Six more than the product of seven and a number is 55.
Which equation and solution correctly represent this sentence?
7 x + 6 = 55; x = 7
7 X+6 = 55; X= 49
X/7 + 6 = 55: x= 7
X/7 + 6 = 55; X= 49

Answer:

42 years

Step-by-step explanation:

if u were 4 years then your brother will be 2 years

if u r 44 then u can see that the difference between your previous age aand your brothers was 2 years

so here u just need to substract 2

44- 2 that will be 42

The area of the circle with the given radius is 201.088 square units.

The area of a circle is the space occupied by the circle in a two-dimensional plane. Alternatively, the space occupied within the boundary/circumference of a circle is called the area of the circle. The formula for the area of a circle is A = πr², where r is the radius of the circle.

Given that, the radius of a circle is 8 units.

Here, area of a circle

= 3.142×8²

= 3.142×64

= 201.088 square units

Therefore, the area of the circle is 201.088 square units.

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Answer: it is -1, because y has no more complete prime factors

Step-by-step explanation:

Answer:

60

x^3

Step-by-step explanation:

3x^-4 (8x + 12x)

apply exponential rule:

= 3 * 1/x^4 *(8x + 12x)

add similar elements

= 3 * 20 * (1/x^4) x

multiply fractions:

= 1 * 3 * 20x

        x^4

simplify:

= 60x

    x^4

finally = 60

             x^3

Collect like terms

3x^-4×(8x+12x)

=3x^-4 * 20x

=60x^-3

=60 * 1/x^3

\( \frac{60}{ x {}^{3} } \)

Answer:

unit rate of lemonade to cranberry juice

= 5:1

Step-by-step explanation:

A recipe for fruit punch calls for 1/2 liter of lemonada and 1/10 liter of cranberry juice

1/2 liter of lemonada= 0.5

1/10 liter of cranberry juice = 0.1

unit rate of lemonade to cranberry juice

= 0.5/0.1

unit rate of lemonade to cranberry juice

= (5*10^-1)/(1*10^-1)

unit rate of lemonade to cranberry juice

= 5/1 *(10^-1)/10^-1)

unit rate of lemonade to cranberry juice

= 5/1

unit rate of lemonade to cranberry juice

= 5:1

The unit rate of lemonade to cranberry juice is 5 : 1.

1/2 liters of lemonada are to be mixed with 1/10 litres of cranberry juice.

In ratio form this is:

1/2 : 1/10

To make it a unit rate of lamonada, you should divide both sides by the ratio of lamonada to cranberry juice in order to take lomonada's ratio to 1.

= 1/2 ÷ 1/2 :  1/10 ÷1/2

= 1 : 0.2

You then need to make the decimal a whole number by dividing both sides by the decimal:

= 1 ÷ 0.2 : 0.2 ÷0.2

= 5 : 1

The unit rate of lamonada to cranberry juice is therefore 5 : 1.

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The quartiles of the distribution are given as follows:

The sample size of the distribution is of:

n = 40.

The first quartile is the value that is greater than 25% of the distribution, hence it is the value at the position which is 25% of the sample size, hence:

The second quartile is the value that is greater than 50% of the  distribution, hence it is the value at the position which is 50% of the sample size, hence:

The third quartile is the value that is greater than 75% of the  distribution, hence it is the value at the position which is 75% of the sample size, hence:

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Answer: 0.3929

Step-by-step explanation:

From the question, we are going to assume that the apartment, park and shop lies on a straight line.

We've been told that Mr. Ledic's apartment to the park is (5x + 6) miles and the trip from the park to the coffee shop is (23x - 8) miles while the coffee shop is nine miles from her apartment. This vsn be written as:

(5x+6)+(23x-8) = 9

28x+6-8=9

28x-2=9

28x=9+2

28x=11

x=11/28

x = 0.3929

Therefore, the value of x is 0.3929

Answer:

a. x = roses

   y= lavender

b. x + y=36

c. 25x + 5y = 480

d. 19 rose bushes and 1 lavender bush

The probability that Aakesh will select a blue marble from each bag is 4/45.

To find the probability that Aakesh will select a blue marble from each bag, we need to calculate the probability of selecting a blue marble from each bag and then multiply those probabilities together.

Let's start with the first bag, which contains 5 marbles: 2 red marbles, 2 blue marbles, and 1 green marble. The probability of selecting a blue marble from the first bag is:

P(Blue from first bag) = Number of blue marbles / Total number of marbles in the first bag

P(Blue from first bag) = 2 / 5

Now, let's move on to the second bag, which contains 9 marbles: 3 red marbles, 2 blue marbles, and 4 green marbles. The probability of selecting a blue marble from the second bag is:

P(Blue from second bag) = Number of blue marbles / Total number of marbles in the second bag

P(Blue from second bag) = 2 / 9

To find the probability of both events happening (selecting a blue marble from each bag), we multiply the individual probabilities together:

P(Blue from both bags) = P(Blue from first bag) * P(Blue from second bag)

P(Blue from both bags) = (2 / 5) * (2 / 9)

P(Blue from both bags) = 4 / 45.

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Answer:

it is 11 years

Step-by-step explanation:

Hope it helps u

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The baker can only make peanut butter cookies and cannot make any chocolate chip cookies with the given amount of ingredients.

Let's denote the number of batches of peanut butter cookies as "x" and the number of batches of chocolate chip cookies as "y."

From the given information, we can set up the following system of equations:

For the flour:

2x + 3y = 26

For the butter:

34x + y = 9

To solve this system of equations, we can use the substitution method or the elimination method. Let's use the elimination method:

Multiply the first equation by 17 (to make the coefficients of x in both equations the same):

34x + 51y = 442

Now we have the system of equations:

34x + y = 9

34x + 51y = 442

Subtract the first equation from the second equation:

34x + 51y - (34x + y) = 442 - 9

50y = 433

Divide both sides by 50:

y = 433/50

Since the number of batches of cookies cannot be fractional, we need to find a whole number solution for y. However, in this case, y is a fraction, indicating that the given amount of butter is not sufficient to make even one batch of chocolate chip cookies.

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Answer: 125 degrees

Step-by-step explanation: <MTB and angle x are corresponding therefore congruent (Equal Measure) so the answer would be 125 degrees.

The measure of x is 125 degree.

The fundamental characteristics listed below make it simple to recognise parallel lines.

Given:

<NTB = 40 (Vertically Opposite Angle)

Now, x = <MTB (Corresponding Angle)

x= <MTN + <NTB

x= 85 + 40

x= 125

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Answer:

The first step is to calculate the average daily balance for the billing cycle. This is done by adding up the daily balances for each day of the billing cycle and then dividing by the number of days in the billing cycle. In this case, the billing cycle is from July 7 to August 6, so there are 31 days in the billing cycle.

The daily balances are as follows:

* July 7: $216.71

* July 14: $268.75

* July 17: $284.37

* July 21: $116.71

* July 24: $260.74

The average daily balance is therefore $226.81.

The next step is to calculate the finance charge. This is done by multiplying the average daily balance by the interest rate and then by the number of days in the billing cycle. In this case, the interest rate is 1.25% and the number of days in the billing cycle is 31 days.

The finance charge is therefore $7.43.

The final step is to calculate the new balance. This is done by adding the finance charge to the previous balance. In this case, the previous balance is $216.71 and the finance charge is $7.43. The new balance is therefore $224.14.

Here is the solution in mathematical form:

* Average daily balance = (216.71 + 268.75 + 284.37 + 116.71 + 260.74) / 31 = 226.81

* Finance charge = 226.81 * 0.0125 * 31 = 7.43

* New balance = 216.71 + 7.43 = 224.14

Step-by-step explanation:

The Propositions are resulting

(a) ∀x∃y(x = y²) is False

(b) ∀x∃y(x² = y) is True.

(c) ∃x∀y(xy = 0) is True.

(d) ∀x∃y(x + y = 1) is True.

(a) ∀x∃y(x = y²)

This proposition states that for every x, there exists a y such that x is equal to y². To determine the truth value, we need to check if this statement holds true for every value of x.

If we take any positive value for x, we can find a corresponding value of y that satisfies the equation.

For example, if x = 4, then y = 2 satisfies the equation since 4 = 2². Similarly, if x = 9, then y = 3 satisfies the equation since 9 = 3².

Therefore, the proposition (a) is false.

(b) ∀x∃y(x² = y)

For any given positive or negative value of x, we can find a corresponding value of y that satisfies the equation.

For example, if x = 4, then y = 2 satisfies the equation since 4² = 2. Similarly, if x = -4, then y = -2 satisfies the equation since (-4)² = -2.

Therefore, the proposition (b) is true.

(c) ∃x∀y(xy = 0)

The equation xy = 0 can only be satisfied if x = 0, regardless of the value of y. Therefore, there exists an x (x = 0) that makes the equation true for every y.

Therefore, the proposition (c) is true.

(d) ∀x∃y(x + y = 1)

To determine the truth value, we need to check if this statement holds true for every value of x.

If we take any value of x, we can find a corresponding value of y that satisfies the equation.

For example, if x = 2, then y = -1 satisfies the equation since 2 + (-1) = 1. Similarly, if x = 0, then y = 1 satisfies the equation since 0 + 1 = 1.

Therefore, the proposition (d) is true.

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Answer:

I'm pretty sure the answer to this is y=3

Answer:

∠ABC = 32

∠DBC = 42

Step-by-step explanation:

∠ABD = ∠ABC + ∠DBC

74 = 5x - 3 + 5x + 7

= 5x + 5x + 7 - 3

74 = 10x + 4

74 - 4 = 10x

70 = 10x

x = 70 / 10

x = 7

∠ABC = 5x - 3

= 5 ( 7 ) - 3

= 35 - 3

∠ABC = 32

∠ABD = ∠ABC + ∠DBC

∠DBC = ∠ABD - ∠ABC

= 74 - 32

∠DBC = 42

The function which represents the charge will be a piecewise function.

The concept used in this question is that of a piecewise function. A piecewise function is a mathematical function that is defined by multiple sub-functions, each of which applies to a certain interval of the function's domain.

In this case, the function that represents the monthly cost charged by CellFirst has two sub-functions: one for the fixed monthly fee and one for the additional fee charged for each additional GB of data used.

Here we have

CellFirst, a cellular company, charges each customer a monthly fee of d dollars for data usage up to x GB.

For each additional GB of data that a customer uses during the month, the company charges an additional fee of dollars.  

Let 'f(x)' be the function that is the cost that the company charges  

When the customer uses x GB for a month then the cost is d

f(x) = d, if 0 ≤ x ≤ x

When the customer uses more x GB for a month then the additional cost will be added to 'd'.

=> d + a(x - x), if x > x  

This function has two different linear parts: the first one represents the fixed monthly fee, which is charged regardless of the data usage, and the second one represents the additional fee charged for each additional GB of data used.

Therefore, The function which represents the charge will be a piecewise function.

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Answer:

.

Step-by-step explanation:

Answer:

Hi!

The graph will look something like this

I hope this helped you!

Answer:

Bias for the estimator = -0.56

Mean Square Error for the estimator = 6.6311

Step-by-step explanation:

Given - A normally distributed random variable with mean 4.5 and standard deviation 7.6 is sampled to get two independent values, X1 and X2. The mean is estimated using the formula (3X1 + 4X2)/8.

To find - Determine the bias and the mean squared error for this estimator of the mean.

Proof -

Let us denote

X be a random variable such that X ~ N(mean = 4.5, SD = 7.6)

Now,

An estimate of mean, μ is suggested as

\(\mu = \frac{3X_{1} + 4X_{2} }{8}\)

Now

Bias for the estimator = E(μ bar) - μ

                                    = \(E( \frac{3X_{1} + 4X_{2} }{8}) - 4.5\)

                                    = \(\frac{3E(X_{1}) + 4E(X_{2})}{8} - 4.5\)

                                    = \(\frac{3(4.5) + 4(4.5)}{8} - 4.5\)

                                    = \(\frac{13.5 + 18}{8} - 4.5\)

                                    = \(\frac{31.5}{8} - 4.5\)

                                    = 3.9375 - 4.5

                                    = - 0.5625 ≈ -0.56

∴ we get

Bias for the estimator = -0.56

Now,

Mean Square Error for the estimator = E[(μ bar - μ)²]

                                                             = Var(μ bar) + [Bias(μ bar, μ)]²

                                                             = \(Var( \frac{3X_{1} + 4X_{2} }{8}) + 0.3136\)

                                                             = \(\frac{1}{64} Var( {3X_{1} + 4X_{2} }) + 0.3136\)

                                                             = \(\frac{1}{64} ( [{3Var(X_{1}) + 4Var(X_{2})] }) + 0.3136\)

                                                             = \(\frac{1}{64} [{3(57.76) + 4(57.76)}] } + 0.3136\)

                                                             = \(\frac{1}{64} [7(57.76)}] } + 0.3136\)

                                                             = \(\frac{1}{64} [404.32] } + 0.3136\)

                                                             = \(6.3175 + 0.3136\)

                                                              = 6.6311

∴ we get

Mean Square Error for the estimator = 6.6311

Answer: See solution and explanations in the attached documents

Step-by-step explanation:

See explanations in the attached documents

The weight of the male that has a body surface area of 2.3 would be = 108kg

The body surface area (BSA) is defined as the parameter that can be used to estimate the surface area of a person's body based on body weight and height.

The formula for BSA = √w×h/3600

The weight of the male = X

The height of the male = 176cm

The BSA = 2.3

From the formula, make w the subject of formula;

w = BSA²× 3600/h

w = 2.3²× 3600/176

w= 5.29×3600 /176

w = 19044/176

w = 108kg

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Answer: 8 and 80

Step-by-step explanation:

8 * 5 = 40

8 * 10 = 80

8 must be the hcf of two separate numbers. So, one of them must be 8, and the other must be greater than 8.

Multiples of 8:

8

16

24

32

40

48

56

64

72

80

The numbers on that list that multiply evenly to 80:

8, 16, 40, 80

16 is the lowest common multiple of 16 and 8

40 is the lowest common multiple of 40 and 8

80 is the lowest common multiple of 80 and 8

So the two numbers are 8 and 80; the highest common factor (HCF) is indeed 8.

The required two numbers that are greater than 8 are 10 and 16.

The Highest Common Factor (HCF) is the greatest number among all common factors of two or more numbers. For example, the HCF of 14 and 8 is 2.

The Least Common Multiple (LCM) is the smallest number that is a multiple of all the numbers in a group. For example, the LCM of 14 and 8 is 56.

Let x and y be two numbers. Then we can write

HCF of x and y × LCM of x and y = x×y

Given that HCF and LCM of the required numbers are 8 and 80 respectively. We have to find two numbers that are greater than 8. Let us assume that a and b be the required numbers.

Using above formula,

a×b = 8×80

i.e. ab = 8×2×40 = 16×40

Clearly, the HCF and LCM of 16 and 40 are 8 and 80 respectively. They are also greater than 8.

So, the required two numbers that are greater than 8 are 10 and 16.

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Answer:

uhm smhtn

Step-by-step explanation:

i really just want points.

Answer:

(0,infinity)

Step-by-step explanation:

.

Answer:

31

Step-by-step explanation:

Let the smallest integer be x.

Since the 4 integers are consecutive (they come right after the other),

2nd integer= x +1

3rd integer= x +1 +1= x +2

4th integer= x +2 +1= x +3

Sum of the integers= 122

x +x +1 +x +2 +x +3= 122

4x +6= 122

4x= 122 -6

4x= 116

x= 116 ÷4

x= 29

3rd number

= 29 +2

= 31

Answer:

Step-by-step explanation:

7x - 4 = 5x - 10

2x - 4  = -10

2x = -6

x = -3

The graph of f(x) is the second one, so the correct option is B.

Here we have f(x), a piecewise function, and we want to see which one of the four graphs is the correct one.

You can see that the first domain of the function is:

x ≤ -4

So we must have a closed circle at x = -4, when the parabola ends.

The second domain is:

-4 < x < 1

So x here is not equal to -4 nor 1, so this part starts and ends with open circles.

finally, the linear part starts with a closed circle.

Also, notice that the line has a negative slope, so it goes down, then we can discard the first option.

Then we can see that the correct option is the second graph.

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Answer:

x>-4

Step-by-step explanation: