pat wants to buy four donuts from an ample supply of three types of donuts: glazed, chocolate, and powdered. how many different selections are possible?

The absorbance of the given sample is 0.2076.

Length of the cuvette = 1 cm

Wavelength of the spectrophotometer = 620nm

Transmittance of the sample = 62%

We know, absorbance is related to transmittance by the formula written below;

A = log(1/T)                                                 equation 1

Also, percent transmittance %T = 100T

or we can write, T = (%T) / 100

On substituting value of T in equation 1 , we get

A = log(100/(%T))    

⇒ A = log(100) - log (%T)      

⇒ A = log([tex]10^{2}[/tex]) - log(%T)

⇒ A=  2log(10) - log(%T)    

We know, log10 = 1. On substituting the value of log 10 in above equation, we get

A = 2 - log(%T)

⇒ A = 2 - log(62)

⇒ A = 2 - 1.7924

⇒ A = 0.2076

The absorbance of the given sample is 0.2076.

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Using the distance formula, the distance between B and C is calculated as: 2.3 units.

The distance formula to apply is: d = [tex]\sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}[/tex].

Given the following:

B (3,−4) = (x1, y1)

C (5,−5) = (x2, y2)

Plug in the values into the distance formula

BC = √[(5−3)² + (−5−(−4))²]

BC = √[(2)² + (−1)²]

BC = √(4 + 1)

BC = √5

BC = 2.236068 ≈ 2.3 units.

Therefore, using the distance formula, the distance between B and C is calculated as: 2.3 units.

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Answer:

Step-by-step explanation:

A

Hello,

[tex] \frac{8 {}^{5} }{8 {}^{ - 9} } = 8 {}^{5 - ( - 9)} = 8 {}^{5 + 9} = 8 {}^{14} [/tex]

The number that fits in the given situation is -20.

Now,

Let us suppose the number is x.

As a result, the next condition is twice the sum, which can be written as:

As a result of the condition, we can write the equation as:

Solve for x: x = 2x + 20

Taking 20 off both sides:

Therefore, the number that fits in the given situation is -20.

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The maximum number of shirts in each row so that all the rows are equal in length is 12.

From the information, the salesclerk is creating a display of 12 polo shirts and 48 team shirts and only one type of shirt can be in each row.

It should be noted that the value van be found by knowing the highest common factor for the numbers.

The highest common factor for 12 and 48 is 12.

Therefore, the correct option is A.

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Answer:

Step-by-step explanation:

The cost of labor per hour is $45.

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The statistical test that should be done to determine if there is a significant difference is the independent t-test.

What're is an independent t-test?

It should be noted the independent t-test or students t-test for two samples should be used.

The Independent Samples T-Test compares the means of two independent groups to determine whether there is statistical evidence that the associated population means are significantly different.

In this case, the biology department needs to decide which lab curriculum yields better student outcomes, the.t text can be applicable.

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The division of the number -33.44/-1.9 is 17.6.

Division is one of four fundamental mathematical operations, along with addition, subtraction, as well as multiplication.

For the given expression;

=  -33.44/-1.9

as, both numerator and denominator is negative values, both negative signs will be cancelled.

Now, divide numerator 33.44 by denominator by 1.9, we get 17.6.

Thus, the division of the number -33.44/-1.9 gives quotient 17.6.

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The slope-intercept equation of a line that passes through the points (-2,5) and (6,-4) is [tex]y=-\frac{9}{8}x+\frac{11}{4}[/tex]

We know that the slope-intercept form of the line is y =  mx + c, where m is the slope of the line and c is the y-intercept of the line.

For given question we have been given two points (-2,5) and (6,-4)

We need to find the slope-intercept equation of a line that passes through the points (-2,5) and (6,-4).

Using two-point form the equation of the line is,

[tex]\frac{y-y_1}{y_2-y_1}=\frac{x-x_1}{x_2-x_1}[/tex]

Let (x1, y1) = (-2,5) and (x2, y2) = (6,-4)

So, the equation of the line is,

[tex]\frac{y-5}{-4-5} =\frac{x-(-2)}{6-(-2)}\\\\ \frac{y-5}{-9} =\frac{x+2}{6+2}\\\\\frac{y-5}{-9} =\frac{x+2}{8}\\\\ 8(y-5)=-9(x+2)\\\\8y-40=-9x-18\\\\8y=-9x-18+40\\\\8y=-9x+22\\\\y=-\frac{9}{8}x+\frac{11}{4}[/tex]

above equation is in the slope-intercept form.

