Using logarithm expressing log b100 in terms of x and y is logb100 = 2y + x
What is the logarithm of a number?The logarithm of a number x to base a written as logₐy is such that when a is raised to the power of x,it equals y.
How to express logb100 in terms of x and y?Since
x = logb2 and y = log b5,We desire to express logb100 in terms of x and y.
So, we proceed as follows.
We have logb100, re-writing this, we have
logb100 = logb(25 × 2)
Now, applying the addition law of logarithm which states that
logab = loga + logb.
So, we have that
logb100 = logb(25 × 2)
logb100 = logb25 + logb2
= logb5² + logb2
Now applying the power rule of logarithm which states that logaⁿ = nloga
So,
logb100 = logb5² + logb2
= 2logb5 + logb2
= 2y + x
So, logb100 = 2y + x
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In a large group of students who completed STA 2023, 20% earned an A in the course, 12% didn’t bring their phone to class and 85% of those who didn’t bring their phone to class earned an A
It is given that:
20% of the students earned an A in STA 2023.
12% of the students didn't bring their phones to class.
85% of the students who didn't bring their phones to class earned an A.
To answer the following questions, we assume whether all students took STA 2023 and brought their phones to class or not.
a) Let's assume that x% of the students earned an A and brought their phones to class. Then, since the remaining (100% - 12%) = 88% of students brought their phone to class but their grade is not specified, we can set up the following equation:
x% + 85% of 12% = 20%
x% + 0.102 = 0.20
x% = 0.098
Therefore, 9.8% of students earned an A and brought their phones to class.
b) Let's assume that y% of the students didn't earn an A and didn't bring their phones to class. Then, we can set up the following system of equations:
x% + y% = 100% - 12%
0.85*(12%) = y%
Solving for y, we get:
y% = 9.6%
Therefore, 9.6% of students didn't earn an A and didn't bring their phones to class.
What is STA 2023?STA 2023 is a course code used by some colleges and universities to refer to an introductory course in statistics. The course usually covers topics such as descriptive statistics, probability theory, statistical inference, hypothesis testing, and regression analysis. STA 2023 is often a required course for students majoring in fields such as social sciences, business, and health sciences, as well as for students pursuing degrees in mathematics or statistics. The specific content and level of difficulty of STA 2023 may vary depending on the institution and the instructor.
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Final question no more lives
who ever gives me correct answer will get brainliest
The time take to fill the pool will be 494 hours.
How to calculate the TimeInlet pipe fills in 38 hours = 1 pool
Inlet pipe fills in 1 hours = 1/38
Drain pipe empty in 39 hours = 1 pool
Drain pipe empty in 1 hour = 1/39
If both pipes are opened together then in pool fills in 1 hour = 1/38 - 1/39
= 1/1482
Therefore, 1/1482 fills in 1 hour.
. Therefore, 1/3 will be:
= 1/3 × 1482
= 494 hours.
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Please help!! Thank you!
Using angle relationships, the missing measures are:
m<3 = 138 degrees.
m<5 = 42 degrees.
m<8 = 138 degrees.
How to Find the Missing Angles?Using angle relationships, each of the measure of the angles can be calculated as follows:
Given that, m<1 = 138 degrees.
m<3 = m<1 [vertical angles are congruent]
Substitute:
m<3 = 138 degrees.
m<5 + m<3 = 180
Substitute:
m<5 + 138 = 180
m<5 = 180 - 138
m<5 = 42 degrees.
m<8 = m<3 [alternate interior angles are congruent]
m<8 = 138 degrees.
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You want to put a 6-inch thick layer of topsoil for a new 28 feet by 17 feet garden. The dirt store only sells topsoil by the cubic yard. How many cubic yards of topsoil will you need to order to fill this garden?
To fill a 6-inch thick layer of topsoil for a new 28 feet by 17 feet garden, you will need 79.33 cubic yards.
How is the volume determined?The volume is the product of the multiplication of the thickness, length, and width.
