b) Work out
(10-3 × 2)²
c) What is the value of the power a if 5ª:
=
125
?

Answer:

2√6(Decimal: 4.898979)

Step-by-step explanation:

−9√24+2√600

=2√6(Decimal: 4.898979)

Simplification: -4 x (5+1) = (-4 x 5) + (-4 x 1)

Take LHS,

-4 x (5+1) = -4x6

 = -24

Take RHS,

(-4 x 5) + (-4 x 1) = -20 + (-4)

= -20-4

= -24

LHS= RHS

Hence -4 x (5+1) = (-4 x 5) + (-4 x 1) this equation is verified.

The fundamental guidelines and procedures to simplify any algebraic statement are as follows: By multiplying factors, remove any grouping symbols like brackets and parenthesis. If the words contain exponents, use the exponent rule to eliminate grouping. Add or remove like words to combine them.

Start by resolving all of the terms included in parenthesis to simplify mathematical equations using the order of operations. The exponents should then be solved, followed by any necessary multiplication. Division problems are next, followed by adding and subtracting to wrap things out.

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Solving for the probability using the z-table, the percentage of customers that have to wait longer than 49 minutes is 1.2 %.

For a normally distributed set of data, given the mean and standard deviation, the probability can be determined by solving the z-score and using the z-table.

First, solve for the z-score using the formula below.

z-score = (x – μ) / σ

where x = individual data value = 49

μ = mean = 40

σ = standard deviation = 4

z-score = (49 - 40) / 4

z-score = (9) / 4

z-score = 2.25

Find the probability that corresponds to the z-score in the z-table. (see attached images)

x = (0.9861 + 0.9893)/2

x = 1.9754/2

x = 0.9877

Subtract it from 1 and multiply by 100 to get the percentage.

% = (1 - 0.9877) x 100

% = 0.0123 x 100

% = 1.23%

% = 1.2 %

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Answer:

[tex] \sf \: \frac{41}{4} q + \frac{ - 5}{2} [/tex]

Step-by-step explanation:

Let's simplify step-by-step.

−3/2(−3/2q+5/3)+8q

Distribute:

=(−3/2)(−3/2q)+(−3/2)(5/3)+8q

=9/4q+−5/2+8q

Combine Like Terms:

=9/4q+−5/2+8q

=(9/4q+8q)+(−5/2)

=41/4q+−5/2

The length of line segment AB  shown in the line graph is is 2 units

With the given line graph it is very obvious that the line segment AB has two point A and B with -4 and -2 as their value

To measure the length we need to subtract the x coordinate of one end point from the another end point

here we will deduct the x coordinate of b point from the x coordinate of A point which is shown below

           - 4 - (-2)

and using the simple integer properties we can solve this problem of line graph

           - 4 + 2

which comes out to be 2

hence, the length of line segment AB  shown in the line graph is is 2 units

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Answer: m<8=97 degrees.

m<5=83 degrees

Step-by-step explanation:

m<8=m<2 ==> Angles 8 and 2 are alternate interior angles, meaning that they're equal.

m<8=97 degrees.

m<8+m<5=180 degrees ==> Both angles 8 and 5 add up to a straight line, and straight lines measure 180 degrees and are called straight angles.

97+m<5=180

97-97+m<5=180-97

m<5=83 degrees

37 • 2 • (0 + 1/2 ) - Inverse property of addition

37 • 2 • 1/2 - Commutative property of addition

37 • 1 - Inverse property of multiplication.

37 - Identity property of multiplication.

Algebraic expressions include at least one variable and at least one operation addition, subtraction, multiplication or division.

We have,

37 • 2 • (-5+ 5+ 1/2)

= 37 • 2 • (0 + 1/2 )  -Inverse property of addition

The inverse property of addition states that:

a + (-a ) = 0 where a ∈ R

= 37 • 2 • 1/2 - Commutative property/Identity property of addition

The commutative property of real numbers states that:

a + b = b + a where a,b ∈ R

= 37 • 1 - Inverse property of multiplication.

The inverse property of real numbers states that:

a + 1/a = 1 where a ∈ R

= 37 - Identity property of multiplication.

The identity property of multiplication of real numbers states that:

a x 1 = a where a ∈ R

Thus,

37 • 2 • (0 + 1/2 ) - Inverse property of addition

37 • 2 • 1/2 - Commutative property of addition

37 • 1 - Inverse property of multiplication.

37 - Identity property of multiplication.

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The complete question is:

For the following problem, match the name of the number property that was used to get to each step from the previous step.

37 • 2 • (-5+ 5+ 1/2)

37 • 2 • (0 + 1/2 )

37 • 2 • 1/2

37 • 1

37

identity property of addition

commutative property

inverse property of multiplication

inverse property of addition

identity property of multiplication

The value of the expression log₈32 by using the change of base formula is 1.67.

Given that the expression is log₈32.

We are required to find the value of the expression using change of base formula.

The change of base formula is basically used at a time when we have to re-write a logarithm operation as a fraction of logarithms with a new base to find the value of the logarithm.

The result given by it is [tex]log_{a}b[/tex]=log b/log a.

The expression is log₈32.

log₈32=log 32/log 8

=log [tex]2^{5}[/tex]/ log [tex]2^{3}[/tex]

=5log 2/3log 2

=5/3

=1.67

Hence we can say that the value of the expression log₈32 by using the change of base formula is equal to 1.67.

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2 x 10^5 miles is the correct answer.

A power of ten in mathematics is defined as one of the integer powers of a number multiplied by ten. Integers can be both positive and negative. To find the multiple of ten, we need to add 10 to itself several times (if the power is a positive integer).

if we have a value that says ten ^5,

then this value is equal to:

= 10 x 10 x 10 x 10 x 10

= 10,0000

Also, by the definition of a multiple of ten, the number 1 is a power of 10 as well if we take the 0th power of 10.

10^0 = 1

Whatever the integer is, it is multiplied by 10 n times. So, the long form of a power of 10 is the number 1, followed by n zeros, where the n number is greater than the 0 value.

Here the distance that is given to us is:

238,855

We can also write it as,

2 x 10 ^ 5.

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The required factor for the given expression is (x + 4)(3x - 1).

In mathematics, factorization or factoring refers to the process of composing a number or other mathematical object from numerous factors, usually smaller or simpler counterparts.

The given expression is 3x² + 11x - 4.

To factor a general quadratic expression of the form ax² + bx +c, we need to consider the product "ac" and find two factors for this number such that their sum is equal to b. during this case, a = 3, b = 11, and c = -4..

Therefore we need to consider the product ac = 3 × (-4) = -12.

Consider the 2 factors 12 and -1 for the product -12.

Then we have the sum is equal to 12 + (-1) = 12 - 1 = 11.

Therefore the expression 3x² + 11x - 4= 3x² + 12x + (-1)x -4= 3x² +12x - x - 4= 3x(x + 4) - (x + 4)= (x + 4)(3x - 1)

Therefore, the required factor for the given expression is (x + 4)(3x - 1).

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The system of the equation has x = 0.

The two equations are,

y = 2x + 6x + 4

y = -4x + 4

Now equating the equation, we have

2x + 6x + 4 = -4x + 4

8x + 4 = -4x + 4

12x = 0

x = 0

Therefore the system of the equation has x = 0.

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Answer:

-7.5

Step-by-step explanation:

[tex]\frac{6 + (-12) + 24 + (-48)}{4} =\frac{-30}{4} =-7.5[/tex]

Answer:

Step-by-step explanation:

its 1

The value of the expression e⁻⁴ is 0.0183 to four decimal places.

We are given the expression:

e⁻⁴

We need to evaluate the expression to four decimal places.

Now, we know that the value of e is:

e = 2.71828182846

Now, e⁻⁴ can also be written as:

e⁻⁴ = 1 / e⁴

Substituting the value of e, we get that:

1 / e⁴ = 1 / (2.71828182846)⁴

= 1 / 54.5981500331

= 0.0183156389

Now rounding off to 4 decimal places, we get that:

= 0.0183

Therefore, the value of the expression e⁻⁴ is 0.0183.

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The range of the function y=1/2x+3 when the domain is {-2, 0, 2, 4} is {-1 , 0.33 , 0.14 , 0.090}

We have given a function y = 1/2x+3 .....(1) and domain {-2, 0, 2, 4} .

