Choose all the expressions that are equal to 45×67 4 5 × 6 7. A. 2435 24 35 B. 4×75×6 4 × 7 5 × 6 C. 4×56×7 4 × 5 6 × 7 D. 6×54×7 6 × 5 4 × 7 E. 6×45×7 6 × 4 5 × 7

Answer:

3

Step-by-step explanation:

On the picture above.

Hope this helps.

Answer:

A

Step-by-step explanation:

Answer:

The answer is A.

Step-by-step explanation:

AP EX

Answer:

Nijah has 6 stickers left.

Step-by-step explanation:

Starting stickers:

45

2/5 are given away:

\(\frac{2}{5}\) * 45

\(\frac{2}{5}\) * \(\frac{45}{1}\)

\(\frac{90}{5}\)

18

1/3 of the remaining are given away:

\(\frac{1}{3}\) * 18

\(\frac{1}{3}\) * \(\frac{18}{1}\)

\(\frac{18}{3}\)

6

Nijah has 6 stickers left.

Answer:

18

Step-by-step explanation:

Find the part she gave to her sister

45 *2/5 = 18

The part remaining is

45 - 18 = 27

She gives 1/3 to Brett

27 * 1/3 = 9

She has 27 - 9 = 18

She has 18 remaining

Answer:

1/4

Step-by-step explanation:

To transform PQR into P'Q'R, dilate the preimage by 1/4, or shrink it by a scale factor of 4 because 3/12 = 1/4

Answer:

down below :)

Step-by-step explanation:

the answer is x = - y/2 + 5/2

your welcome hope this helped

The average weight of a random sample of 50 NFL players is 244.4 pounds.

An equation shows the relationship between two or more numbers and variables.

For a samples size (n) in normally distributed population, the sample mean is normally distributed, with mean μX=μ and standard deviation σX=σ/√n.

Hence for a sample of 50 NFL players with an average weight of 244.4 pounds:

Mean = mean = 244.4 pounds

The average weight is 244.4 pounds.

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Answer: 8

Step-by-step explanation: Using Pemdas, you have to do what is in the parenthesis first, so 6+3 is 9 and 4-5 is -1. Our new equation is 9 + -1. One math rule is that when you are adding with a negative, ignore the equal sign and just solve it. Our new equation is 9-1 which is 8.

When the radius is 9 cm, the area of the circular pool is increasing at a rate of 288π cm square/min.

To find how fast the area of the circular pool is increasing when the radius is 9 cm, we can use the formula for the area of a circle, which is A = πr^2, where A represents the area and r represents the radius.

Given that the radius is increasing at a rate of 4 cm/min, we can differentiate the formula for the area with respect to time (t) using the chain rule:

dA/dt = dA/dr * dr/dt

Here, dA/dt represents the rate of change of the area with respect to time, dr/dt represents the rate of change of the radius with respect to time, and dA/dr represents the derivative of the area with respect to the radius.

To find dA/dr, we can differentiate the formula for the area of a circle:

dA/dr = d/dt (πr^2)

= 2πr * dr/dt

Plugging in the given values, we have:

dr/dt = 4 cm/min

r = 9 cm

Substituting these values into the equation for dA/dr:

dA/dr = 2π(9) * 4

= 72π cm^2/min

Now, we can find dA/dt by multiplying dA/dr by dr/dt:

dA/dt = (72π cm^2/min) * (4 cm/min)

= 288π cm^2/min

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Answer:

A. (x² + 12)·(x + 2)

Step-by-step explanation:

Question; Factor x³ + 2·x² + 12·x + 24, using the grouping method

The given polynomial is presented as follows;

x³ + 2·x² + 12·x + 24

Using the grouping method, we have;

(x³ + 2·x²)( + 12·x + 24)

Which gives;

x²·(x + 2) + 12·(x + 2)

Therefore, we get;

(x² + 12)·(x + 2)

The correct option is A. (x² + 12)·(x + 2).

Answer:

D) 8x²-172x+120

Step-by-step explanation:

Length=2(-2x+20)+6

Width=-2x+20

(-4x+40+6)(-2x+20)

(-4x+46)(-2x+20)

8x²-80x-92x+920

8x²-172x+920

Answer:

The first one is mean absolute deviation and the second one is did not improve

Step-by-step explanation:

I took the test

The MAD is greater for this year’s 100-meter dash, which suggests that all 30 students did not improve equally.

The sum of all values divided by the total number of values determines the mean (also known as the arithmetic mean, which differs from the geometric mean) of a dataset. The term "average" is frequently used to describe this measure of central tendency.

The given table is:

                  Mean     MAD

Last Year    16.2 s     1.2

This Year    14.7 s      1.9

Looking at this table we can see that this year, the meantime is smaller than the one from last year, so the runners are faster on average.

The mean absolute deviation is bigger, but the change in the mean is bigger.

difference of the mean   16.2 - 14.7 = 1.5

difference of the MAD  1.9 - 1.2 = 0.7

This means that the average speed of the runners increased since last year,

and the fact that the MAD increased means that not all the runners increased their speed at the same rate, so now the speeds of the different runners are not as alike as last year.

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Complete question is;

Bart believes that mice exposed to microwaves will become extra strong (maybe he's been reading too much Radioactive Man). He decides to perform this experiment by placing 10 mice in a microwave for 10 seconds. He compared these 10 mice to another 10 mice that had not been exposed. His test consisted of a heavy block of wood that blocked the mouse food. He found that 8 out of 10 of the microwaved mice were able to push the block out of the way. 7 out of 10 of the non-microwaved mice were able to do the same.

Identify the following;

1) Control group

2) Independent variable

3) Dependent variable

4) What should bart's conclusion be?

5) How could Bart's experiment be improved?

Answer:

1) Mice not exposed to the microwave.

2) Amount of microwave radiation hitting the mice.

3) The strength of the mice exposed to the radiation.

4) Conclusion should be inconclusive.

5) Can be improved in 3 ways listed under explanation.

Step-by-step explanation:

1) The control group is the mice that were not exposed to the microwave heating. This is because a control group is a set of samples that are kept separate and not exposed to the independent variable.

2) The independent variable is the cause of the research. So in this case the independent variable is the amount of microwave radiation because the study is on how mice exposed to microwaves become extra strong.

3) Dependent variable: The dependent variable will be the strength of the mice that are exposed to the microwave radiation because the extra amount of strength depends on the radiation.

4) Bart's conclusion should be Inconclusive because even though there is difference in the results gotten from the exposure, they are not that significantly different and thus we can say that there is an equal chance of an effect or no effect.

5) Bart's experiment can be improved by the following;

- Using a larger sample size

- Increasing the amount of groups so as to have a varied amount of microwave radiation received by the exposed mice

- Increasing the mass of the block that's in front of the food.

Answer:

(B) has the closest values.

Step-by-step explanation:

Solve the triangle: A = 51°, b = 14, c = 6

A. a ≈ 14.9, C ≈ 28.1, B ≈ 100.9

B. a ≈ 11.2, C ≈ 24.1, B ≈ 104.9

C. a ≈ 14.9, C ≈ 24.1, B ≈ 104.9

Using the cosine rule,

a^2 = b^2+c^2-2bc (cos(A))

= 196+36 - 2(14)(6)cos(51)

=  196+36 - 105.72

= 126.27

a = sqrt(126.27)

= 11.24

using sine rule,

sin(C)/sin(A) = 6/11.24

sin(C) = 6/11.24*sin(51)= 0.41495

C = arcsin(0.41495 = 24.5 degrees, reasonably close to the given value, probably due to the answer used the rounded value of a.

B = 180-51-24.5 =104.5

Out of the given options, only (B) has the correct value of a and C

Answer:

The \(n^{th}\) term of A.P sequence

tₙ = 9 n - 26

Step-by-step explanation:

Step(i):-

Given sequence

                   - 17 , -8 , 1 .......

first term   = -17

Second term =  - 8

The difference of first two terms

                        d = - 8 -(-17) = -8+17 = 9

The difference of next two terms

                        d = 1 - (-8) = 1+8 =   9

∴ The given sequence is  in A.P ( Arthimetic progression)

Step(ii):-

The \(n^{th}\) term of A.P sequence

                \(t_{n} = a + ( n-1 ) d\)

Given a = - 17 and  d = 9

                \(t_{n} = -17 + ( n-1 ) 9 = - 17 + 9 n -9 = 9 n - 26\)

Final answer:-

The \(n^{th}\) term of A.P sequence

tₙ = 9 n - 26

Answer:

32 - 4 = 28 units^2

Step-by-step explanation:

Rectangle area = width x length

4 x 8 = 32

Rectangle minus the missing right triangle.

Triangle area: (base x height)/2

Right triangle = (4 x 2)/2 = 4

The cost of the jam Elmo uses to make the sandwiches =$1.65

What is the cost of the jam Elmo uses to make the sandwiches?

B globs of Peanut butter at 4 cents = 4B

J blobs of Jam at 5 cents = 5J

The number of sandwiches is given by the linear equation,

N(4B + 5J ) =$ 2.53

N(4B + 5J ) = 253 cents    ---(1)

The factors of 253 = 1, 11, 23, 253.

Since N > 1 , N is 11 or 23

Considering N = 11

11(4B + 5J ) = 253

4B + 5J  = 23   ---(2)

The possible values of B and J to satisfy the linear equation:

B = 2 and J = 3

Substituting B and J in (2)

4B + 5J  = 23

4 (2) + 5(3) = 23

8 + 15 = 23

23 = 23

The linear equation is verified.

The cost of jam Elmo uses to make the sandwiches =N( 5J)

                                                                                       =11 (5*3)

                                                                                       = 11 *15

                                                                                        = 165 cents or $1.65

The complete question is:

elmo makes N sandwiches for a fundraiser. for each sandwich he uses B globs of peanut butter at 4 cents per glob and J blobs of jam at 5 cents per blob. the cost of the peanut butter and jam to make all the sandwiches is $2.53. assume that B, J, and N are positive integers with N>1. what is the cost of the jam elmo uses to make the sandwiches?

What is a linear equation?

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The depth of water in tank A is modeled by a differentiable and increasing function h.

This means that the function h describes how the depth of water changes as time passes.

The fact that it is differentiable means that the function has a well-defined slope at every point, which indicates how quickly the depth is changing. This means that the function is continuous and smooth, with no sharp turns or corners.
Furthermore, the fact that the function is increasing means that the depth is always getting higher over time.

This makes sense since water is constantly being added to the tank.

Hence, the depth of water in tank A is described by a differentiable and increasing function h, which means that the function has a well-defined slope at every point and that the depth is always getting higher over time.

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Answer:

The answer is 0

Step-by-step explanation:

2n^3 + 3n + 10 can be written as a polynomial of the form Q(n^3), where Q(n^3) represents the set of polynomials of the form a(n^3).

To prove that the expression 2n^3 + 3n + 10 is in the set Q(n^3), where Q(n^3) represents the set of polynomials of the form a(n^3), we need to show that the expression can be written in the form a(n^3) for some constant "a".

Let's start by factoring out the common factor of n^3 from each term:

2n^3 + 3n + 10 = n^3(2 + 3/n^2 + 10/n^3)

Now, let's rewrite the expression as a single term multiplied by n^3:

2n^3 + 3n + 10 = (2 + 3/n^2 + 10/n^3)n^3

Simplifying the expression inside the parentheses:

= (2n^3 + 3n^2 + 10n^3)/n^3

= (12n^3 + 3n^2)/n^3

= 12 + 3/n

ow, we can see that the expression can be written in the form a(n^3), where a = 12 and n^3 = 3/n.

Therefore, we have shown that 2n^3 + 3n + 10 can be written as a polynomial of the form Q(n^3), where Q(n^3) represents the set of polynomials of the form a(n^3).

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The range of the data provided in the boxplot given the minimum number and the maximum number is 2.

A box plot is used to study the distribution and level of a set of scores. The box plot consists of two lines known as the whiskers and a box. The left whisker represents the lowest number in the dataset. The right whisker represents the highest number in the dataset. The difference between these numbers is the range.

The box can be used to determine the first quartile, median and the third quartile. These values can be determined using the lines on the box.

The range of a data set is the difference between the highest number and the lowest number. Range is used to measure the variance of a dataset.

Range = highest number - lowest number

7.5 - 5.5 = 2

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Answer:

22.5 miles

Step-by-step explanation:

There are 3, 20 minute increments in an hour, and 1 and a half 20 minute increments in half an hour, so, you simply add 3 + 1.5 which equals 4.5.

Then, multiply 5 (miles) by 4.5 to get 22.5 (miles).

The value of \(x=-\frac{1}{5}\) and \(y=\frac{31}{5}\).

The given equations are \(y=4x+7\) and \(y=9x+8\).

We have to solve these equations using the substitution method.

Substitution Method

In this method we find the value of one variable from one equation using elimination method and then put that value of that variable in other equation. In simple word we substitute value of one variable from one equation to the other equation.

In the given equation the two equation are

\(y=4x+7\dots\dots\dots\)Equation \((1)\)

\(y=9x+8\dots\dots\dots\)Equation \((2)\)

Putting the value of \(y\) from the Equation \((1)\) in the Equation \((2)\)

\(4x+7=9x+8\)

Subtract \(8\) on both side

\(4x+7-8=9x+8-8\)

Simplifying

\(4x-1=9x\)

Subtract \(4x\) on both side

\(4x-1-4x=9x-4x\)

Simplifying

\(-1=5x\)

\(5x=-1\)

Divide by \(5\) on both side

\(\frac{5}{5}x=-\frac{1}{5}\)

\(x=-\frac{1}{5}\)

Now putting the value of \(x\) in equation \((1)\)

\(y=4(-\frac{1}{5})+7\)

Simplifying

\(y=-\frac{4}{5}+7\)

\(y=-\frac{4}{5}+7\times\frac{5}{5}\)

\(y=-\frac{4}{5}+\frac{35}{5}\)

\(y=\frac{-4+35}{5}\)

\(y=\frac{31}{5}\)

Hence, the value of \(x=-\frac{1}{5}\) and \(y=\frac{31}{5}\).

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The following pairs of equations have its second equation valid

7 + 5x= 3 - 2x and 7 + 7x = 3

1/(x - 5) = 10 and 1 = 10(x - 5)

The invalid equations are;

3(x - 4) = 15 and x - 4 = 15

x^2 = 6x and x = 6

1. 7 + 5x= 3 - 2x and 7 + 7x = 3

Add 2x to both sides

7 + 5x + 2x = 3

7 + 7x = 3

Valid

2. 3(x - 4) = 15 and x - 4 = 15

3x - 12 = 15

Invalid

3. x^2 = 6x and x = 6

find the square root of both sides

√x² = √6x

x = √6x

Invalid

4. 1/(x - 5) = 10 and 1 = 10(x - 5)

cross product

1 × 1 = 10(x - 5)

1 = 10(x - 5)

Valid

Therefore, 7 + 5x= 3 - 2x and 7 + 7x = 3;

1/(x - 5) = 10 and 1 = 10(x - 5) are the valid equations.

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The truth values for the given complex statements are:

3. False

4. False

5. False

6. True

7. False

8. Undefined

9. True

10. True

11. True

12. False

13. True

14. True

15. True

16. False

17. True

18. False

19. True

20. False

To determine the truth value of each complex statement, we'll use the given truth values:

A = True

B = True

C = True

X = False

Y = False

Z = False

Let's evaluate each statement:

3. B • Z

B = True, Z = False

Truth value = True • False = False

4. X V Y

X = False, Y = False

Truth value = False V False = False

5. ~C v Z

C = True, Z = False

Truth value = ~True v False = False v False = False

6. B - Z

B = True, Z = False

Truth value = True - False = True

7. (A v B) Z

A = True, B = True, Z = False

Truth value = (True v True) • False = True • False = False

8. ~(THIS)

"THIS" is not defined, so we cannot determine its truth value.

9. B v (Y • A)

B = True, Y = False, A = True

Truth value = True v (False • True) = True v False = True

10. A • (Z v ~Y)

A = True, Z = False, Y = False

Truth value = True • (False v ~False) = True • (False v True) = True • True = True

11. (A • Y) v (~Z • C)

A = True, Y = False, Z = False, C = True

Truth value = (True • False) v (~False • True) = False v True = True

12. (X v ~B) • (~Y v A)

X = False, B = True, Y = False, A = True

Truth value = (False v ~True) • (~False v True) = False • True = False

13. (Y • C) ~ (B • ~X)

Y = False, C = True, B = True, X = False

Truth value = (False • True) ~ (True • ~False) = False ~ True = True

14. (C • A) v (Y = Z)

C = True, A = True, Y = False, Z = False

Truth value = (True • True) v (False = False) = True v True = True

15. (A • C) (~X • B)

A = True, C = True, X = False, B = True

Truth value = (True • True) (~False • True) = True • True = True

16. (A • Y) (~Z • C)

A = True, Y = False, Z = False, C = True

Truth value = (True • False) (~False • True) = False • True = False

17. ~[(A • Z) (~C • ~X)]

A = True, Z = False, C = True, X = False

Truth value = ~(True • False) (~True • ~False) = ~False • True = True

18. [(A • Z) (~C • ~X)]

A = True, Z = False, C = True, X = False

Truth value = (True • False) (~True • ~False) = False • True = False

19. (A • Z) v (Y = Z)

A = True, Z = False, Y = False

Truth value = (True • False) v (False = False) = False v True = True

20. A • ~A

A = True

Truth value = True • ~True = True • False = False

Therefore, the truth values for the given complex statements are:

3. False

4. False

5. False

6. True

7. False

8. Undefined

9. True

10. True

11. True

12. False

13. True

14. True

15. True

16. False

17. True

18. False

19. True

20. False

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Answer:

b

Step-by-step explanation:

b