribute the negative in Step 3.

A system of equations is the given term math for two or more equations with the same variables. The solution of these equations represents the point of the intersection.

You can solve a system of equations by the adding or substitution methods. In the addition method, you eliminate a variable, on the other hand, in the substitution method you replace a variable for the other.

The question gives:3x-2y=7 (1)y=x+2The question shows that Carolyn applies the substitution method because she replaces the variable y (equation 2) in equation 1. See the given step 2.

3x – 2y = 7

3x – 2(x + 2) = 7

3x – 2x - 4 = 7 - here it is the mistake. (Carolyn did not correctly distribute the negative).

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From the construction of the triangle ABC we get that the measure length of BC is approximately 4.22cm

To construct triangle ABC, we can follow these steps:

To measure the length of BC in triangle ABC, we can use the law of sines.

The law of sines states that in any triangle ABC:

a / sin(A) = b / sin(B) = c / sin(C)

Where a, b, and c are the lengths of the sides of the triangle opposite to the angles A, B, and C, respectively.

In our triangle ABC, we know AB = 6 cm, angle BAC = 96 degrees and angle ABC = 35 degrees. We can find the measure of angle ACB by using the fact that the sum of the angles in a triangle is 180 degrees:

angle ACB = 180 - angle BAC - angle ABC

= 180 - 96 - 35 = 49 degrees

Now, we can apply the law of sines to find the length of BC:

BC / sin(35) = 6 / sin(96)

BC = 6 × sin(35) / sin(96)

Using a calculator, we can evaluate this expression to get:

BC ≈ 4.22 cm

Therefore, the length of BC in triangle ABC is approximately 4.22 cm.

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