In order to find the range putting x = -2 in equation (1) , we get

y=1/(2(-2)+3

y=1/-4+3

y=1/-1

y = -1

Putting x = 0 in equation (1) , we get

y=1/2(0)+3

y=1/0+3

y=1/3

y = 0.33

Putting x = 2 in equation (1) , we get

y=1/2(2)+3

y=1/4+3

y = 1 / 7

y = 0.14

Putting x = 4 in equation (1) , we get

y=1/2(4)+3

y=1/8+3

y= 1 / 11

y = 0.090

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Based on the fact that the correlation coefficient was 0.1 in the plot of Bacteria versus Time, the reason is B. The bacteria have grown at an exponential rate and a line poorly fits the data.

The correlation coefficient shows the relationship between two variables. It is between -1 and 1 and figures closer to 0 denote a weak correlation.

In this instance, Bacteria is known to increase exponentially which means that a linear regression model would make a line that poorly fits the data. This would lead to a low correlation coefficient when it should instead be high.

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Answer: Answer is C

Step-by-step explanation:

Answer:

The equation of a line in slope intercept form is

y=mx+c

in integers form y=2x+3

Answer:

Step-by-step explanation:

-4x^3 + 28x^2 - 20x

= 4x(-x^2 + 7x - 4)

Based on the given task content, the division of 4,550 by 64 is approximately 71.09 to two decimal places.

4,550 divided by 64

The divisor which is a number or expression that another number divides is 4,550

The dividend which is the number or the expression which is used to divide another is 64

The quotient here simply refers to the result which is obtained by dividing one number by another.

4,550 divided by 64

= 4,550 / 64

= 71.09375

This result above can be correctly approximated to two decimal places, that is, two values after the decimal point.

Approximately,

71.09375

= 71.09

This is a number expressed in the decimal system (base 10), particularly fractional numbers.

For instance, in the illustration below:

13¼ = 13.25 as a decimal number.

So therefore, the division of 4,550 by 64 is approximately 71.09 to two decimal places.

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Since the ratio is 12 : 5, the statement which is true is there are more than twice as many cows as there are sheep.

The ratio between the number of cows to number of sheep in a field is given as:

12 : 5

Now,

let the number of sheep be 5 x.

So, the number of cows will be 12 x.

So, we get that:

12 x > 2 ( 5 x)

12 x > 10 x

So, the statement which is true will be:

there are more than twice as many cows as there are sheep

Therefore, since the ratio is 12 : 5, the statement which is true is there are more than twice as many cows as there are sheep.

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Answer:93000

Step-by-step explanation:

The answer choice that correctly represents the quotient of 28134 divided by 71 is 28134/71

The quotient statement is given as

28134 divided by 71

In mathematics, quotient  is represented by division using the symbol /

i.e. the quotient of a and b is a/b

Using  the above as a guide, we have the following quotient expression

28134/71

Hence. the answer choice that correctly represents the quotient of 28134 divided by 71 is 28134/71

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The inequality that represent the possible length of the third side is

                    7 < x < 17

According to the triangle inequality theorem, the sum of any two sides of a triangle must be greater than the measure of the third side of the triangle.

We have been given measure of two sides which are 5 and 12. Then the possible length for the third side has two condition

Let the third side be x unit.

First condition,      x + 5 > 12

                              x > 7

Second condition,  12+ 5 > x

                                  17 > x

Hence the inequality that represent the possible length of the third side is

                    7 < x < 17

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Answer:

(- 1 , 1 )

Step-by-step explanation:

Answer:

12 is the fill in

Step-by-step explanation:

It should be noted that the total cost (t) after 8% sales tax is added to an Items price (p): 1.08p. This is true.

It should be noted that tax simply has to do with the compulsory levy that's paid by the individuals and firms to the government.

It should be noted that from the information, the total cost (t) after 8% sales tax is added to an Items price (p): 1.08p. This will be confirmed this:

Price = p

Tax = 8%

New price = Price + Tax

New price = p + (8% × p)

New price = p + 0.08p.

New price = 1.08p

Therefore, it should be noted that the total cost (t) after 8% sales tax is added to an Items price (p): 1.08p. This is true.

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The total cost (t) after 8% sales tax is added to an Items price (p): 1.08p. True or false?

Answer: 9

Step-by-step explanation: