To make a batch of four dozen cookies, Denis needs 1 3/4 cups of four, 1 cup of sugar, and 1/3 cup of milk. Calculate the amount of each ingredient that Denis needs to make 12 dozen cookies

Answer:

We have the proportion: 8/10 = 100/y

We can solve for y by cross-multiplying.

That is, 8y = 100 * 10 Simplifying the right-hand side, 8y = 1000

Dividing both sides by 8 to solve for y, y = 125

Hence, the value of y is 125.

Finally, we have the expression: y = √80We can simplify this expression by factoring 80 into its prime factors:80 = 2 * 2 * 2 * 2 * 5

Taking the square root of 2 * 2 * 2 * 2, we have:√(2 * 2 * 2 * 2) = 2 * 2 = 4

Therefore, y = 4√5The value of y is 4√5.

Step-by-step explanation:

Hope this helps!! Have a good day/night!!

The average temperature on Saturday was 62.6 °F, then the actual temperature will be equal to 17 °C.

The four fundamental operations of arithmetic are addition, subtraction, multiplication, and division of two or even more items.

Included in them is the study of integers, especially the order of operations, which is important for all other areas of mathematics, notably algebra, data management, and geometry.

As per the given information in the question,

The temperature on Saturday was 62.6 F

Then, the actual temperature will be,

C = 5/9(F -32)

C = 5/9(62.6 - 32)

C = 5/9(30.6)

= 17 °C

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Assuming no denominator equals zero, b^4/a expression is equivalent to the given expression a^3b^5/ a^4b

Definition of Expression in Math? An expression in math is a sentence with a minimum of two numbers or variables and at least one math operation. This math operation can be addition, subtraction, multiplication, or division.

The applicable rules of exponents are ...

 (a^b)/(a^c) = a^(b-c)

 a^-b = 1/a^b

The expression can be rewritten as ...

a^3b^5/ a^4b

The expression can be rewritten as ...

b^4/a

complete question

Assuming no denominator equals zero, which expression is equivalent to the given expression?.

a^3b^5/ a^4b

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The given information is:

- The function of decay is:

Where A0 is the initial amount of strontium-90, A is the amount present at time t (in years).

- The initial amount is 800 grams.

a. What is the decay rate of strontium-90?

The given formula is written in the form:

Where r is the decay rate in decimal form, so:

The decay rate is -2.44%.

b. How much strontium-90 is left after 30 years?

Replace t=30 and solve:

There is 384.8 grams after 30 years.

c. When will only 200 g of strontium-90 be left?

A(t)=200g, then replace it and solve for t:

There will be 200 g left after 56.8 years.

d. What is the half-life of strontium-90?

The half-life is when A(t)=A0/2, then if we replace this into the decay formula we obtain:

The half-life of strontium-90 is 28.4 years.

Answer:

4.8ft

Step-by-step explanation:

Answer:

y=3x-13

Step-by-step explanation:

Since the parallel equations have equal slope.

The equation of line parallel to y=3x+7 will be y=3x+k.

(4,-1) lies in the line so it satisfies the equation amd we get the value of k as -13 and finally we substitute the value of k in the eqn and we finally get the equation as 3x-y-13=0 or you can also write it as y=3x-13

Answer:

\(\boxed{5 \cdot \sqrt{2} \cdot \sqrt[6]{5} }\)

Step-by-step explanation:

\(\sqrt[3]{250} \cdot \sqrt{\sqrt[3]{10} }\)

\(\sqrt{\sqrt[3]{10} } \implies (10^\frac{1}{3} )^\frac{1}{2} =10^\frac{1}{6} =\sqrt[6]{10}\)

\(\therefore \sqrt{\sqrt[3]{10} }=\sqrt[6]{10}\)

\(\text{Solving }\sqrt[3]{250} \cdot \sqrt{\sqrt[3]{10} }\)

\(250=2 \cdot 5^3\)

\(\sqrt[3]{250}=\sqrt[3]{2\cdot 5^3}=5 \sqrt[3]{2}\)

Once

\(\sqrt[6]{2} \cdot \sqrt[6]{5} = \sqrt[6]{10}\)

We have

\(5 \sqrt[3]{2} \cdot \sqrt[6]{2} \cdot \sqrt[6]{5}\)

We can proceed considering the common base of exponentials

\(\sqrt[3]{2} \cdot \sqrt[6]{2} = 2^{\frac{1}{3}} \cdot 2^{\frac{1}{6} } = 2^{\frac{3}{6} } = 2^{\frac{1}{2} }=\sqrt{2}\)

Therefore,

\(5 \sqrt[3]{2} \cdot \sqrt[6]{2} \cdot \sqrt[6]{5} = 5 \cdot \sqrt{2} \cdot \sqrt[6]{5}\)

Correct, the primary focus of billers and coders is on Parts A and B of Medicare as these are the parts that cover hospital and medical insurance.

Parts C and D are not usually involved with billers and coders, as they involve providing medical insurance coverage for beneficiaries. Part C, also known as Medicare Advantage, is a type of private health insurance plan that is offered by a Medicare-approved private insurance company. Part D is the prescription drug coverage part of Medicare. While billers and coders may have some knowledge about Parts C and D, their main focus is on billing and coding for the services covered under Parts A and B.

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The general equation of a line is y = mx+b, m being the slope and b the intercept on the y-axis.

We are given the line 7y-4x=-14, let's organize the equation like the general form:

In order to be parallel to your line, a line has to have the same slope as your line. So the slope has to be 4/7.

Thus any line parallel to the line y=4/7x-2 has an equation of the form y=4/7x+b, where b is any number.

By looking at the answer options, we can select the second option y= 4/7x-1

False.A linear transformation T : Rn → Rm is not completely determined by its effect on the columns of the n × n identity matrix.

The columns of the identity matrix represent the standard basis vectors in Rn, which are the vectors with all components equal to zero except for one component that is equal to one. The effect of a linear transformation on the standard basis vectors provides some information about how the transformation affects certain directions in the input space, but it does not fully characterize the transformation.

To see why this statement is false, let's consider an example. Suppose we have a linear transformation T : R2 → R2. The identity matrix in this case is a 2 × 2 matrix with the columns [1 0] and [0 1]. The effect of T on the first column [1 0] could be any vector in R2, let's say T([1 0]) = [a b]. Similarly, the effect of T on the second column [0 1] could be another vector in R2, let's say T([0 1]) = [c d].

Now, we have the information about the effect of T on the columns of the identity matrix, which is T([1 0]) = [a b] and T([0 1]) = [c d]. However, this information alone is not sufficient to uniquely determine the linear transformation T. There could be infinitely many linear transformations that satisfy these conditions. For example, we could have T([x y]) = [ax + cy, bx + dy], where a, b, c, and d are arbitrary real numbers.

In this example, we can see that the effect of the linear transformation on the columns of the identity matrix only gives us partial information about T, but it does not fully determine the transformation. The linear transformation can have different effects on vectors that are not in the standard basis. In general, a linear transformation T maps every vector in the input space Rn to a corresponding vector in the output space Rm, and its behavior on the standard basis vectors alone does not capture the complete transformation.

Therefore, we can conclude that a linear transformation T : Rn → Rm is not completely determined by its effect on the columns of the n × n identity matrix. Additional information about the transformation's behavior on other vectors or basis sets is needed to fully determine the transformation.

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Answer: -1

Step-by-step explanation: 8-5= 3

-4-(-7)=3 2-3=-1

the pattern is “-3”

The probability that X is between 57 and 105 is 0.8914.

Given:

* X is normally distributed with mean=90 and standard deviation=12

* P(57 < X < 105)

Solution:

* Convert the given values to z-scores:

   * z = (X - μ) / σ

   * z = (57 - 90) / 12 = -2.50

   * z = (105 - 90) / 12 = 1.25

* Use the z-table to find the probability:

   * P(Z < -2.50) = 0.0062

   * P(Z < 1.25) = 0.8944

* Add the probabilities to find the total probability:

   * P(57 < X < 105) = 0.0062 + 0.8944 = 0.8914

Therefore, the probability that X is between 57 and 105 is 0.8914.

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Based on the data in the table, if a cow is randomly selected from farm B, the probability that its feed includes seaweed is 0.597 (Option D) and without is 0.57

Note that the total number of feed with sea weed is 74.
And the total number of cows on the farm B is 124.

Thus, the cows whose feed includes seaweed is 74/124

= 0.59677419354

≈ 0.597

The Probability of those whose feed is without sea weed is

Note that the total number of feed without sea weed is 40.
And the total number of cows on the farm B is 76.

Thus, the probability is 40/70
= 0.5714285714

≈ 0.571

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Answer:

-5

Step-by-step explanation:

Coordinate of A = -7

Coordinate if B = 5

Distance of AB = |-7 - 5| = |-12| = 12

We are asked to find the coordinate of the point that would be ⅙ from the A to B, which is ⅙ of AB.

Let's find what ⅙ of AB is.

AB = 12

Therefore, ⅙ of AB = ⅙*12 = 2.

From point A (-7), we move 2 points towards B which will give us ⅙ from A to B.

The coordinate = -7 + 2 = -5

-5 is the coordinate of the point with a fraction distance of ⅙ from A to B.

a. The population are all subscribers to Bloomberg BusinessWeek in North America.

b. The annual income is a quantitative variable.

c. The ownership of an American Express card is a categorical variable.

d. The study involves cross-sectional data.

e. Bloomberg BusinessWeek might infer that a part of its subscribers who has annual income of $75,000 or more are having an American Express credit card.

The population is the whole set of units from where information is to be obtained and about what inferences are to be made. The population of interest in this study are all subscribers to Bloomberg BusinessWeek in North America.

Quantitative variables are those which can be measured numerically. In this study, the annual income is a quantitative variable because it can be expressed in numbers.

Categorical variables are those which cannot be quantified. Categorical variable can only take on a fixed value. In this case, the question “Do you have an American Express credit card?” can only take on two values, Yes or No. Thus, the ownership of an American Express credit card is a categorical variable.

Cross-sectional data refers to data from many but similar individual groups at a given point in time. For e.g., prices of different varieties of rice on a particular day. In this study, the data gives two different values which describe the same population at the same time. So, it involves cross-sectional data.

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Although part of your question is missing, you might be referring to this full question: A Bloomberg BusinessWeek North American subscriber study collected data from a sample of 2861 subscribers. Fifty-nine percent of the respondents indicated an annual income of $75,000 or more, and 50% reported having an American Express credit card.

a. What is the population of interest in this study?

b. Is annual income a categorical or quantitative variable?

c. Is ownership of an American Express card a categorical or quantitative variable?

d. Does this study involve cross-sectional or time series data?

e. Describe any statistical inferences Bloomberg BusinessWeek might make on the basis of the survey.

A. The correlation coefficient (r) is given as 29.4%. To find r, divide by 100: r = 0.294. This indicates a positive, but weak, correlation between drop height and duration for the 90 roller coasters.

B. The coefficient of determination (R^2) is the square of the correlation coefficient (r). Calculate R^2 = (0.294)^2 ≈ 0.086. This means that approximately 8.6% of the variation in ride duration can be explained by the variation in drop height.

C. For the Tower of Terror, the regression model may not provide an accurate prediction of ride duration based on its drop height, as it is an outlier with a large drop but a short ride duration. The weak correlation between drop height and duration for the remaining 90 coasters suggests that this model may not be a good predictor for unusual cases like the Tower of Terror.

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Answer:

This was $14 less than twice what she spent for a blouse . How much ... From the first two equations, we have A=12B=12(3C)=32C ... How many days will it require for the son to plow the field alone?

Step-by-step explanation:

The height of Veronica's scale model in  inch is 10.5 inch.

A scale factor is a numerical value that can be used to alter the size of any geometric figure or object in relation to its original size. It is used to find the missing length, area, or volume of an enlarged or reduced figure as well as to draw the enlarged or reduced shape of any given figure. It should be remembered that the scale factor only affects how big a figure is, not how it looks.

Given:

3 inches = 50 feet.

So, 1 feet = 3/50 inch

Then, height of Concert Venue in feet

175 feet = 175 x 3/50

             = 525/50

             = 105/ 10

              = 21/2

              = 10.5 inch

Hence, the height is 10.5 inch.

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The depth of the pond will fall below 4 feet in approximately 17.3 years if the current rate of decay continues.

Given that

The depth of the pond decreases at a rate of 2% per year

The current depth of the pond is 5 feet

We need to find out in approximately how many years the depth of the pond will fall below 4 feet.

Use the formula for exponential decay:

\(A = A_0 e^{(kt)\)

Where:

A is the current depth of the pond (5 feet)

A₀ is the initial depth of the pond (also 5 feet)

k is the decay rate, which is equal to -2% or -0.02

t is the time in years

Find out when the depth of the pond will fall below 4 feet,

So we can set A = 4 and solve for t:

4 = 5exp(-0.02t)

Dividing both sides by 5, we get:

0.8 = exp(-0.02t)

Taking the natural logarithm of both sides, we get:

ln(0.8) = -0.02t

Solving for t, we get:

t = ln(0.8) / (-0.02)

 = 17.3 years (approximately)

Therefore, the depth of the pond will fall below 4 feet in approximately 17.3 years if the current rate of decay continues.

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Answer:

1.25x

Step-by-step explanation:

Given that :

25% Increase in number of blog views can be expressed as (x + 0.25x)

Another way to make this representation is :

Total number of blog views + 25% of total

Total should add up to 100%

Let number of views = x

Hence,

(100% + 25%) of x

125% of x

125%x

= 1.25x

Step-by-step explanation:

m ~ 6.9

6.9! = 4122.7

4122.7 average 4125

n ~ 8.9

8.9! = 289867.7

289867.7 average 281600

Answer: We have to find the sin(theta) provided the cos(theta) function, the visualization of the problem is as follows:

The diagram visualization is:

Therefore the x is:

Therefore the answer is:

The answer is Option(C).

Answer:

120.

Step-by-step explanation:

Using the Pythagoras theorem:

(30√2)^2 = x^2 + x^2         where x =length of each side of the square

1800 = 2x^2

x^2 = 900

x = 30.

So the perimeter = 4*30 = 120.

Answer:

14-6

Step-by-step explanation:

The correct option is a. A causal relationship cannot be concluded but the results can be extended to the population.

In an observational study, where the researcher observes and analyzes data without directly manipulating variables, finding a statistically significant relationship indicates an association between the variables. However, it does not establish a causal relationship. Other factors or confounding variables may be influencing the observed relationship.

Since causation cannot be inferred in observational studies, option (a) is the correct answer. The results can still be extended to the population because the sample represents the population of interest, but causality cannot be determined without further evidence from experimental studies or additional research methods.

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Answer: 75% off the original price.

Step-by-step explanation:Say an item is $100.  50% off $100 is of coarse $50.

Now 50% off that price is $25.

So the new price is now $25 which is 75% off.

Answer:

c. 75%

Step-by-step explanation:

just took the test

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There were 240 student tickets sold and 120 adult tickets sold.

Let's assume the number of student tickets sold is represented by "S" and the number of adult tickets sold is represented by "A."

According to the given information, the total number of tickets sold is 360:

S + A = 360     (Equation 1)

The revenue from selling student tickets at $6 each and adult tickets at $9 each is $2,580:

6S + 9A = 2,580   (Equation 2)

To solve this system of equations, we can use the substitution method.

First, we solve Equation 1 for S:

S = 360 - A

Substituting this value into Equation 2:

6(360 - A) + 9A = 2,580

2,160 - 6A + 9A = 2,580

3A = 2,580 - 2,160

3A = 420

A = 420 / 3

A = 140

Substituting the value of A back into Equation 1 to solve for S:

S + 140 = 360

S = 360 - 140

S = 220

Therefore, there were 220 student tickets sold and 140 adult tickets sold.

There were 220 student tickets sold and 140 adult tickets sold.

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Answer:

\(\huge\boxed{\sf x = 60\°}\)

Step-by-step explanation:

So,

100 + x + 20 = 180

x + 120 = 180

x = 180 - 120

x = 60°

\(\rule[225]{225}{2}\)