distributive property 80 + 56

Answer:

Step-by-step explanation:

Given 22 raspberry and 55 strawberry scones, you want to know the number of equal-sized bags Michael can fill with scones, and the number in each bag.

The answer statement you're asked to fill tells you that you solve this problem by finding the GCF of 22 and 55. If you look at the factors, you can see what the largest common factor is:

  22 = 2·11

  55 = 5·11

The greatest common factor of 22 and 55 is 11. When the scones are divided equally among 11 bags, there will be 2 raspberry and 5 strawberry scones in each bag.

The greatest number of bags Michael can fill is 11 bags because the GCF of 22 and 55 is 11 . Each bag can have 2 raspberry and 5 strawberry scones.

The simplified value of  [tex]\sqrt[4]{1296} /25[/tex] is 0.24.

Simply put, to simplify is to make something simpler. Simplifying an equation, fraction, or issue in mathematics entails taking something complex and making it simpler. The issue is made simpler by calculations and problem-solving strategies. We can simplify fractions by removing all common elements from the numerator and denominator and putting the fraction in its simplest/lowest form.

Given  [tex]\sqrt[4]{1296} /25[/tex]

factors of 1296 are = 2⁴ x 3⁴

[tex]\sqrt[4]{1296}[/tex] = [tex](2^{4} *3^{4}) ^{\frac{1}{4} }[/tex]

[tex]\sqrt[4]{1296}[/tex] = 6

[tex]\sqrt[4]{1296} /25[/tex]  = 6/25

[tex]\sqrt[4]{1296} /25[/tex] = 0.24

Hence the value is 0.24.

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The probability that a registrant has failed the afternoon session given he/she has passed the morning session is 0.3125.

Let A be the event of registrants passing the morning session

Let B be the event of registrants passing the afternoon session

Here given that

n(A) = 80%

n(B) = 70%

n(notA ∩ notB) = 5%

We need to find P(notB/A)

According to the formula the conditional probability

P(X/Y) = P(X ∩ Y)/P(Y)

Hence, P(notB / A) = P(notB ∩ A) / P(A)

Now (notB ∩ A) = n(A) - n(A ∩ B)

Also by De Morgan's law

not X ∩ not Y = not(X U Y)

Hence,

(not A ∩ not B) = not(X U Y)

or, 1 - n(A) - n(B) + n(A∩B) = 0.05

or, n(A ∩ B) = 0.05 + 0.5 = 0.55

Hence,

(not B ∩ A) = 0.8 - 0.55

= 0.25

Hence,

P(notB/A) = 0.25/0.8

= 0.3125

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Answer:

JK6, MN3

Step-by-step explanation:

The letters go down in the alphabet, but skipping a letter. After GH is IJK, but we skip the I to follow the pattern. The numbers go down by 3: 9-3 = 6. Same thing for MN3!

According to the uniform distribution, there is a 0.625 = 62.5% chance that a randomly chosen passenger will have to wait longer than 2.25 minutes.

The boundaries of a uniform distribution are a and b.

The likelihood of discovering a value greater than x is:

P(X > x)=b-x/b-a

In this issue, the distribution of time is evenly spaced between 0 and 6 minutes, therefore

a=0 b=6

P(X > x)= 6-2.25/6-0

=0.625

0.625 = 62.5% probability that a randomly selected passenger has a waiting time greater than 2.25 minutes.

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2√2 units is the distance between the given points (2, 3) and (4, 1).

An object's entire motion, independent of direction, is its distance.

Regardless of where it started or ended, distance is the amount of space that an object has covered.

We can determine an object's actual size by knowing how far it is from us.

To get the distance between two points, one usually uses the formula:

d=((x2 - x1)2 + (y2 - y1)2)

So, we have the formula:

d=((x2 - x1)2 + (y2 - y1)2)

The points are: (2, 3) and (4, 1)

Now apply values in the formula and calculate as follows:

d=((x2 - x1)2 + (y2 - y1)2)

d=√(2−4)2+(3−1)2

d=√(−2)2+22

d=√4+4

d=√8

d=2√2 units

Therefore, 2√2 units is the distance between the given points (2, 3) and (4, 1).

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70 grade must the student earn on the last exam to get an average of an 80 for the marking period.

Division is the process of splitting a number or an amount into equal parts.

Division is one of the four basic operations of arithmetic, the ways that numbers are combined to make new numbers. The other operations are addition, subtraction, and multiplication.

here, we have,

given that,

A student received grades of 84, 87, and 79 on the first three exams.

let, x grade must the student earn on the last exam to get an average of an 80 for the marking period.

i.e. (84+87+79+x)/4=80

solving, we get,

x=70

Hence, 70 grade must the student earn on the last exam to get an average of an 80 for the marking period.

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Answer:21 minutes given the speed of 5 km/h. Calculated as 1.8 km multiplied by 60 mins and then divided by 5 km. .5 is how many minutes? A car travels at 40kmph how far does it travel in 45 minutes? How many minutes are there in 35 km?

Step-by-step explanation:

If 5 pounds of raspberries costs 22.50, 1 pound will cost 4.50.

To put it simply, we can take 22.50 and divide it by 5. We do this because we are trying to solve for the price of 1, not 5.

22.50 ÷ 5 = 4.50

Therefore, 1 pound of raspberries costs 4.50.

Answer:

4.50$

Hope this helps!

Step-by-step explanation:

1 pound = $?

5 pounds = $22.50

1 pound * 5 = 5 pounds

$? * 5 = $22.50

$? = $22.50 ÷ 5

$? = 4.50

8) If the interior angle of regular polygon measures 170°, then it has 36 sides.

9) If the sum of all the interior angles of a polygon is 1980∘. then, the given polygon has 13 sides.

10) Where the sum of the interior angles of a polygon = 5400°, then the polygon has 32 sides.

11) Where the measure of the seven angles in a nonagon measure 138°, 154°, 145°, 132°, 128°, 147°, and 130°, and the two remaining angles are equal in measure, the measure of each angle is 143°

A nonagon or enneagon is a nine-sided polygon or 9-gon in geometry. The word nonagon is a prefix hybrid construction derived from Latin that has been used interchangeably since the 16th century in French nongone and since the 17th century in English.

8) First let's solve for the regular triacontanol (that is a regular polygon with 36 sides.

Note that the formula for solving the Interior angle of a polygon is:

Interior Angle = [(n-2) 180°] /n

Where n is the number of sides:

Thus, entering the information given, we have:

Interior angle =  170 thus,

170° =  [(n-2) 180°] /n

170°n = (n-2) 180°

170°n-180°n = -360°

-10°n = -360°

n = -360°/-10°

n = 36

Thus, the polygon that has an interior angle of 170° has 36 sides.

9) Where the sum of interior angles = 1980°

To get the number of sides, we must use the formula below:

Sum of Interior Angles (S) = (n-2) x 180°

Where n is the number of sides of the Polygon

Since S = 1980°, we say

1980 = (n - 2) x 180

⇒ n -2 = 1980/180

⇒ n - 2 = 11

n = 11 + 2

n = 13,

Therefore, where the sum of interior angles = 1980°, the number of sides is 13.

10) If the sum of interior angles = 5400°,

using the same process in 9 above, we say:

5400 = (n - 2) x 180

n - 2 = 5400 /180

n - 2 = 30

n = 30 + 2

n = 32;

Therefore where the sum of interior angles = 5,400°, the number of sides is 32.

11) Where the measure of the seven angles in a nonagon measure138°, 154°, 145°, 132°, 128°, 147°, and 130°, and  the two remaining angles are equal in measure, then the measure of each angle is determined as follows;

Note that the sum of the interior angles of a nonagon is 1260°

Thus, to arrive at the remaining angles, we say:

138°+154°+145+ 132°+ 128°+ 147°+ 130° + 2x = 1260 (recall that the remaining angles are equal)

⇒ 974 + 2x = 1260

2x = 1260 - 974

x = (1260- 974) /2

x = 143

Therefore, the measure of the two remaining angles which are equal are 143 degrees.

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Answer:

36

Step-by-step explanation:

48 x 3/4

Each of the top three teams has the greatest possible number of total points: 24. 

There are a total of 15 games in the tournament (6 teams playing each other twice). If a team wins all of its games, it will earn 3 points for each win, for a total of 3 x 6 = 18 points. If a team also earns points for a draw, it can earn an additional 3 points.

Finally, if a team earns points for a loss, it can earn an additional 3 points.

So the greatest possible number of total points for each of the top three teams is:

Step-by-step:

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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.

36x² + 48x + 16 is the simplified shape of the given quadratic equation (6x 4)².

ax²+bx+c=0, with a not, equal to 0 is a quadratic equation, which is a second-order polynomial equation in a single variable. It has at least one solution because it is a second-order polynomial equation, which is guaranteed by the algebraic fundamental theorem. The answer could be simple or complicated.

Given a Quadratic function in terms of x, (6x + 4)²

Simplification of the given equation is

=>  (6x + 4)²

=>  (6x + 4) * (6x + 4)

=> 36x² + 24x + 24x + 16

=>  36x² + 48x + 16

therefore,   36x² + 48x + 16 is the simplified form of the given quadratic equation  (6x + 4)².

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Answer:

Putting -7 in place of x

Step-by-step explanation:

h(x) = 5.7 −19x

h(-7)= 5.7 - 19(-7)

         5.7 + 133

         138.7

The value of the function at -7 is 138.7.

x + y = 11

Putting -7 in place of x

-7 + y= 11

y = 18

Answer: Since sin(theta) = 4/5 and pi/2 < theta < pi, theta is in the third quadrant.

In the third quadrant, cos(theta) is negative and sin(theta) is positive.

Using the double angle formula for cosine, cos 2theta = 2cos^2(theta) - 1 = 2(cos^2(theta) - (sin^2(theta)/2)) - 1

cos^2(theta) = 1 - sin^2(theta) = 1 - (4/5)^2 = 1 - 16/25 = 9/25

so,

cos 2theta = 2(9/25) - 1 = 18/25 - 25/25 = -7/25

Step-by-step explanation:

The value of the cos(2θ) will be equal to -24/25.

The relationships between the sides and angles of triangles are the subject of the mathematical discipline of trigonometry. It is based on research into the characteristics of the trigonometric functions used to describe these relationships, including sine, cosine, and tangent.

First, we can find the value of cos(θ) using the Pythagorean identity:

cos(θ = √(1 - sin^2(θ)) = √(1 - (4/5)²) = √(9/25) = 3/5

Since pi/2 < θ < π, we know that cos(θ) < 0. Therefore, cos(θ) = -3/5.

Next, we can use the double-angle formula for cosine to find cos(θ):

cos(θ) = 2cos²(θ) - 1

Substituting the value of cos(theta) that we found earlier, we get:

cos(2θ) = 2(-3/5)² - 1 = -24/25

Therefore, the value of the cos(2θ) = -24/25.

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The measure of the angle ∠BAD will be 110°. Then the correct option is B.

It is the close curve of an equidistant point drawn from the center. The radius of a circle is the distance between the center and the circumference.

The central angle is double the angle at the periphery that was subtended by the same chords.

DR is the tangent to Circle O. If m of angle DB = 140°. Then the equation is given as,

∠BCD = (1/2) arc DB

∠BCD = (1/2) x 140°

∠BCD = 70°

We know that the sum of the opposite angle of the cyclic quadrilateral is 180°. Then we have

∠BAD + ∠BCD = 180°

∠BAD + 70° = 180°

∠BAD = 110°

The measure of the angle ∠BAD will be 110°. Then the correct option is B.

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The missing graph is given below.

A production possibility curve (PPC) is a graphical representation of the maximum combinations of two, or more, products that can be produced with a set of limited resources.

It is a visual representation of the constraints of production, and is a tool used to illustrate the basic economic problem of "what to produce and how to produce it". A production possibility curve (PPC) is a graphical representation of the maximum combinations of two, or more, products that can be produced with a set of limited resources.

The production possibility curve illustrates the trade-off between two products. The curve shows the maximum possible output of one product (X-axis) for a given quantity of the other product (Y-axis). The curve is drawn under the assumption of full employment and efficient use of resources. Points that lie outside the curve are not possible to achieve with the given resources, and points that lie inside the curve indicate that the resources are not being used efficiently.

The central problem of what to produce and how to produce is illustrated by the production possibility curve. The curve shows that when producing more of one product, there is less available for the other product. To produce more of both products requires an increase in resources, either in terms of labour, capital, or technology, which is ultimately limited. Therefore, the production possibility curve demonstrates the need to make decisions on what to produce and how to produce, in order to make the most efficient use of limited resources.

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Answer: (4,7)

Step-by-step explanation:

Find the intersection of the graph and plot it.

Answer:

I. opposite sides are equal

Answer:

i. Opposites sides are equal

ii. Opposite sides are parallel

iii. All angles are right angles

Step-by-step explanation:

The final conclusion is that the null hypothesis, that 90% of Americans check mail daily, is likely true based on the given information.

In statistics, the null hypothesis is a statement that there is no significant difference between a particular measure of a population (such as the proportion of Americans who check their mail daily) and a specific value (in this case, 90%). The initial conclusion, that the null hypothesis reflects the population measure, suggests that the evidence supports the idea that 90% of Americans do check their mail daily. This conclusion can be strengthened or weakened by further statistical analysis, such as a hypothesis test, but with the information given it seems that the null hypothesis that 90% of Americans check mail daily is likely true.

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The length of DF is 18.

It is a two-dimensional figure which has three sides and the sum of the three angles is equal to 180 degrees.

We have,

From the figure,

∠FEG = ∠DEG

This means,

The side opposite to the angles is also equal.

So,

FG = GD

3a = a + 6

3a - a = 6

2a = 6

a = 3

Now,

DF = 3a + (a + 6)

DF = 4a + 6

DF = 4 x 3 + 6

DF = 12 + 6

DF = 18

Thus,

DF = 18.

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Answer:

80 peeps

Step-by-step explanation:

Etta needs to add the source of the information to better arrange these notes.

A note is a place where information about a specific item is recorded for later reference. The main goals of taking notes are to promote active learning and create study materials for tests. You should be able to organise material into an understandable format that will aid in your learning process by developing note-taking skills.

As a result, it is clear from the question that Etta is making notes for the purpose of creating a webpage about healthy eating. Once her notes have been organised with the relevant facts and information, Etta will need to cite her sources.

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A function is a mathematical relationship between two sets of variables, usually expressed as an equation. A function can be represented in three different ways:

This can be helpful in understanding the behavior of the function and how the output value changes with different input values. Understanding and interpreting different representations of a function is a fundamental part of mathematics.

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The inequality standard form that describes this situation 5x + 4y ≤ 28, option A.

The cost of hot dogs can be expressed as 5 tickets times x hot dogs, and the cost of burgers can be expressed as 4 tickets times y burgers.

The total number of tickets the campers can use is 28 tickets, so the total cost of the hot dogs and burgers must be less than or equal to 28 tickets: 5x + 4y ≤ 28

This inequality in standard form describes the situation where the camp counselor bought food tickets for her campers and they can use up to 28 tickets in total.

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The full question is:

At an arts festival, a camp counselor bought food tickets for her hungry campers. The campers can use them to get hot dogs, which cost 5 tickets apiece, and burgers, which cost 4 tickets apiece. In total, the campers can use up to 28 tickets, which is how many the counselor bought. Select the inequality in standard form that describes this situation. Let x be the number of hot dogs and y be the number of burgers.

a. 5x + 4y ≤ 28

b. 5x + 4y ∠ 28

c. 4x + 5y ≤ 28

d. 4x + 5y ∠ 28

I can't read that. Please write it neater and bigger, I'm sure I can help you then.

The long run probability that both machines are working is then given by π2.

To find the steady state solution, we first need to write down the transition rate matrix of the chain, which describes the rates at which the system transitions between states. The states in this case are the number of machines that are working (0, 1, or 2), and the transition rates are determined by the failure and repair rates of the machines.

The matrix will be 3x3 and the diagonal elements will be the negative sum of the corresponding row in the matrix.

Let's call P(i,j) the probability of being in state i and transitioning to state j.

P(0,1)=1, P(1,0)=1, P(1,2)=1 and P(2,1)=1

The transition rate matrix will be

[ -3 1 0]

[ 1 -6 2]

[ 0 3 -5]

The steady state solution can be found by solving the equation Pπ = π, where π is the steady state probability vector and P is the transition rate matrix.

The long run probability that both machines are working is then given by π2.

You can also use Linear Algebra to solve the equation Pπ = π and find the steady state probability vector.

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