Becca made 3 dozen cookies with 2/3 of a batch of her mother's cookie dough. How many cookies will she make if she uses that entire batch?

the answer is 39.9 %

So the Rational Zeros Theorem states that the potential zeros are ± P/Q, with P = factors of the constant and Q = factors of the leading coefficient.

In this case, the constant is -3 and the leading coefficient is 2.

With P and Q established, divide them all as such:

[tex]\pm \frac{1}{1}, \pm \frac{3}{1}, \pm \frac{1}{2}, \pm \frac{3}{2}\\\\\pm 1,\pm 3, \pm \frac{1}{2}, \pm \frac{3}{2}[/tex]

In short, your potential zeros are ± 1/2, ± 3/2, ± 1, and ± 2.

Final answer:

To calculate 3 to the 7th power times 3 to the power of negative 4, you add the exponents since the base is the same. This results in 3 cubed (33), which equals 27.

Explanation:

The question asks to calculate 3 to the 7th power times 3 to the power of negative 4. This can be simplified using the rules of exponents. When multiplying powers with the same base, you add the exponents. So for this problem, you would do the following:

3⁷ *3⁻⁴ = 3⁷⁺⁽⁻⁴⁾

3³ because 7 + (-4) equals 3

Therefore, the answer is 33 which is 3*3*3, equaling 27.

Moreover, a negative exponent like 3 to the power of negative 4 indicates that the number 3 is on the denominator, yielding 1 over 3 raised to the 4th power or 1/34.

Answer:

the answer is 1470.

Step-by-step explanation:

If you multiple 35 by 42, you get 1470. To check the answer, you can divide 1470 by 35 and get 42. You can also divide 1470 by 42 to get 35.

To round 17,509 to the nearest thousand, you look at the hundreds digit. If it's 5 or above, you round up. Therefore, 17,509 rounded to the nearest thousand is 18,000.

To round the number 17,509 to the nearest thousand, we first need to look at the digit in the hundreds place; in this case, it's 5. In rounding, if this digit is 5 or above, we round up the preceding number. Since the digit in the hundreds place is 5, we round up the number in the thousand's place from 7 to 8 making the number 18,000. On the other hand, if the digit in the hundreds place was 4 or lower, we would keep the number in the thousands place the same. So, 17,509 rounded to the nearest thousand is 18,000.

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[tex]a_1=5\\\\a_n=a_{n-1}-3\\\\a_2=a_1-3\to a_2=5-3=2\\\\a_3=a_2-3\to a_3=2-3=-1\\\\a_4=a_3-3\to a_4=-1-3=-4\\\\Answer:\ \{5,\ 2,\ -1,\ -4\}[/tex]

1 1/3 cups of raisins are needed to make 1/2 of a recipe

To find the quantity of raisins for half of the recipe, which originally called for 2 2/3 cups, you'd divide 2 2/3 cups by 2, which equals 1 1/3 cups.

This is a question about fractions and division. If a full recipe requires 2 2/3 cups of raisins and you want to make just 1/2 of the recipe, you need to divide the quantity of the raisins by 2.

In fraction form, 2 2/3 is equivalent to 8/3 (as 2*3 + 2 = 8). Then, to find half of this amount, we divide 8/3 by 2. We can do this by multiplying 8/3 by 1/2, which gives us 4/3. Therefore, 1/2 of the recipe requires 4/3, or 1 1/3 cups of raisins.

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Whenever you add a rational and an irrational number, the result is an irrational number.

So, since 3/4 is rational, if you add any irrational number you will get an irrational number as a result.

Answer:

Y = 10

Step-by-step explanation:

The denominator of a fractional exponent represents the degree of root.

For example

[tex]x^{\frac{1}{3}} = \sqrt[3]{x}\\x^{\frac{1}{4}} = \sqrt[4]{x}\\x^{\frac{1}{5}} = \sqrt[5]{x}[/tex]

The denominator of a rational exponent represents the root or nth root of the base number. It is expressed in the form of a fraction where the numerator represents the power and the denominator represents the root or nth root. Rational exponents are used in simplifying expressions and performing calculations involving roots and powers.

