Suppose A, B, C are matrices so that C = AB. Also suppose that the rows of A are aſ,. am, the columns of A are A1, ..., An. Also, the rows of B are b], ,...,6% and the columns of B are B1, Also, the rows of C are cſ, ..., Cm and the columns of Care C1, ..., Cp. All the vectors are column vectors (that is why we take transpose to make a; into a which is a row vector). Also, the elements of A, B, C are denoted by Aij, Bij, Cij respectively. Write a summation formula for Cij, Cj, cT. Hint: to really benefit from this exercise, do not just "write the for- mula." Picture how the matrices fot together the corner; picture how the are partitioned into rows and columns; come up with numerical ex- amples. 7

Mrs. Banks has enough fruit to make the 44 qt of jelly she wants, but she will have 4 lb of leftover fruit.

Here we have to use the arithmetic operations. First, we need to convert the total quantity of jelly to gallons since we have the amount of fruit needed per gallon. One gallon is equal to 4 quarts, so 44 quarts is equal to 11 gallons.

Next, we can calculate how much fruit is needed for 11 gallons of jelly by multiplying the amount of fruit needed per gallon by the number of gallons

11 gallons x 6 lb of fruit per gallon = 66 lb of fruit needed

Since Mrs. Banks only has 70 lb of fruit, she has enough to make the 44 qt of jelly she wants, but she will have 4 lb of leftover fruit:

70 lb of fruit - 66 lb of fruit needed = 4 lb of leftover fruit

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The given question is incomplete, the complete question is:

Mrs. Banks wants to make 44 qt of jelly with 70 lb of fruit. If each gallon of jelly needs 6 lb of fruit, will

she have enough fruit? How much leftover fruit does she have, or how much extra fruit is needed?

The PQRS and TSUV are congruent parallelograms, they have the same shape and size. angle PQR is congruent to angle TSU, since they are opposite angles in parallelograms PQRS and TSUV, respectively. so angle TSU in parallelogram TSUV is congruent to angle PQR.

The following are a parallelogram's characteristics:

The two opposing sides are level and parallel.

The opposing angles line up evenly.

The following or adjacent angles are extra.

Every angle will be at a right angle if even one of the other angles is.

PQRS and TSUV are congruent parallelograms, which denotes that their dimensions are the same. The parallelograms' corresponding angles are therefore equal.

Angle PQR is an interior angle in the parallelogram PQRS that is opposite to the adjacent angle PQS, whereas angle UTS is an internal angle in the parallelogram TSUV that is opposite to the adjacent angle TSV.

We can infer that angle PQR and angle UTS are related angles and are hence congruent because PQRS and TSUV are congruent.

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Answer:

A

Step-by-step explanation:

By combinations, we get that there are 20,020 possible 6-topping pizzas.

Given that a pizza parlor offers a choice of 16 different toppings, we need to find the number of 6-topping pizzas that are possible. No double-orders of toppings are allowed. What is the number of 6-topping pizzas that are possible?

The formula for combinations is as follows:

ncr = (n!)/(r! * (n - r)!) where n = 16 (total number of toppings available)

r = 6 (number of toppings required for a pizza)

ncr = (16!)/(6! * (16 - 6)!)

⇒ ncr = (16!)/(6! * 10!)

⇒ ncr = (16 * 15 * 14 * 13 * 12 * 11)/(6 * 5 * 4 * 3 * 2 * 1)

⇒ ncr = (16 * 3 * 5 * 7 * 13 * 11)/(3 * 2 * 2)

⇒ ncr = 20,021

In this situation, the order of the toppings does not matter. Therefore, we cannot have a repeat of the same toppings, as mentioned. Hence the answer to the question is no. Thus, there are 20,020 possible 6-topping pizzas.

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The values of unknown angles in the given figures are:

(a) a° = 117°, b° = 117°, c° = 63°, d° = 78°

(b) e° = 31°, f° = 66°

(c) g° = 69°, h° = 83°

(d) i° = 45°, j° = 60°

Angles are formed when two rays join at a common point. The common point can also be called as a node or vertex, and the two rays are called angle arms. Angles are usually represented by the "∠" symbol. The word angle is derived from the Latin "Angulus". Learn more about lines and angles here.  Angle types are based on angle values ​​in degrees. You can also express angles in radians, or pi (π). 180° is equivalent to pi radians.  

For the given figures:

a° = 117° [ Vertically opposite angles]

b° = 117° [Corresponding angle]

c° = 180° - 117° [Linear pair]

c° = 63°

d° = 78° [Corresponding angle]

e° = 31° [Alternate interior angles]

f° = 66° [Alternate interior angles]

g° = 69° [Corresponding angle]

h° = 83° [Alternate interior angles]

j° = 60° [Alternate interior angles]

i° = 180 - (75 + 60) [Angle sum property of triangle]

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Cindy and tom, working together, can rake the yard in 8 hours. Working alone, Tom takes twice as long as Cindy, it takes Cindy to rake the yard 2 hours

To find the time it takes Cindy to rake the yard alone, let's use the following steps:Let x be the time taken by Cindy to rake the yard alone . Then the time taken by Tom to rake the yard alone will be 2xIt is given that Cindy and Tom can rake the yard in 8 hours when they work together.

Using the formula for working together, we get:[tex]\[\frac{1}{x} + \frac{1}{2x} = \frac{1}{8}\][/tex] Multiplying the equation by the least common multiple of the denominators, we get:[tex]\[16 + 8 = 2x\][/tex] Simplifying, we get:[tex]\[2x = 24\][/tex]Dividing both sides by 2, we get:[tex]\[x = 12\][/tex]Therefore, it takes Cindy 12 hours to rake the yard alone.

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(a) the tare οf the rice is 800 grams. and (b) the tare percentage οf the rice is 3.10%.

A rate, number, οr amοunt in each hundred

a. The tare οf the rice is the weight οf the packaging οr cοntainer used tο hοld the rice. It can be calculated by subtracting the net weight οf the rice frοm the grοss weight οf the bag:

Tare weight = Grοss weight - Net weight

Tare weight = 25.8 Kg - 25 Kg

Tare weight = 0.8 Kg

Tο cοnvert this tο grams, we can multiply by 1000:

Tare weight = 0.8 Kg × 1000

Tare weight = 800 grams

Therefοre, the tare οf the rice is 800 grams.

b. The tare percentage οf the rice is the percentage οf the grοss weight that is accοunted fοr by the tare weight. It can be calculated using the fοrmula:

Tare percentage = (Tare weight / Grοss weight) × 100%

Substituting the values we fοund earlier, we get:

Tare percentage = (800 g / 25.8 Kg) × 100%

Tare percentage = 3.10%

Therefοre, the tare percentage οf the rice is 3.10%.

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The pοint that satisfies bοth inequalities is the pοint inside this triangular regiοn.

An inequality is a mathematical statement that cοmpares twο values οr expressiοns and indicates whether they are equal οr nοt, οr which οne is greater οr smaller.

Since the shading is nοt included, we will need tο use the lines themselves tο determine the cοrrect regiοn οf the cοοrdinate plane.

The first inequality y > (3/2)x - 5 has a slοpe οf 3/2 and a y-intercept οf -5. This means the line will have a pοsitive slοpe and will be lοcated belοw the pοint (0,-5).

The secοnd inequality y < (-1/6)x - 6 has a negative slοpe οf -1/6 and a y-intercept οf -6. This means the line will have a negative slοpe and will be lοcated abοve the pοint (0,-6).

Tο find the pοint that satisfies BOTH inequalities, we need tο lοοk fοr the regiοn οf the cοοrdinate plane that is belοw the line y = (3/2)x - 5 AND abοve the line y = (-1/6)x - 6. This regiοn is the triangular-shaped area that is bοunded by the twο lines and the x-axis.

The pοint that satisfies bοth inequalities is the pοint inside this triangular regiοn.

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Answer:

Proofs attached to answer

Step-by-step explanation:

Proofs attached to answer

The estimated probability is 0.9537 (rounded to four decimal places).Hence, the answer is 0.9537.

Question: Nine percent of men are color blind. Researchers need at least 60 men with this trait, so they randomly select 700 men. Estimate the probability that at least 60 color-blind men are in the sample. Use a TI-83, TI-83 plus, or TI-84 calculator to find the probability. Round your answer to four decimal places. Provide your answer below:

Solution:

Let the probability of the man having the trait of color blindness be p. Then, p = 0.09, and the sample size is n = 700.Mean and Variance of Binomial Distribution are:μ = np and σ² = np(1 − p)Here, p = 0.09, n = 700μ = np = 700(0.09) = 63Andσ² = np(1-p) = 700(0.09)(0.91) = 5.679Now we need to find the probability that at least 60 color-blind men are in the sample.i.e., P(X≥60)By using the Central Limit Theorem, we can approximate this binomial distribution as a normal distribution with mean μ = 63 and variance σ² = 5.679.P(X≥60) can be calculated using the following formula:P(Z≥((60-63)/√(5.679))) = P(Z≥(-1.684))Now we need to look at the z-table or use the calculator to find the value of P(Z≥(-1.684))P(Z≥(-1.684)) = 0.9537 (rounded to four decimal places)Therefore, the estimated probability is 0.9537 (rounded to four decimal places).Hence, the answer is 0.9537.

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Answer: 4.5

Step-by-step explanation:

A^2 +B^2 =C^2

A^2 + 6^2 =7.5^2

A^2 + 36= 56.25

A^2= 20.25

A= square root of 20.25

A= 4.5

Answer:

54

Step-by-step explanation:

Add six each time -> 24 + 6 = 30 + 6 = 36 etc

The equation to show the relationship between x and y is y = 0.08x, where y is the amount of sales tax in dollars for the item and x is the cost of the item in dollars before tax.

Tax is a compulsory financial charge or some other type of levy imposed upon a taxpayer by a governmental organization in order to fund various public expenditures. A failure to pay, along with evasion of or resistance to taxation, is punishable by law. Taxes consist of direct or indirect taxes and may be paid in money or as its labour equivalent. Most countries have a tax system in place to pay for public, common or agreed national needs and government functions. Some levy a flat percentage rate of taxation on personal annual income, but most scale taxes based on annual income amounts.

This equation reflects the fact that the amount of sales tax for an item is 8% of its cost before tax.

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Sales tax: The equation to show the relationship between x and y is x + y = C,

An equation is a mathematical statement that expresses two mathematical expressions to be equal. It usually consists of two numbers, variables, or a combination of the two. An equation may be used to calculate a desired result, or to determine the relationship between two variables. Equations can also be used to test whether a statement is true or false. Most equations are written in the form of "a = b," where a and b are two numbers or variables.

where C is the cost of the item plus the sales tax. This equation can be explained mathematically as follows: the cost of the item (x) is added to the amount of sales tax (y) to give the total cost of the item with tax (C).

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Thus, we have [tex]r = 2πr2 + 8πr[/tex], which can be written as [tex]2πr2 + 8πr - r = 0[/tex].

Factor out r to get r(2πr + 8π - 1) = 0. We can then use the quadratic formula

to solve for [tex]r:r(A) = (-8π ± sqrt(64π2 - 8π)) / 4π= (-2 ± sqrt(16π2 - 2π)) / π= (-2 ± 2π√15) / π[/tex]Thus, [tex]r(A) = (-2 + 2π√15) / π or r(A) = (-2 - 2π√15) / π.[/tex]

Part a:Domain of the function A(r)The expression for the total surface area of a cylinder is 2πr2 + 2πrh, where r is the radius of the circular base of the cylinder and h is the height of the cylinder. However, in this question, the cylinder is defined as having a height of 4 inches, and the area expression A(r) is given as A(r) = 2πr2 + 8πr.  

To determine the domain of this function, we must look at the values of r that are permitted in the expression. A(r) = 2πr2 + 8πrThe domain of this function A(r) is all real numbers greater than or equal to zero

.Part b:Inverse function of A(r)Write the radius r as a function of AInverse functions are functions that undo each other's operations. In other words, given a function f(x), its inverse function g(x) undoes the effects of f(x).To find the inverse function of A(r), we must first switch the roles of A and r.

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If there are 500 students in total, the number of students who made the honor roll is 10 students, given that the ratio of students who made the honor roll to the total number of students is 1:50.

The number of students who made the honor roll can be found using proportions. Here's how to do it:

Let X be the number of students who made the honor roll.

The proportion can be set up using the given ratio as follows:

1:50 = X:500

Cross-multiplying this equation and solving for X gives:

50X = 500

X = 10

Therefore, 10 students made the honor roll.

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A null hypothesis refers to a statistical hypothesis that assumes that there is no difference between two groups or variables. The null hypothesis may either be rejected or not rejected based on the statistical results obtained from a hypothesis test. A hypothesis test is a statistical test that is conducted to either accept or reject the null hypothesis based on the statistical results obtained.

When is the null hypothesis rejected?The null hypothesis is rejected when the p-value is less than or equal to a preconceived level of significance, α (usually set at 0.05 or 0.01).The null hypothesis is rejected when the calculated test statistic (such as t-test, z-test, or F-test) is greater than or equal to the critical value corresponding to the level of significance α.

When is the null hypothesis not rejected?The null hypothesis is not rejected when the p-value is greater than the preconceived level of significance, α. This means that there is not enough evidence to reject the null hypothesis.The null hypothesis is not rejected when the calculated test statistic is less than the critical value corresponding to the level of significance α. This means that there is not enough evidence to reject the null hypothesis.

In conclusion, the null hypothesis is rejected when the p-value is less than the preconceived level of significance α or when the calculated test statistic is greater than or equal to the critical value corresponding to the level of significance α. On the other hand, the null hypothesis is not rejected when the p-value is greater than the preconceived level of significance α or when the calculated test statistic is less than the critical value corresponding to the level of significance α.

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 The probability of [tex]3X1-1X2 + 3X3[/tex] being greater than 20 is given by[tex]P(3X1-1X2 + 3X3 > 20) = 1- Φ((20-3μ1+μ2-3μ3)/(√3σ11+σ22+3σ33))[/tex].

In this case, [tex]μ1=10, μ2=10, μ3=10, σ11=0.3, σ22=0.3, σ33=0.3,[/tex] so the probability of [tex]3X1-1X2 + 3X3[/tex] being greater than 20 is 1-Φ(-1.0).

1. To answer this question, we can use the formula for a multivariate normal distribution.

The probability of the profit for selling chocolate being greater than 6 million is given by P(X1 > 6) = 1- Φ(6-μ1)/(√σ11). In this case, μ1=10, σ11=0.3, so the probability of the profit being greater than 6 million is 1-Φ(2.667).

2. To answer this question, we need to use the formula for the conditional probability of a multivariate normal distribution.

The probability of the profit for selling chocolate being greater than 6 million, given the sales of marshmallow is 5 million and the sales of graham cracker is 5 million, is given by

[tex]P(X1>6 | X2=5, X3=5) = 1- Φ((6-μ1-Σ12*5-Σ13*5)/(√σ11-Σ12²-Σ13²))[/tex]. In this case,

[tex]μ1=10, σ11=0.3, Σ12=0.3, Σ13=0.3,[/tex]so the probability of the profit being greater than 6 million is 1-Φ(-0.1).

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The minimum cost for shipping management will be $372.00.

Delivery cost from the northern warehouse to Customer A = $1. 50

Delivery cost from the northern warehouse to Customer B = $0. 80

Delivery cost from the southern warehouse to Customer A = $1. 10

Now,

Let the number of sheets delivered from the north-side warehouse to Customer A be = x

Let the number of sheets delivered from the north-side warehouse to Customer B = y

Let the number of sheets delivered from the south-side warehouse to Customer A. = z

Therefore, the objective function to be minimized is:

1.5x + 1.2y + 0.8z + 1.1(240 - x - y - z).

x + z + s1 = 160

y + (240 - x - z) + s2 = 90

x - 100 + s3 = 0

y - 140 + s4 = 0

After satisfying the orders, there will be 60 sheets of drywall board in the north side warehouse and 70 sheets in the south side warehouse.

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Answer:

x = 3

Step-by-step explanation:

Solving systems of linear equations via substitution:

[tex]2x-6y=-6[/tex]

[tex]y=1.5x-2.5[/tex]

We are already given the value of y, so to find the value of x, we need to plug in the y value in the other equation.

[tex]2x-6(1.5x-2.5)=-6[/tex]

Distribute 6

[tex]2x-9x+15=-6[/tex]

Combine our like terms

[tex]-7x+15=-6[/tex]

Subtract 15 to both sides

[tex]-7x=-21\\[/tex]

Divide by -7

[tex]x=3[/tex]

Thus, the money lost by the store is found to be $100.

Subtraction is the activity or procedure of determining the variance between two amounts or numbers. The phrase "taking away one numeral from another" is also used to describe the act of subtracting one number from another. Making payments, sending cash to pals, and many more situations call for the use of subtraction.

Several words found in a subtraction statement are frequently employed when subtracting two numbers:

In the given question:

Money stolen $100.

Worth of goods purchased = $70.

Returned money by shopkeeper = $30.

Total amount = $100 + $70 + $30.

$100 is again payed by the shopkeeper.

Thus, subtracting:

Amount = $200 - $100

Thus,

Loss = $100.

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The representation of 122 would depend on the base system being used. In a decimal (base-10) system, 122 would be represented as 122

The base system that would record this tally as 122 depends on the context in which the tally is being used.

If we assume that the tally is being used to represent a quantity or count, and we are using a base-10 (decimal) system, then 122 would be represented as 122 in decimal notation.

However, if the tally is being used in a different context or in a different base system, then the representation of 122 may be different. For example:

In a base-2 (binary) system, 122 would be represented as 1111010

In a base-8 (octal) system, 122 would be represented as 172

In a base-16 (hexadecimal) system, 122 would be represented as 7A

Therefore, the specific base system used to represent the tally must be known or specified in order to determine the correct representation of 122.

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The required time is mathematically given as

t-150 minutes.

This is further explained below.

We know that the volume of the prism is given by.

[tex]\text{Volume}=\text{(Base Area)}\times\text{height}[/tex]

[tex]\text{Base Area}=\dfrac{1}{2}\times(1.4+0.6)\times2[/tex]

[tex]\text{Base Area}=2\ \text{m}^2[/tex]

Now,

[tex]\text{Volume}=2\times1=2\ \text{m}^3[/tex]

Given that there is a twenty percent drop in the level of the pond during the first thirty minutes.

Because of this, the volume increases.

[tex]\text{Volume}=2\times0.8=1.6\ \text{m}^3[/tex]

Now, the rate of emptying the tank is,

[tex]=\dfrac{2-1.6}{30} =\dfrac{1}{75} \ \text{m}^3/ \text{min}[/tex]

In conclusion, We also know that,

$$

[tex]\text{time}=\dfrac{\text{volume}}{\text{rate}}[/tex]

[tex]\text{time}=\dfrac{2}{\frac{1}{75} } =150 \ \text{min}[/tex]

Therefore, Colin must wait for the pond to drain for a total of 150 minutes.

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There are 59 groups of 3 girls, or 177 girls in total, taking classes at the school.

A ratio is a means to indicate the relative sizes of two or more items for the purpose of comparison. It can be shown with a colon or as a fraction. Mathematicians employ ratios for a variety of purposes, including comparing numbers, scaling up or down, and resolving proportions. Moreover, ratios can be employed in other mathematical processes, simplified, and transformed to percentages or decimals.

Given that for every three girls there are 4 boys in class.

Thus, the proportion can be given as:

4x = 236

x = 59

Now, the proportion of girls are 3x.

3(59) = 177 girls.

Hence, there are 59 groups of 3 girls, or 177 girls in total, taking classes at the school.

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Answer:

The ratio of green legos to missing legos is:

42 : 3

Simplifying this ratio by dividing both sides by 3, we get:

14 : 1

Therefore, for every one missing green lego, there are 14 green legos.

The last two rows of the table should be completed as follows:

Input   Output

8       22.80

10      28.50

An algebraic expression is a mathematical phrase that contains numbers, variables, and operations. It is used to represent a single quantity or value, and can be written in terms of one or more variables.

The rule given is an algebraic expression, x, which is the input, multiplied by 2.85, which is the output. Using this information, we can determine the cost of 10 muffins.

To find the cost of 10 muffins, we can use the algebraic expression given. First, we will multiply 10, the number of muffins, by 2.85, the cost of one muffin. This gives us a total of 28.50. Therefore, the cost of 10 muffins is 28.50.

Using this same rule and process, we can also determine the cost of any number of muffins. For example, if we want to know the cost of 15 muffins, we can simply multiply 15 by 2.85, giving us a total of 42.75.

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The minimum value of the sum of squares is 3 when all three numbers are equal to 1.

Given the condition that the product of three positive integers x, y, and z is 1 and the sum of the squares is a minimum, we have to find out the three numbers that satisfy this condition.The three numbers that satisfy the condition arex = 1, y = 1, and z = 1 because the product of any number and 1 is the number itself, and the sum of the squares of all the numbers is also 1. Thus, the answer is (1,1,1).It can be proved mathematically that the answer (1, 1, 1) is correct:Product of three positive integers is 1 if and only if all three numbers are equal to 1.If three positive integers a, b, and c have a fixed sum, then the sum of the squares of two of the integers is the minimum when they are equal to each other and their sum is equal to half of the fixed sum.Thus, the sum of the squares of the three numbers is 1 + 1 + 1 = 3, and the minimum value of the sum of squares is 3 when all three numbers are equal to 1.

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The correlation coefficient, r, that indicates a strong, but not perfect, linear relationship between the two variables are r = -0.85 and  R = 0.90.

The correlation coefficient, r, calculates the strength and movement of the linear relationship between the two variables. It ranges from -1 to 1. Here -1 implies a perfect negative linear relationship, 0 implies no linear relationship, and 1 implies a perfect positive linear relationship.

A strong correlation should be close to -1 or 1 but not an equal value. In the given options strong, but not perfect, linear variables are r = -0.85 and 0.90 are closer to the r values.

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According to the inscribed angle theorem the measure of angle Y is 43 degrees.

As the inscribed angle equals half of the central angle, the inscribed angle theorem is also known as the angle at the centre theorem. The centre angle is always the same since the endpoints are fixed, regardless of where it is on the same arc between the ends. The measure of the central angle is equal to double the measure of the inscribed angle occupied by the same arc, according to this theorem. OR. Half of a central angle that subtends the same arc is an inscribed angle. OR. The angle in a circle's centre is twice as large as any angle at its perimeter that the same arc occupies.

We know that, an inscribed angle is half of a central angle that subtends the same arc.

Here the given arc = 86 degrees.

The inscribed angle is half the arc of the circle thus,

angle Y = 1/2(86)

angle Y = 43 degrees.

Hence, according to the inscribed angle theorem the measure of angle Y is 43 degrees.

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you get the intercept (0) by seeing where the like passed through and you get the gradient (-1x) by looking at the intercept, going along one digit (to 1) and then seeing how much you go down to get to the blue line so in this case you have gone -1 down. hope this helps

Y=-X+0

Answer:

The line is

y= -x

Step-by-step explanation:

when y= -1

x=1

when y=1

x= -1

The center, 6,  is less frequent than the neighbor values, but the single dot that best represents the data still is 6.

Each point on the dot plot over each number represents the amount of times that we have that value in the data set.

Here the center is 6, and we can see that we have only one point in 6, while in the neighbors we can see more points, then we can see that the center is less populated than the neighbor values.

Now, what single dot would best represent the data?

To answer that we need to get the mean of the data set,

Counting the values in the graph, and dividing by the number of points, we have:

mean = (3 + 4 + 4 + 5 + 5 + 6 + 7 + 7 + 8 + 8+ 8+ 9)/12 = 6.16

Which we can round to 6.

So that is the single dot that best represents the data.

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