I need help with this (a. b. and c.)

The statement 'A vector b is a linear combination of the columns of a matrix A is and only if the equation Ax = b has at least one solution.' is True.

We first thought of a matrix as a rectangular array of numbers. When the number of rows is m and columns is n, we say that the dimensions of the matrix are m×n.

A vector is most simply thought of as a matrix with a single column. There are two operations we can perform with vectors: scalar multiplication and vector addition. Both of these operations have geometric meaning.

Given a set of vectors and a set of scalars we call weights, we can create a linear combination using scalar multiplication and vector addition.

The product of two matrices can be seen as the result of taking linear combinations of their rows and columns. This way of interpreting matrix multiplication often helps to understand important results in matrix algebra.

The statement 'A vector b is a linear combination of the columns of a matrix A is and only if the equation Ax = b has at least one solution.' is True.

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The value of the standardized test statistic is D. 1.77.

A standardized test statistic is a measure of the difference between a sample statistic and the population parameter it estimates, expressed in units of the standard deviation.

The value of the standardized test statistic can be calculated using the formula:

(x - μ) / (s / √n)

where x is the sample mean, μ is the population mean, s is the population standard deviation, and n is the sample size.

Given the information provided in the question, the standardized test statistic is:

(20.3 - 20) / (1.2 / √50) = 1.7678

Rounding to two decimal places, the answer is D. 1.77.

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Answer:

see below

Step-by-step explanation:

7300 investment

annual rate 6.6% compounded monthly = 6.6/12 months = 0.55% per month

t years = t*12 months

so function is = 7300 * (1+6.6%/12)^12t

APY = (1+0.55%)^12 - 1 = 1.068-1 = 0.068 = 6.8%

A boy walked 7km on a bearing of 60°. Represented this information on a diagram given below.

A bearing in mathematics is the angle, measured in degrees and anticlockwise from north. Typically, bearings are given as a three-figure bearing. For instance, 30° clockwise from north is typically expressed as 0°.

"Pieces that aid objects' rotation" are bearings. They support the rotating shaft that moves the machinery. Cars, planes, power generators, and other devices all use bearings.

To lessen friction between two spinning or sliding surfaces, a bearing is a mechanical component.

There are many different types of bearings, including ball and roller bearings, linear bearings, and mounted versions that may use either, and they are used for rotating or linear shaft applications. Bearings are mechanical assemblies that include rolling elements and typically inner and outer races.

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The mistake Derek did was d = 8.

The correct step is d = 9.

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

Example:

2x + 4 = 55 is an equation.

We have,

8d = 72

Step 1:

Divide both sides with 8.

8d/8 = 72/8

[ 8 x 9 = 72 ]

So,

d = (8 x 9)/ 8

d = 9

Thus,

Derek's mistake is d = 8.

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To prove that triangles ABD and ΔABC are congruent by SSS, what needs to be true is: A. BC ≅ BD.

For two triangles to be congruent to each other by the SSS Congruence Theorem, the triangles must have three pairs of corresponding sides that are congruent to each other.

In the image given, we can deduce that the two triangles have the following properties:

AB ≅ AB (reflexive property)

AC ≅ AD (given)

This means that have two pairs of corresponding congruent sides. Therefore, in order to prove that ΔABD ≅ ΔABC by SSS, what needs to be true is: A. BC ≅ BD.

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The value for a1 in geometric series 2, -6, 18, -54, ..... is a1 = 2, and the recursive formula is a(n) =a^(n-1)·(-3) for n≥2.

What is geometric series?

A geometric series is a collection of terms in mathematics that have an unlimited number and a fixed ratio between each term. A geometric series is typically expressed as a + ar + ar² + ar³ + ..., where r is the common ratio between neighbouring terms and a is the coefficient of each term.

The given geometric series is -

2, -6, 18, -54, ..... (1)

Let A(n) be the geometric series defined in (1).

Then the first term A(1) = 2

The second term A(2) = -6

We need to find the common ratio from one term to the next.

r =  common ratio  

The formula for r is -

r =  subsequent term / previous term = -6/2 = -3

The third term A(3) = 18

The r value for A(3) is -

r =  subsequent term / previous term = 18/-6 = -3

The fourth term A(4) = -54

The r value for A(4) is -

r =  subsequent term / previous term = -54/18 = -3

The formula for a(n) terms will be -

a(n) =a^(n-1)·(-3)

Therefore, the recursive formula is a(n) =a^(n-1)·(-3).

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The numeric value of the expression for this problem is given as follows:

[tex]\sqrt{2} + 1[/tex]

The expression for this problem is defined as follows:

[tex]\frac{4 - 3\sqrt{2}}{(\sqrt[4]{2} - \sqrt[4]{8})^2}[/tex]

Applying the square of the subtraction in the denominator, we have that:

[tex]{(\sqrt[4]{2} - \sqrt[4]{8})^2 = \sqrt[4]{4} - 2\sqrt[4]{2}\sqrt[4]{8} + \sqrt[4]{64}[/tex]

[tex]{(\sqrt[4]{2} - \sqrt[4]{8})^2 = 4^{\frac{1}{4}} - 2\sqrt[4]{16} + \sqrt[4]{4^3}[/tex]

[tex]{(\sqrt[4]{2} - \sqrt[4]{8})^2 = (2^2)^{\frac{1}{4}} - 2 \times 2 + 3[/tex]

[tex]{(\sqrt[4]{2} - \sqrt[4]{8})^2 = \sqrt{2} - 1[/tex]

Hence the simplified expression is given as follows:

[tex]\frac{4 - 3\sqrt{2}}{\sqrt{2} - 1}[/tex]

Rationalizing the denominator, we have that:

[tex]\frac{4 - 3\sqrt{2}}{\sqrt{2} - 1} \times \frac{\sqrt{2} + 1}{\sqrt{2} + 1}[/tex]

Applying the subtraction of perfect square, the denominator simplifies to one, hence the value of the expression is given by the numerator as follows:

[tex](4 - 3\sqrt{2})(\sqrt{2} + 1) = 4\sqrt{2} + 4 - 3 \times 2 - 3\sqrt{2}[/tex]

[tex][tex](4 - 3\sqrt{2})(\sqrt{2} + 1) = \sqrt{2} + 1[/tex]

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Check the picture below.

so following the inscribed quadrilateral conjecture, let's get those equations that add  up to 180°.

[tex](2y+74)+(7x+1)=180\implies 2y+7x+75=180\implies \underline{2y+7x=105} \\\\[-0.35em] ~\dotfill\\\\ (2y+100)+(6x-10)=180\implies 2y+6x+90=180\implies \underline{2y+6x=90} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{using the 1st equation}}{2y+7x=105}\implies 2y=105-7x \\\\\\ \stackrel{\textit{using the 2nd equation}}{2y+6x=90}\implies 2y=90-6x\implies \stackrel{\textit{substituting from above}}{105-7x=90-6x} \\\\\\ 105=90+x\implies \boxed{15=x}[/tex]

[tex]\stackrel{\textit{since we know that}}{2y+7x=105}\implies 2y+7(15)=105\implies 2y+105=105 \\\\\\ 2y=0\implies y=\cfrac{0}{2}\implies \boxed{y=0}[/tex]

Answer: The simplified expression is 6x - 23

Step-by-step explanation: To simplify the expression (12x-13)-2(3x+5) we will follow the order of operations:

First, we simplify the inner parentheses: 2(3x+5) = 6x + 10

Next, we substitute this simplified version back into the original expression: (12x-13)-(6x+10)

Now we can simplify the expression by combining like terms: 12x-13-6x-10 = 6x - 23

So the simplified expression is 6x - 23

Answer:6x-23 this your answer to simplify the expression I hope this helps have a good day

Step-by-step explanation:

(12x-13)-2(3x+5)

Remove unnecessary parentheses

12x-13-2(3x+5)

then do this

distribute -2 through the parentheses

12x-13-6x-10

Collect like terms which something like this

6x-13-10

then last thing you do is

Calculate the difference which is like this

6x=23

In general, the maximum order of the spectrum that can be observed with a diffraction grating is limited by the grating equation.

This equation states that mλ = d(sinθi - sinθr), where m is the order of the diffraction, λ is the wavelength of light, d is the spacing between the grating lines, θi is the angle of incidence, and θr is the angle of diffraction. Since d is fixed and θi is typically kept constant, the maximum order of the spectrum that can be observed is limited by the angle of diffraction (θr). This angle can be calculated using the equation θr = sin-1[(mλ/d)+sinθi]. Thus, the maximum order of the spectrum is limited by the value of θr, which is determined by the wavelength of light and the spacing between the grating lines.