The denominator of a rational exponent represents the root or nth root of the base number. A rational exponent is expressed in the form of a fraction, where the numerator represents the power to which the base is raised, and the denominator represents the root or nth root. For example, in the rational exponent 3/2, the base number is raised to the power of 3 and then the cube root is taken.

When the numerator of the rational exponent is 0, it signifies that the number is raised to the power of 0, which always results in 1. On the other hand, when the denominator is 1, it signifies that there is no root involved, and the number is simply raised to the power indicated by the numerator.

Understanding rational exponents is essential in simplifying expressions, solving equations, and performing calculations involving roots and powers.

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Your answer will be (x-4y)(x+3y)

To factor the polynomial x^2-xy-12y^2, we rewrite the polynomial, recognize the common numbers that add to -1 and multiply to -12, factor by grouping, and finally factor out the common binomial term to get the final answer: (x-4y)(x+3y).

To factor the polynomial x^2-xy-12y^2, first you need to recognize that this is a quadratic equation in the form of ax^2+bx+c. Here, a=1, b=-1, and c=-12y^2. The next step involves factoring this quadratic equation. The standard method for factoring such an equation would be to find two numbers that add to b (the coefficient of x) and multiply to c (the coefficient of y^2).

In this case, we are looking for two numbers which add to -1 and multiply to -12. Those numbers are -4 and 3. Therefore, we can rewrite the middle term of the equation (xy) as (-4xy + 3xy). So the equation becomes x^2-4xy+3xy-12y^2.

Now, we can factor by grouping, which means factoring out common factors from each of the two groups: x(x-4y)+3y(x-4y). Finally, we can factor out the common binomial term to get the factored form of the polynomial: (x-4y)(x+3y).

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This question is based on multiplication.

Given situation is -

by recycling 1 ton of paper , the amount of water saved is = 6953 gallons

So, by recycling 4 tons of paper , the amount of water saved will be=

[tex]6953*4[/tex]

= [tex]27812[/tex] gallons

Hence, 27812 gallons of water are saved by recycling 4 tons of paper.

The question in English

A small farmer in the interior of Par, when measuring his rectangular terrain, realized that his dimension is in reason 5/7. If the terrain area is 2240 m2, then its largest dimension in meters is

Let

x--------> the smallest dimension of the rectangular terrain

y--------> the largest dimension of the rectangular terrain

we know that

the area of the rectangular terrain is

[tex]A=x*y[/tex]

[tex]A=2,240\ m^{2}[/tex]

so

[tex]2,240=x*y[/tex] -------> equation A

[tex]\frac{x}{y}=\frac{5}{7}[/tex]

[tex]x=\frac{5}{7}y[/tex] -------> equation B

substitute the equation B in equation A

[tex]2,240=[\frac{5}{7}y]*y\\\\5y^{2}= 15,680\\ \\y^{2}=3,136\\ \\y=56\ m[/tex]

therefore

the answer is the option D

[tex]56\ m[/tex]

Answer:

-1075

Step-by-step explanation:

The other person was right they forgot to make it a negative

There are two sequence in mathematics, one is arithmetic and other is geometric sequence. Therefore, the 64th term of the arithmetic sequence is -1075.

In an arithmetic sequence, the difference between consecutive terms, called common difference, is always the same. Another sequence is the geometric sequence.

The nth term of an arithmetic sequence is given by:

[tex]a_{n}[/tex]=a₁+(n-1)d

In which  is the first term from−4,−21,−38 is a₁  -4

Common difference between two consecutive terms is d=-38-(-21)=-17

substituting in the above equation an=a1+(n-1)d

[tex]a_{n}[/tex]=-4+(n-1)(-17)

Since we have to find the 64th term of the arithmetic sequence we have to put n=64

[tex]a_{n}[/tex]=-4+(64-1)(-17)

 [tex]a_{n}[/tex]   =-4+(63)(-17)

[tex]a_{n}[/tex] =-1075

Therefore, the  64th term in the arithmetic sequence -4, -21, -38 is -1075.

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To factor the expression 5ac + 10ab - 2c^2 - 4bc, we first factor out common factors from the pairs of terms which results in 5a(c + 2b) - 2c(c + 2b). Then, we factor out the common binomial (c + 2b) to get the fully factored form: (5a - 2c)(c + 2b).

The expression given is 5ac + 10ab - 2c^2 - 4bc. To factor this expression, we need to look for common factors in the terms. Let's take each pair of terms and factor it.

For the first two terms (5ac and 10ab), the common factor is 5a. Factoring these gives: 5a(c + 2b).

The last two terms (-2c^2 and -4bc), -2c is the common factor. Factoring these gives: -2c(c + 2b).

So our expression becomes 5a(c + 2b) - 2c(c + 2b). Finally, we factor out the common binomial term (c + 2b) to get the fully factored form: (5a - 2c)(c + 2b).

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Divide the total amount made with the amount of hours worked

Ruth makes $35 working 5 hours

35/5 = 7

Ruth makes $7 an hour

Now multiply 7 with 8

7 x 8 = 56

Ruth makes $56 in 8 hours

~Rise Above the Ordinary

The speed of sound in scientific notation is 3.00 x 10⁸ m/s

speed of light, the speed at which light waves propagate through different materials. In particular, the value for the speed of light in a vacuum is now defined as exactly 299,792,458 meters per second.

Given here is the speed of sound is about thirty-four thousand centimeters per second. Therefore the speed of light in scientific notation is  3.00 x 10⁸ m/s

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Answer:

3.4 x 10^4 centimeters per second.

The correct answer is y=−1/16

Answer:

A. [tex]y=-\frac{49}{16}[/tex]

Step-by-step explanation:

Since, the directrix of a parabola [tex](x - h)^2 = 4p (y - k)[/tex] is,

y = k - p

Here, the given parabola,

[tex]\frac{1}{4}(y+3)=(x-2)^2[/tex]

By comparing,

We get,

k = - 3,

[tex]4p=\frac{1}{4}\implies p=\frac{1}{16}[/tex]

Hence, the directrix of the given parabola is,

[tex]y=-3-\frac{1}{16}[/tex]

[tex] y=\frac{-48-1}{16}[/tex]

[tex]\implies y = -\frac{49}{16}[/tex]

Option 'A' is correct.

The statements about the experimental probability are as follows;

For the experimental outcomes to be closer to the predicted outcome, the number of trials should be increased.;

If the number of trials is changed, the experimental probability also changes. ;

If the number of trials is changed, the predicted number of outcomes also changes.

If the number of trials is changed, the number of experimental outcomes also changes.

Given

Frederick designed an experiment in which he spun a spinner 20 times and recorded the results of each spin.

He spun 4 five times.

The experimental outcomes refer to the number of repetitions with no limits.

The statements about the experimental probability are as follows;

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Increasing the number of trials in Frederick's experiment will make the experimental outcomes closer to the predicted outcome. The law of large numbers explains how the experimental probability tends to approach the theoretical probability as the number of trials increases.

The statement that is true is 'For the experimental outcomes to be closer to the predicted outcome, the number of trials should be increased.' When Frederick spins the spinner 20 times, the experimental probability of spinning a 4 is based on a relatively small number of trials. To get a more accurate result that aligns with the predicted probability, he should increase the number of trials.

According to the law of large numbers, as the number of trials in a probability experiment increases, the experimental probability of an event tends to get closer and closer to the theoretical probability. Therefore, by increasing the number of trials, Frederick can obtain a more reliable experimental probability result.