The thickness of the topsoil = 6 inches
12 Inches = 1 Feet
6 inches = 0.5 Feet (6/12)
The length of the garden = 28 feet
The width of the garden = 17 feet
The thickness of the soil = 0.5 feet
Volume of the topsoil = 28 x 17 x 0.5
= 238 ft³
3 Feet to 1 Yard
238 ft³ = 238/3 yards
= 79.33 cubic yards
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If the market price is below the equilibrium price, which of the following will occur?
Answer:
Shortage
Step-by-step explanation:
If the market price of a product is set below the equilibrium price, it will create a shortage of the product because the demand exceeds the supply.
2. 34 is 34% of what number?
put these decimals lease to greatest 2.16,2.1682,2.2,2.016?
Answer:
2.016, 2.16, 2.1682, 2.2
How to put anything from least to greatest?
The decimals that you have put are the following:
2.16
2.1682
2.2
2.016
How to do it:
If you look at the decimals the last one, 2.016 does not have a 1 or a 2 instead it has a 0 so that would be a our first decimal in the least to greatest form.
We can also include the third one 2.2 is the only one that has a 2 so now we know that 2.2 will go last.
Lets compare the first and second ones which are 2.16 and 2.1682 and I think we obviously know that the answer is 2.1682 because it is greater then 2.16.
So now here are the decimals from least to greatest:
2.016, 2.16, 2.1682, 2.2
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WILL MARK BRAINLIST A one of a kind necklace is worth $3200. The value of the necklace increases by 9% each year.
Which explicit and recursive formulas can be used to model the situation.
Drag and drop each formula to the corresponding box.
The Formula will be in form of exponential function that is y=$3200(1.09)ˣ
where x= no. of years.
What exactly are exponential functions?
An exponential function is a mathematical function with the formula f (x) = aˣ, where "x" is a variable and "a" is a constant that is termed the function's base and must be greater than zero. The transcendental number e, which is approximately equal to 2.71828, is the most often used exponential function basis.
Growth that is exponential
The amount expands extremely slowly at first, then rapidly in Exponential Growth. The rate of change accelerates with time. As time passes, the pace of growth accelerates. The quick expansion is designed to represent a "exponential rise".
The exponential growth formula is: y = a (1+ r)ˣ, where r is the growth percentage.
Now,
Initial value=$3200
% increase=9%
then
Amount in x years will be =3200(1+9/100)ˣ
=3200(109/100)ˣ
=3200(1.09)ˣ
Hence,
The Formula will be in form of exponential function that is y=$3200(1.09)ˣ
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A business must budget its money. Fractions for each part of one store's budget are listed below.
Which of the following comparisons is TRUE?
Attention Grabbers Bookstore Budget
Advertising 1/6
Rent 7/12
Supplies 1/4
A] The bookstore spends more on advertising than rent.
b} The bookstore spends more on supplies than advertising.
c}The bookstore spends more on advertising than supplies.
d]The bookstore spends more on supplies than rent.
==========================================================
Explanation:
Let's go through each answer choice to see which are true and which are false.
A.
The fractions for advertising and rent are 1/6 and 7/12 respectively. The LCD is 12, so let's get 1/6 to have a denominator of 12. Multiply top and bottom by 2 to get 1/6 = 2/12.
Now we can compare the fractions 2/12 (aka 1/6) and 7/12. Clearly 7/12 is larger. It's like saying "having 7 slices of pizza is more than 2 slices of pizza". Therefore, the claim that more was spent on advertising compared to rent is false.
----------------------
B.
1/4 = 3/12 when multiplying top and bottom by 3
3/12 was spent on supplies and 2/12 was spent on advertising
We see that more was spent on supplies, so claim B is true
----------------------
C.
This claim is false because it contradicts claim B.
Another way to see why it's false is to use a calculator to get these decimal values
advertising = 1/6 = 0.17 approximatelysupplies = 1/4 = 0.25 exactlySince 0.17 is not larger than 0.25, this means 1/6 is not larger than 1/4.