Therefore, the slope-intercept equation of a line that passes through the points (-2,5) and (6,-4) is [tex]y=-\frac{9}{8}x+\frac{11}{4}[/tex]

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Devante spent 2 dollars 43 cents

In this question,

A gum is 21 cents a pack and candy bars are 45 cents each.

Devante buy 3 packs of gum.

So for 3 packs of gum total amount would be,

3 × 21 = 63 cents

Devante buy 4 candy bars.

So for the four candy bars the total amount would be,

4 × 45 = 180 cents

Total purchase would be,

63 cents of packs of gum + 180 cents of candy bas

= 243 cents

We know that 1 dollar = 100 cents

S0, 243 cents = 2.43 dollars

Therefore, Devante spent 2 dollars 43 cents

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The function g(x) models a downward facing parabola shape which is option A

The function g(x) have the solutions which are given in the form of coordinates

This can be solved on a sheet of graph using coordinate geometry  

(-3,0), (-2,-4) , (-1, -6) , (0, -6 ), (1,-4),(2,0)  and (3,6)

If we will plot all the given seven points given on the graph and join the points we would get a downward sloping parabola model which looks like reverse 'U' shaped  whose highest point is between -1 and 0 that is -0.5

lies in second quadrant of the graph sheet.

Hence the given function g(x) models a parabola shape which is option A

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Step-by-step explanation:

Hope that helps!!

The length of the  Boca Grand Causeway is  126,000 feet

Multiplication is the continual addition of two or more numbers of equal sizes. The value gotten after multiplication is the product. Multiplication is one of the basic mathematical operations. The sign used to denote multiplication is x. Other basic mathematical operations include addition, subtraction and division.

Length of the Boca Grand Causeway = length of the golden gate bridge x 14

9,000 x 14 = 126,000 feet

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Answer:

72 months

Step-by-step explanation:

6 x 12 = 72

The statements that could be represents the expression 40×(-18) is

The expression= 40×(-18)

A hot air balloon descends 18 inches per a second for 40 seconds=40×(-18)

A hot air balloon ascends 40 inches per a second for 18 seconds=40×18

Trey withdraws $18 from his checking account once a week for 40 weeks=40×(-18)

Suzanne deposits $18 into her savings account once a week for 40 weeks=40×18

Morty withdraws $40 from his checking account once a month for 18 months=40×(-18)

Hence, The statements that could be represents the expression 40×(-18) is

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It would take 10 months to equate the population of both the towns

Let the number of months required to equate the population of both the town( Town A and Town B) be x

This question can be solved using linear equations

So, town A's population would be current population adjusted with migration of people  which is 42975-125x+150x

And town B's population would be current population adjusted with migration of people  which is 45225 -200x

As at the end of x months the population of the two towns is equal, so equating both the linear equations

 42975 -125x +150x = 45225-200x

Now solving the equation for x

150x-125x+200x= 45225-42975

225x=2250

Therefore x= 2250/225= 10

Hence it would take 10 months to equate the population of both the towns

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Answer:  3[tex]\sqrt4[/tex]

Step-by-step explanation:

Simplified radical form of the square root of 45

Square root of 45 can be expressed as, √45 = √(9 × 5) = 3√5. 45 is not a perfect square, so, it remains within roots. The simplified radical form of the square root of -45 is 3√5.

Answer:

3√5i

Step-by-step explanation:

[tex]\sqrt{-45}=\sqrt{-1}\sqrt{45}\\\sqrt{-1}\sqrt{45}\\i\sqrt{45}\\**Prime\:Factorization*\\3 \times 3 \times 5 = 45\\=3\sqrt{5}i[/tex]

➲ Hope this helps.

The coordinates of the vertices of the new triangle are A'(-1,1) ,B'(-4,3), C'(-3,6)

Rotation means the circular movement over the object around the center.

Vertices of triangle = A(1,1) , B(3,4), C(6,3)

Triangle is rotated counterclockwise about the origin 90°.

Then

the new coordinates of triangle are A', B', C'

A(1,1) = A'(-1,1)

B(3,4) = B'(-4,3)

C(6,3) = C'(-3,6)

The coordinates of the vertices of the new triangle are A'(-1,1) ,B'(-4,3), C'(-3,6)

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Answer:

Below.

Step-by-step explanation:

a. True - it states that 4 is an element of Set P.

b False - 5 is an element of set Q .

   5 ∈ Q.

c. P ∩ Q = Ф True - This says that there are no common elements in P and Q   which is true.  Ф is the 'empty set'.

d. True: n(P) = 4 means there are 4 elements in P.

e. True: there are 4 elements in P and in S.

   S can be written as {3, 4, 5, 6} - that is the integers which are greater      than 2 and less than or equal to 6. The Z means the set of integers.

The answer is k⁴n⁶/3 after solving the expression.

Given, the expression is kn/3k⁻³n⁻⁵

now we must simplify the expression with the help of the negative exponent rule.

A base that is on the fraction line's denominator side can be indicated by a negative exponent. In other words, according to the negative exponent rule, a number with a negative exponent should be added to the numerator and vice versa.

that is, a⁻ⁿ = 1/aⁿ

therefore,  kn/3k⁻³n⁻⁵ = knk³n⁵/3

Multiply the monomials.

Monomials should be multiplied by adding the exponents to the coefficients before moving on to the variables. You can sum the exponents of monomials while multiplying them by the same base. The Product of Powers Property is used to describe this.

k⁴n⁶/3

Hence we get the answer after simplification as k⁴n⁶/3

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Answer:

Step-by-step explanation:

Answer:

y = 6x + 9

Step-by-step explanation:

parallel lines have equal gradients.

y - y1 = m(x -x1)

since the lines are parallel your m = 6.

y - y1 = 6(x - x1)

(x1 ; y1) is given (0 ; 9)

y - 9 = 6 (x -0)

y = 6x + 9

A speculative statement about the relationship between two or more variables is known as a b - hypothesis.

Variables:

A variable is a measurable trait or characteristic that is subject to change under different conditions.

Given,

Here we need to find what is meant by a speculative statement about the relationship between two or more variables.

The definition of Hypothesis is,

It is basically a testable statement about the relationship between two or more variables or a proposed explanation for some observed phenomenon.

So, a speculative statement about the relationship between two or more variables is known as a b - hypothesis.

So, the option (b) - Hypothesis is correct.

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Answer: $5 for each candy bar.

Step-by-step explanation: Sarah bought a drink for $4 so, $44-$4=$40(leftover), now she bought 8 candy bars for $40:8=$5 (each candy bar cost)

The equality property that justifies the statement "If m∠ 1=25 and m∠2=25 , then m∠1=m∠2" is; Substitution Property

The substitution property of equality states that 'If a variable C is equal to another variable D, then C can be substituted in place of D in any equation/expression and D can be substituted in place of C in any equation/expression.

Now, we are given the expressions;

If m∠ 1  = 25 and m∠2 = 25 , then m∠1 = m∠2.

Thus, we can also say that the property used here is called substitution property because the parameters were interchanged and still equal.

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Answer:

Xyz E number

Step-by-step explanation:

I think Xyz is right

Answer:

  A.  AB = xyzx

Step-by-step explanation:

You want AB when A = BC, B = x, and C = yz.

You can evaluate the unknown expression by making substitutions until you can't anymore.

  AB = (BC)(B) . . . . . . . . substitute BC for A

  AB = ((x)(yz))(x) . . . . . . substitute x for B (2 places), yz for C

  AB = xyzx . . . . . . . . . . remove the unnecessary parentheses

The solutions to the inequalities are h ≥ -14, v ≥ -19 and m ≤ 10

To do this, we simply solve the expressions one after the other

So, we have:

-3h ≤ 42

Divide both sides by -3

So, we have

h ≥ -14

-v/2 ≤ 9.5

Multiply both sides by -2

v ≥ -19

-4/5m ≥ -8

Multiply both sides by -5/4

m ≤ 10

Hence, the solutions to the inequalities are h ≥ -14, v ≥ -19 and m ≤ 10

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