None of the other statements are true. If the number of trials is changed, the number of experimental outcomes does not change because the number of trials is fixed at 20 in this case. The predicted number of outcomes also does not change because Frederick is not changing the nature of the spinner or the possibilities it can land on. Similarly, the theoretical probability remains the same regardless of the number of trials. Finally, changing the number of trials does not affect the theoretical probability. The theoretical probability is based on the properties of the spinner and would remain constant.

we are given

system of equations

First equation is

[tex]3x-2y=31[/tex]

Second equation is

[tex]3x+2y=-1[/tex]

now, we can find augmented matrix

[tex]A=\begin{pmatrix}3&-2&31\\ 3&2&-1\end{pmatrix}[/tex]

now, we can change it into reduced row echelon form

step-1: multiply the 1st row by 1/3

[tex]A=\begin{pmatrix}1&-2/3&31/3\\ 3&2&-1\end{pmatrix}[/tex]

step-2:add -3 times the 1st row to the 2nd row

[tex]A=\begin{pmatrix}1&-2/3&31/3\\ 0&4&-32\end{pmatrix}[/tex]

step-3:multiply the 2nd row by 1/4

[tex]A=\begin{pmatrix}1&-2/3&31/3\\ 0&1&-8\end{pmatrix}[/tex]

step-4: add 2/3 times the 2nd row to the 1st row

[tex]A=\begin{pmatrix}1&0&5\\ 0&1&-8\end{pmatrix}[/tex]

so, we get

[tex]x=5,y=-8[/tex]

Answer is (5,-8)

Solution is (5,-8)

3x – 2y = 31

3x + 2y = -1

first we write it in matrix form

3  -2   | 31   -------------> Row 1

3   2   | -1  -------------> Row 2

We use row operations and get matrix in 1   0    and 0  1  form

Subtract Row 2 by row 1.  R2 -> R2 - R1. So R1 remains the same

3  -2   | 31   -------------> Row 1

0   4   | -32  -------------> Row 2

Divide row 1 by 3, R1-> R1/3. So R2 remains the same

1   [tex]\frac{-2}{3}[/tex]   | [tex]\frac{31}{3}[/tex]    -------------> Row 1

0   4   | -32  -------------> Row 2

Divide row 2 by 4. R2 -> R2/4

1   [tex]\frac{-2}{3}[/tex]   | [tex]\frac{31}{3}[/tex]    -------------> Row 1

0   1   | -8  -------------> Row 2

Now we need to get 0 in the place of -2/3

Multiply Row 2 by 2/3  and add it with Row 1. R1 --> 2/3 times R2 + R1

1   [tex]1*\frac{2}{3}+\frac{-2}{3}[/tex]   | [tex]-8*\frac{-2}{3}\frac{31}{3}[/tex]    -------------> Row 1

0   1   | -8  -------------> Row 2

Now simplify the fraction

1   0   | 5    -------------> Row 1

0   1   | -8  -------------> Row 2

So from this we can see that x=5  and y = -8

Solution is (5,-8)

Given : f(x)=2x+1 and g(x)=x^2-1.

We need to find  (f/g)(x).

Note: In the given options, we have 2x + 1 and  x^2 - 7 parts.

So, let us take f(x)=2x+1 and g(x)=x^2-7.

[tex](f/g)(x) =\frac{f(x)}{g(x)}[/tex]

Plugging f and g functions in the formula.

[tex](\frac{f}{g})(x)=\frac{(2x+1)}{(x^2-7)}[/tex]

Also, it would be undefined for x = ± square root 7 becaue it would give 0 in the denomiantor.

Therefore, correct option is C. 2x + 1 / x^2 - 7, x ≠ ± square root 7.

Its not correct because the answer would be 1,440 (rounded) this is no where near as close as 222.3.

117 * 19

= 120 * 20  to the nearest 10

=  2400   which indicates that 2223 is a reasonable answer.

−24−(−19) =

- 24 + 19 =

-5