----------------------
D.
We could use any of the methods mentioned in the previous sections, but I'll go another route.
For now assume that the fractions for supplies and rent (1/4 and 7/12 respectively) are equal.
Let's use cross multiplication to say the following:
1/4 = 7/12
1*12 = 4*7
12 = 28
Clearly the two sides are different so the original fractions aren't equal. To fix this error, replace each equal sign with a "less than" sign like so
1/4 < 7/12
1*12 < 4*7
12 < 28
Think of it like working backward up the chain. Start with 12 < 28 which is clearly true, and you can work backwards to end up with 1/4 < 7/12.
The fact we end up with 1/4 < 7/12 shows the claim "The bookstore spends more on supplies than rent" is false. It's the other way around: the bookstore spent more on rent compared to supplies.
----------------------
Summary: We found only choice B to be true. The other statements were false.
Question content area top
Part 1
Find the measure of side a.
Side a will be 58cm.In mathematics, a side is a feature of a geometric shape.
A side: What is it?The "A-side" of a record, which is the main song, is issued as a single. The "A-side" of an album is the side that this track is on. The word "side" is most frequently employed as a noun, however it can also be used as an adverb or a verb. The shapes we observe are made of points and lines (line segments) (vertices).
Finding the side, we obtain:
Given ∠A= 30°, b =100 cm .
In ΔABC,
tan A = [tex]\frac{a}{100}[/tex],
tan 30°= [tex]\frac{a}{100}[/tex]
0.577×100=a
a=57.7≅58 cm.
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A school administrator wants to know what proportion of teachers in their state have a Master's degree. The administrator takes an SRS of
100
100100 teachers from a statewide database containing every teacher, and they find
55
5555 teachers in the sample have a Master's degree. The administrator wants to use this data to construct a one-sample
z
zz interval for a proportion.
Which conditions for constructing this confidence interval did their sample meet?
Choose all answers that apply:
Choose all answers that apply:
(Choice A)
A
The data is a random sample from the population of interest.
(Choice B)
B
n
p
^
≥
10
n
p
^
≥10n, p, with, hat, on top, is greater than or equal to, 10 and
n
(
1
−
p
^
)
≥
10
n(1−
p
^
)≥10n, left parenthesis, 1, minus, p, with, hat, on top, right parenthesis, is greater than or equal to, 10
(Choice C)
C
Individual observations can be considered independent.
A) The data is a random sample from the population of interest. - Yes, it is mentioned that the administrator takes an SRS (Simple Random Sample) of 100 teachers from the statewide database containing every teacher.
What do you mean by SRS (Simple Random Sample)?Simple Random Sample (SRS) is a statistical technique for selecting a sample from a population, where each individual or item in the population has an equal chance of being selected for the sample. In other words, a simple random sample is a representative subset of a population where every individual or item in the population has an equal chance of being selected for the sample.
To take a simple random sample, each individual in the population is assigned a unique number, and then random numbers are generated to select the required number of individuals for the sample. This method ensures that the sample is not biased towards any particular subset of the population, and that the sample is representative of the whole population.
A) The data is a random sample from the population of interest. - Yes, it is mentioned that the administrator takes an SRS (Simple Random Sample) of 100 teachers from the statewide database containing every teacher.
B) np^≥10n p^ ≥10n, p, with, hat, on top, is greater than or equal to, 10 and n(1−p^)≥10n(1− p^ )≥10n, left parenthesis, 1, minus, p, with, hat, on top, right parenthesis, is greater than or equal to, 10 - Since the problem does not provide the value of p, we cannot determine if the condition np^≥10n and n(1−p^)≥10n are satisfied.
C) Individual observations can be considered independent. - The problem does not provide information about whether the individual observations can be considered independent. However, we can assume that since it is a random sample, the observations are independent.
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Mrs. Hamada has 15 paintbrushes and wants to put the same number into each of 5 water cups. Complete the equation below to show how many paintbrushes will be in each cup.
Answer:
3 paintbrushes
Step-by-step explanation:
15 divided by 5 is 3.
So, Mrs. Hamada will put 3 paintbrushes in each cup.
Which of the following equations represents a parabola with a vertical axis of symmetry, vertex at (10, –4), and p = –3?
(y + 10)2 = 12(x – 4)
(y – 10)2 = –12(x + 4)
(x + 10)2 = 12(y – 4)
(x – 10)2 = –12(y + 4)
(x - 10)² = -12 (y + 4) represents a parabola with a vertical axis of symmetry, vertex at (10, –4), and p = –3 .
What's a vertical parabola?
A vertical parabola has its axis of symmetry at x = h, and the vertex is (h, v). With this information, you can find the focus and directrix. The focus is the distance from the vertex to the focus is 1/(4a), where a can be found in the equation of the parabola (it is the scalar in front of the parentheses).
we know that
If the axis of symmetry is parallel to the y-axis, then we have a vertical parabola
The equation of a vertical parabola is equal to
4p(y - k) = (x - h)²
where
(h,k) is the vertex
In this problem we have
(h,k) = (10, –4)
p= -3
substitute
4*(-3)(y - (-4)) = (x - 10)²
-12 (y + 4) = (x - 10)²
or
(x - 10)² = -12 (y + 4)
Hence , option D is correct.
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write an algebraic expression for the following when a number is doubled and then decreased by 5 the result is 21
ASAP!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answer:
Step-by-step explanation:
First you identify your variable, for our sake lets use x:
x= number in question
Next you write the equation given in the question:
2(x-5)= x+25
Next you use the distributive property and multiply 2 by both x and negative 5 to get:
2x-10=x+25
Now you want to get all of the x's to one side so you subtract the x on the right, fro the one on the left giving you:
x-10=25
Then you simply add 10 to 25 giving you the answer of x=35
Plot and connect the points in the order listed below. When you are done, find the area of the resulting figure.
A(-5,4)A(−5,4), B(4,4)B(4,4), C(4,1)C(4,1), D(1,1)D(1,1), E(4,-3)E(4,−3), F(4,-6)F(4,−6), G(-5, -6)G(−5,−6)
The total area of the figure with points A(-5,4), B(4,4), C(4,1), D(1,1), E(4,-3) F(4,-6), G(-5, -6) is 51 square units.
What is Graph?Graph is a mathematical representation of a network and it describes the relationship between lines and points.
Divide the figure is into two rectangles and a triangle.
The points B, C, E, and F form a rectangle with base BC and height 7 units.
The points A, D, and G form a rectangle with base AG and height 5 units. The points C, D, and E form a triangle with base CE and height 4 units.
The length of BC is 4 - 4 = 0, so the area of the rectangle with base BC is 0.
The area of the rectangle with base AG is (4 - (-5)) x 5 = 45 square units. The area of the triangle with base CE is (4 - 1) x 4 / 2 = 6 square units.
Therefore, the total area of the figure with points A(-5,4), B(4,4), C(4,1), D(1,1), E(4,-3) F(4,-6), G(-5, -6) is 45 + 6 = 51 square units.
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A company made 500 flashlights and found that 5 were defective. If the company makes 12,500 flashligh
O 120
O125
0 250
O 1,250
The company can expect to find 125 defective flashlights in a production run of 12,500. The correct option is B, 125.
What is flashlights?Flashlight can be defined as a portable, battery-operated device used for illumination. It typical unit consists of one or more dry cell batteries arranged in a line inside a battery compartment that forms the handle of the light.
Assuming the proportion of defective flashlights remains the same, the number of defective flashlights in a production run of 12,500 would be:
(5/500) x 12,500 = 125
Therefore, the company can expect to find 125 defective flashlights in a production run of 12,500. The answer is option B, 125.
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Help me with this question….
The number that is most likely an irrational number is given as follows:
D. 4.279458105...
What are rational and irrational numbers?Rational numbers are numbers that can be represented by fractions, such as numbers that have no decimal parts, or numbers in which the decimal parts are terminating or repeating.
Irrational numbers are numbers that cannot be represented by fractions, being non-terminating and non-repeating decimals, such as non-exact square roots.
For this problem, the option D gives the irrational number, as it is the lone non-repeating decimal. For the others, we have that:
Option A: 26 is the repeating decimal part.Option B: 3 is the repeating decimal part.Option C: due to the large number of zeros, the number is the exact decimal 2.8.More can be learned about rational and irrational numbers at brainly.com/question/5186493
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An electric clock is stopped by a power failure. What is the probability that the second hand is stopped between the 4 and the 9?
Answer: the answer is 5/12
Calculate the marked price on a bag of Cement selling 570 ksh after a discount of 5% is offered.
Answer:
541.5 ksh
Step-by-step explanation:
For each of the following graphs, the two given polygons are similar. Write precisely a single dilation (coordinates of center and coefficient) by which the image (labeled with primed letters) was obtained.
Polygon ABCD was dilated by a scale factor of 2 to create A'B'C'D'.
What is dilation?Dilation is the increase or decrease in the size of a figure by a scale factor of k, thereby creating an image. Resizing an object is accomplished through the transformation of dilation. The objects can be enlarged or shrunk using dilation. The result of this transformation is an image that has the same shape as the original shape. The size of the shape varies, though. A dilation should either stretch or contract the original shape. The term "scale factor" describes this transformation.
From the diagram:
Scale factor = A'B' / AB = 6/3 = 2
Center = (6, -6)
Polygon ABCD was dilated by a scale factor of 2 to create A'B'C'D'.
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Rob loaded 9 trucks in 1 hour find his loading speed per hour
Answer:
9 trucks/hour
Step-by-step explanation:
If he loaded 9 trucks in one hour, his loading speed is 9 trucks per hour.
Solve for x
This is Similarity in right triangles lesson 7.4
If you can explain the process please do. Thank you
The unknown in the similar triangles are as follows;
x = 15 units
x = 16 units
How to find the sides of similar triangles?Two triangles are said to be similar when they have two corresponding angles congruent and the sides proportional to each other.
Let's solve for x in the triangles as follows:
using the proportion,
2.
9 / x = x / 25
cross multiply
25 × 9 = x²
x² = 225
x = √225
x = 15 units
3.
x / 12 = 12 / 9
cross multiply
9x = 144
x = 144 / 9
x = 16 units
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The function f (x) = 125,000 (1.028)x models the change in population of Pool City, where x represents the number of years since 2010. Which statement is NOT true?
A.) The domain of the function includes all real values of x .
B.) The point (1, 128500) represents the population of Pool City in 2011.
C.) The population of Pool City in 2010 is 125,000.
D.) The function has an asymptote at y = 125,000 .
3. If 17 and 36 are the lengths of two sides of a triangle, what is the range of possible values for the length of the third side?
Answer:
19 < x < 53
Step-by-step explanation:
given 2 sides of a triangle then the third side x is in the range
difference of 2 sides < x < sum of 2 sides , that is
36 - 17 < x < 36 + 17
19 < x < 53
Add the two expressions 3z - 4 and 2z + 5
We obtain the sum of the expressions as 5z + 1. The solution has been obtained by using arithmetic operations.
What are arithmetic operations?
Four fundamental mathematical operations which can be used to express any real number are known as arithmetic operations. The four operations are addition, subtraction, multiplication and division.
We are given two expressions as 3z - 4 and 2z + 5.
In order to add the expressions, we will add the like terms.
On adding the like terms, we get
⇒(3z - 4) + (2z + 5)
⇒3z + 2z - 4 + 5
⇒5z + 1
Hence, we get the expression as 5z + 1.
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Please help fast!! What is the domain of the relation?
A: (-5,0,3,4)
B: (-4,-1,0,1,3)
C: (-5,-2,0,1,4)
D: (-5,-4,-2,-1,0,1,3,4)
Look at the picture below
The correct option is A {-5, 0, 3, 4}.
What do you mean by Domain?In mathematics, the domain of a function is the set of all possible input values (independent variable) for which the function is defined. In other words, the domain is the set of values that we can substitute for the independent variable in a function to produce a meaningful output.
For example, consider the function f(x) = 2x. Here, we can substitute any real number for x and get a meaningful output. Therefore, the domain of this function is all real numbers, or (-∞, ∞). However, if we consider the function g(x) = 1/x, we can see that we cannot substitute 0 for x because division by 0 is undefined. Therefore, the domain of this function is all real numbers except 0, or (-∞, 0) U (0, ∞).
The domain of a relation is the set of all possible values for the independent variable (x) for which there exists a corresponding value of the dependent variable (y). In this case, the given coordinates are (1,3), (4,1), and (-5,-4).
The domain of the relation would be the set of x-values that correspond to the given coordinates. So, the domain of this relation is {-5, 1, 4}.
Therefore, the correct answer is A: {-5, 0, 3, 4}.
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G(x)=-4x^2+36/x+3
What key features does f(x), shown in the graph, share
with g(x), shown in the equation? Select three options.
at least one x-intercept
at least one y-intercept
Dan oblique asymptote
O a vertical asymptote
the domain of x
The function g ( x ) in the graph has one x-intercept , y intercept and an oblique asymptote , a vertical asymptote
What are Asymptotes?An asymptote is a line that a curve approaches but never touches. A line where the graph of a function converges is known as an asymptote. When graphing functions, asymptotes are typically not required
There are 3 types of asymptotes
Horizontal asymptote (HA) - It is a horizontal line and hence its equation is of the form y = k. Horizontal Asymptote is when the function f(x) is tending to zero
Vertical asymptote (VA) - It is a vertical line and hence its equation is of the form x = k. Vertical asymptotes are defined when the denominator of a rational function tends to zero
Slanting asymptote (Oblique asymptote) - It is a slanting line and hence its equation is of the form y = mx + b
Given data ,
Let the function be represented as g ( x )
Now , the value of g ( x ) is
g ( x ) = ( -4x² + 36 ) / ( x + 3 )
On simplifying , we get
g ( x ) = -4 ( x² - 9 ) / ( x + 3 )
On further simplification , we get
g ( x ) = -4 ( x + 3 ) ( x - 3 ) / ( x + 3 )
g ( x ) = -4 ( x - 3 )
g ( x ) = -4x + 12
Now , the function has a vertical asymptote at ( 0 , 12 )
The function has a horizontal asymptote at ( 3 , 0 )
Hence , the function is solved
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Answer:
at least one x-intercept
at least one y-intercept
domain of x
Step-by-step explanation:
took ed2023
which is a true statement about two numerical sets of data that have negative association
Answer:
Option D.
Step-by-step explanation:
Negative correlation also called an " inverse correlation " is a relation between 2 variables where-by they behave in opposite manner. When one variable moves ---> in an increasing /\ direction, the other variable moves in a decreasing \/ direction.
Thus, Option D.
You want to put a 6-inch thick layer of topsoil for a new 28 feet by 17 feet garden. The dirt store only sells topsoil by the cubic yard. How many cubic yards of topsoil will you need to order to fill this garden?
To volume to fill the rectangular garden is 8.99 cubic yard
What is the volume to fill the gardenTo determine the volume of amount of sand required to fill the garden, we can simply convert the dimensions from inches and feet into yard.
inch to yard
6 inch = 0.17 yard
Feet to yard
28 feet = 9.33 yard
17 feet = 5.67 yard
The volume of the rectangular garden is given as;
v = l * w * h
l = lengthw = widthh = heightSubstituting the values;
V = 0.17 * 9.33 * 5.67
v = 8.99 cubic yard
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A bakery can make 42 cheesecakes for every 6 blocks of cream cheese. Which table represents the relationship between the number of cheesecakes the bakery makes and the number of blocks of cream cheese the bakery uses?
Answer:
Step-by-step explanation:
