Olaf needs a total of 3 cups of sugar to make 4 cakes. Write and solve an equation to find the number of cups of sugar he needs for each cake. Which number line shows the number of cups of sugar Olaf needs for each cake?

1. A number line going from negative 1.5 to positive 1.5. A point is at positive 0.75.
2. A number line going from negative 1.5 to positive 1.5. A point is at positive 1.
3. A number line going from negative 1.5 to positive 1.5. A point is at positive 1.30.
4. A number line going from negative 1.5 to positive 1.5. A point is at positive 1.5.

The value of c is 25 in the perfect square trinomial x^2 + 10x + c.

The value of c in the perfect square trinomial x^2 + 10x + c can be determined by examining the entries in the table. The missing values in the table represent the terms that complete the perfect square trinomial, allowing us to find the value of c.

In the given table, the first column is labeled "x squared" and contains entries x, x, x, x, x. The second column is labeled "x" and is left blank. The third, fourth, fifth, and sixth columns are all labeled "x" and are also left blank.

To find the value of c in the perfect square trinomial x^2 + 10x + c, we need to consider the entries in the table. The expression x^2 represents the first column of the table, which has entries x, x, x, x, x. The expression 10x represents the sum of the entries in the second, third, fourth, fifth, and sixth columns. Since these columns are blank in the table, the sum is 0.

Therefore, to complete the perfect square trinomial, the value of c would be the square of half the coefficient of x, which is (10/2)^2 = 25.

Hence, the value of c is 25 in the perfect square trinomial x^2 + 10x + c.

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the initial expression is:

Answer:

B

Step-by-step explanation:

the electromagnet lasts only as long as there is supply of electric current

Answer:

The answer is 3, 5, and 9

the value of k for which the matrix has one real eigenvalue of algebraic multiplicity 2 is k = 0

The given matrix is

   [ -6   k ]

A = [  1   -1 ]

The characteristic polynomial is given by

| -6 - λ    k     |      

|                 |  = (λ + 3)² - k = λ² + 6λ + 9 - k

|  1    -1 - λ   |

To have a real eigenvalue of algebraic multiplicity 2, we need the discriminant of the characteristic polynomial to be 0:

(6)² - 4(1)(9 - k) = 0

36 - 36 + 4k = 0

4k = 0

k = 0

Therefore, the value of k for which the matrix has one real eigenvalue of algebraic multiplicity 2 is k = 0

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Answer: maybe the answer is 4 miles sorry if I got it wrong hope it helps :/

Step-by-step explanation:

Answer:

\( - 7x + 34\)

Step-by-step explanation:

\(5x - 4(3x - 9) - 2 \\ 5x - 12x + 36 - 2 \\ = - 7x + 34\)

hope this helps

brainliest appreciated

good luck! have a nice day!

Answer:

-7x + 34

Step-by-step explanation:

Hopefully this is simplify...

5x - 12x + 36 - 2

-7x + 34

Answer:

2.44$

Step-by-step explanation:

75$ - 18.56 (weights) = 56.44

56.44$ - 54 (worms) = 2.44$ extra

The derivative of f(x) is f'(x) = -2, so we can substitute these values into the formula to get δy = -2 * 0.2 = -0.4.

This problem involves using the concept of the derivative to calculate the change in the output variable y, given a small change in the input variable x.

Specifically, we are given the function y = f(x) = -2x, the value of x at which we want to evaluate the change, x = 2, and the size of the change in x, δx = 0.2.

To find the corresponding change in y, δy, we can use the formula δy = f'(x) * δx, where f'(x) is the derivative of f(x) evaluated at x.

In this case, the derivative of f(x) is f'(x) = -2, so we can substitute these values into the formula to get δy = -2 * 0.2 = -0.4.

This tells us that a small increase of 0.2 in x will result in a decrease of 0.4 in y, since the derivative of the function is negative.

This problem illustrates the concept of local linearization, which is the approximation of a nonlinear function by a linear function in a small region around a point.

The derivative of the function at a point gives us the slope of the tangent line to the function at that point, and this slope can be used to approximate the function in a small region around the point.

This approximation can be useful for estimating changes in the output variable given small changes in the input variable.

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Answer:

(a)18

(b)1089

(c)Sunday

Step-by-step explanation:

The problem presented is an arithmetic sequence where:

We want to determine the number of Sundays in the 120 days before Christmas.

(a)In an arithmetic sequence:

\(\text{The nth term}, T_n=a+(n-1)d\\T_n \leq 120\\$Therefore:$\\1+7(n-1) \leq 120\\1+7n-7\leq 120\\7n-6\leq 120\\7n\leq 120+6\\7n\leq 126\\$Divide both sides by 7$\\n\leq 18\)

Since the result is a whole number, there are 18 Sundays in which Aldsworth advertises.

Therefore, Aldsworth advertised 18 times.

(b)Next, we want to determine the sum of the first 18 terms of the sequence

1,8,15,...

\(\text{Sum of a sequence}, S_n=\frac{n}{2}( 2a+(n-1)d)\\S_{18}=\frac{18}{2}( 2*1+(18-1)*7)\\=9(2+17*7)\\=9(2+119)\\=9*121\\S_{18}=1089\)

The sum of the numbers of days published in all the advertisements is 1089.

(c)SInce the 120th day is the 18th Sunday, Christmas is on Sunday.

Surface area = (1/2 x 6 x 4) + (1/2 x 6 x 4) + (12 x 7) + (12 x 7) + (4 x 12)

                      =  12 + 12 + 84 + 84 + 48

                      = 240 cm²

∴ Answer: B

Hope this helps! :]

P.s. Can you mark me as the Brainliest?

Answer:

0.039 hectolitres are left in the can

Step-by-step explanation:

One hectolitre equals 100 liters

The can:

10-3.8-2.3=3.9 liters

In hectolitres:

3.9/100 = 0.039

Hope this helps

Answer:

i think the c answer is 5

Step-by-step explanation:

Answer:

$3.80 per book

Step-by-step explanation:

I divided 19 by 5 to get the price per book

The probability that exactly 2 or fewer pieces will be cherry flavored is 0.238 or 0.211 to the nearest hundredth when rounded off. The correct option is b) .

Let us first compute the probability of selecting two cherry flavored pieces out of 5 and then we can add the probability of selecting only one cherry flavored piece and also no cherry flavored piece.

P(Exactly 2 cherry flavored pieces) = P(Cherry and Cherry and not Cherry and not Cherry and not Cherry) + P(Cherry and not Cherry and Cherry and not Cherry and not Cherry) + P(Cherry and not Cherry and not Cherry and Cherry and not Cherry) + P(not Cherry and Cherry and Cherry and not Cherry and not Cherry) + P(not Cherry and Cherry and not Cherry and Cherry and not Cherry) + P(not Cherry and not Cherry and Cherry and Cherry and not Cherry) + P(not Cherry and not Cherry and not Cherry and Cherry and Cherry)

P(Exactly 2 cherry flavored pieces) = [(8/40) * (7/39) * (32/38) * (31/37) * (30/36)] + [(8/40) * (32/39) * (7/38) * (31/37) * (30/36)] + [(8/40) * (32/39) * (31/38) * (7/37) * (30/36)] + [(32/40) * (8/39) * (7/38) * (6/37) * (30/36)] + [(32/40) * (8/39) * (31/38) * (6/37) * (30/36)] + [(32/40) * (31/39) * (8/38) * (6/37) * (30/36)] + [(32/40) * (31/39) * (30/38) * (8/37) * (7/36)]P(Exactly 2 cherry flavored pieces) = 0.238.

Therefore, the probability that exactly 2 or fewer pieces will be cherry flavored is 0.238 or 0.211 to the nearest hundredth when rounded off.

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The simplified radical expression by rationalizing the denominator is, \(\frac{-6}{\sqrt{5y}}\times\frac{\sqrt{5y}}{\sqrt{5y}}\) = \(\frac{-6\sqrt{5y}}{5y}$$\) = $\frac{-6\sqrt{5y}}{5y}$.

To simplify the radical expression by rationalizing the denominator, multiply both numerator and denominator by the conjugate of the denominator.

The given radical expression is \($\frac{-6}{\sqrt{5y}}$\).

Rationalizing the denominator

To rationalize the denominator, we multiply both the numerator and denominator by the conjugate of the denominator, \($\sqrt{5y}$\)

Note that multiplying the conjugate of the denominator is like squaring a binomial:

This simplifies to:

(-6√(5y))/(√(5y) * √(5y))

The denominator simplifies to:

√(5y) * √(5y) = √(5y)^2 = 5y

So, the expression becomes:

(-6√(5y))/(5y)

Therefore, the simplified expression, after rationalizing the denominator, is (-6√(5y))/(5y).

\($(a-b)(a+b)=a^2-b^2$\)

This is what we will do to rationalize the denominator in this problem.

We will multiply the numerator and denominator by the conjugate of the denominator, which is \($\sqrt{5y}$\).

Multiplying both the numerator and denominator by \($\sqrt{5y}$\), we get \(\frac{-6}{\sqrt{5y}}\times\frac{\sqrt{5y}}{\sqrt{5y}}\) = \(\frac{-6\sqrt{5y}}{5y}$$\)

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Answer:

identity property

Step-by-step explanation:

The sum of 0 and any number is that number is the identity property of addition

a+0=a

15+0=15

Its communative property

\(\boxed{\sf a+b=b+a}\)

Lets come to question

\(\\ \sf\longmapsto 15+0=15\)

\(\\ \sf\longmapsto 15+0=0+15\)

Hence verified

The relative wind speed will the person sense is -5.2mph.

Speed can be explained as the  distance traveled per unit of time which is how the object is moving, and it is a  scalar quantity  having magnitude of the velocity vector.

Speed of man  =2.95 mph

Speed of wind  =-2.25 mph

Relative wind speed V_R is mathematically given directly as

Vr= Vw-Vm

=-2.25 mph -2.95 mph

= -5.2mph

Therefore, relative wind speed will the person sense is -5.2mph.

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Answer:

50-15.20 = 34.8 - 8p

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

We have the ratio of students that are from Florida and the ones that are not. For every 3 students from florida, 1 isn't. Therefore we can create the following ratio:

Where x is the number of Florida's students and y is the number of students that are not from that place. We can rewrite the equation as follows:

The sum of "x" and "y" must be equal to the number of students in the university. So we have:

If we replace the value of the first equation on the second, we can solve for y.

Therefore, we can determine the number of students from Florida, by using the first equation:

There are 9000 students from Florida.

To have exactly 3 kings in a hand, we need to choose 3 kings out of 4 and 2 non-kings out of 48. This can be done in 4512 ways.


To calculate the number of hands containing exactly 3 kings, we need to use the concept of combinations. We know that there are 4 kings in a deck of 52 cards. To choose 3 kings out of 4, we can use the combination formula, also known as "n choose k," which is written as nCk.

So, the number of ways to choose 3 kings out of 4 is 4C3 = 4.

Next, we need to choose 2 non-kings out of the remaining 48 cards. This can be done using the combination formula again. The number of ways to choose 2 non-kings out of 48 is 48C2 = 1128.

Now, we can use the multiplication principle to find the total number of hands containing exactly 3 kings. We multiply the number of ways to choose 3 kings by the number of ways to choose 2 non-kings:

Total number of hands = 4C3 * 48C2 = 4 * 1128 = 4512.

Therefore, there are 4512 hands that contain exactly 3 kings when 5 cards are randomly chosen from a standard deck.

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If A and B are independent, then the correct statements are P(A and B) = 0.12 and P(A or B) = 0.58.

Let's evaluate each statement:

P(B/A) = 0.4:

This statement is incorrect. If events A and B are independent, the occurrence of event A does not affect the probability of event B.

Therefore, P(B/A) would still be equal to the probability of B, which is 0.4 in this case.

P(A and B) = 0.12:

This statement is correct. The probability of the intersection of independent events A and B is calculated by multiplying their individual probabilities. In this case, P(A and B) = P(A) * P(B) = 0.3 * 0.4 = 0.12.

P(A/B) = 0.3:

This statement is incorrect. If events A and B are independent, the occurrence of event B does not affect the probability of event A. Therefore, P(A/B) would still be equal to the probability of A, which is 0.3 in this case.

P(A or B) = 0.58:

This statement is incorrect. To calculate the probability of the union of two events, we need to consider whether the events are mutually exclusive or not.

If events A and B are independent, but not mutually exclusive, we can calculate P(A or B) as P(A) + P(B) - P(A and B). In this case, P(A or B) = 0.3 + 0.4 - 0.12 = 0.58.

Therefore, the correct statements are:

The statements regarding P(B/A) = 0.4 and P(A/B) = 0.3 are incorrect in the context of independent events A and B.

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A linear function is a function that has a constant rate

A linear function can take any of the following forms

y = mx + b

y - y1 = m(x - x1)

Ax + By = c

Where m represents the slope/rate, and b represents the initial value

The options are not clear.

So, I will give examples of a linear function

Examples are:

y = 2x + 3

2y = 5x - 2

2x + 3y = 10

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R2 value less than 1 does not necessarily mean that the regression analysis is incorrect or that the observation data is suspect.

Rather, it suggests that there may be additional factors to consider when interpreting the results.

The statement "If R2 is less than 1, the regression analysis is incorrect" is not entirely true.

R2 is a statistical measure that indicates the proportion of the variance in the dependent variable that is explained by the independent variable(s). R2 values range from 0 to 1, where 0 indicates no correlation and 1 indicates perfect correlation.

If R2 is less than 1, it simply means that the independent variable(s) are not able to explain all of the variation in the dependent variable.

This does not necessarily mean that the regression analysis is incorrect.

In fact, it is common for regression analyses to have R2 values that are less than 1.

The key is to interpret the R2 value in conjunction with other statistical measures and to consider the research question being addressed.

Some possible implications of having an R2 value less than 1 might include:

The independent variable(s) have a weaker relationship with the dependent variable than anticipated.

There may be other factors that are influencing the dependent variable that are not accounted for in the regression analysis.

The sample size may be too small to detect a significant relationship between the independent and dependent variables.

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The conclusions with regards to the similar right triangles, Yvonne needs to prove the Pythagorean Theorem are;

PQ/PR = PS/PQ and QR/PR = RS/QR

Pythagorean Theorem outlines the relationship between the length of the hypotenuse side and the lengths of the legs of a right triangle. The theorem states that the sum of the squares of the lengths of the legs of a right triangle, is equivalent to the square of the length of the hypotenuse side.

The specified similar triangles are;

ΔPQR ~ ΔQSR ~ ΔPSQ

PQ/PS = PR/PQ...(1)

(PQ)² = PS·PR

QR/RS = PR/QR...(2)

(QR)² = RS·PR

(PQ)² + (QR)² = PS·PR + PR/RS = PR·(PS + RS) = PR×PR = (PR)²

(PQ)² + (QR)² = (PR)²

Equations (1) and (2), can be expressed as follows;

PQ/PS = PR/PQ...(1)

Multiply both sides by PS/PR

PQ/PS × (PS/PR) = PR/PQ × (PS/PR)

PQ/PS × (PS/PR) = PQ/PR

PR/PQ × (PS/PR) = PS/PQ

Therefore;

QR/RS = PR/QR...(2)

Multiplying both sides by (SR/PR). we get;

QR/SR × (RS/PR) = QR/PR

PR/QR × (RS/PR) = RS/QR

Therefore, the conclusions about the triangles, Yvonne can use in her proof of the Pythagorean Theorem are;

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Step-by-step explanation:

y/8=-10-5

y/8=-15

y=15×8

y=120

Answer:

the last option

2(x-9)=12;x=15

Answer:

2(x-9) = 12; x = 15

Step-by-step explanation:

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