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The number of days a software engineer can go without wearing the same combination of three items will be 36.

A permutation is an act of correctly arranging things or pieces. Combinations are a method of taking stuff or pieces from an assortment of items or sets in which the order of the items is irrelevant.

A software engineer owns 3 pairs of pants, 4 shirts, and 3 pairs of shoes. Then the number of different ways is given as,

⇒ ³C₁ × ⁴C₁ × ³C₁

⇒ 3 x 4 x 3

⇒ 36

The number of days a software engineer can go without wearing the same combination of three items will be 36.

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Researchers might study the role of predators in natural selection by testing the hypothesis that animals with camouflage colorings have a greater chance of survival when they are exposed to predators.

They can do this by setting up an experiment in which they expose animals with different colorings, including camouflage, to predators and then measure the survival rate of the different colorings. This would test if animals with camouflage colorings have a higher chance of survival when they are exposed to predators.

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Answer:

2

Step-by-step explanation:

The set of items that are part of both sets F and G is indicated by the symbol F G. It is the group of equilateral triangles that are also isosceles triangles, to put it another way.

Due to its three congruent sides, every equilateral triangle is an isosceles triangle. F G = F hence equals "equilateral triangles." By eliminating the unnecessary component, we can make F G simpler.

Consequently, F G = "equilateral triangles"

When seen collectively, a set is a group of items. The elements or members of the set are the things that make it up. Any mathematical object, such as integers, functions, or other sets, may be one of the elements of a set.

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The alternative hypothesis for this test would be that the new dog food extends the average lifespan of dogs beyond 10 years.

Mathematically, the alternative hypothesis can be stated as:

Ha: μ > 10, where μ is the population mean of the lifespan of dogs on the new dog food.

In this scenario, the null hypothesis is that the average lifespan of dogs on the new dog food is equal to 10 years, which is the commonly accepted average lifespan of dogs. However, the purpose of the study is to determine if the new dog food can extend the lifespan of dogs beyond this average.

Thus, the alternative hypothesis is that the average lifespan of dogs on the new dog food is greater than 10 years. This is represented mathematically as Ha: μ > 10, where μ is the population mean of the lifespan of dogs on the new dog food.

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Answer:

24.5 days i believe

If he continued at the same rate, he would travel  370 miles in 10 hours.

A proportion is described as an equation having two ratios that are set equal to each other.

It is the mathematical comparison of numbers or variables.

In mathematics, the different types of fractions are;

From the information given, we have that;

sauv drove 296 miles in 8 hours

Then,

If 296 miles  = 8 hours

x miles = 10 hours

cross multiply

8x = 2960

Make 'x' the subject of formula

x = 370 miles

Hence, the value is 370 miles

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The like terms are listed as follows:

-y, 7y and y/2.

Like terms are terms that share these two features:

If two terms are like terms, then they can be either added or subtracted.

Hence the first option is the only option in which all the three terms are like terms, as:

The remaining options have terms with different letters(second and third), or different exponents (fourth), hence they are not like terms.

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According to the pie chart given -

a) The worker saved GH¢ 20.00.

b) 2/5 fraction of worker's salary was spent on food.

c) The worker spent GH¢ 120.00 on food.

What is a pie chart?

One sort of graph that illustrates the information in the circular graph is a pie chart. It is a sort of graphical representation of data where the slices of pie depict the relative sizes of the data. A list of numerical and categorical variables is necessary for a pie chart. Pie in this context refers to the entire thing, and slices to its component portions.

The rent charges is = GH¢ 80.00

The savings can be obtained by ratio method -

Savings is depicted by 24° and rent by 96° in the pie chart.

So, the ratio will be 24/96.

Then the savings value will be -

(24/96) × 80

(1/4) × 80

20

Therefore, the savings value is GH¢ 20.00.

The total angle of pie chart is 360°.

Savings is depicted by 24°, rent by 96°, entertainment by 48° and clothing by 48° in the pie chart.

The angle for food will be -

360° - (24° + 96° + 48° + 48°)

360° - 216°

144°

Now the fraction that is for food -

144/360

2/5

Therefore, food covers 2/5 part of pie chart.

The amount spent on food can be obtained by formula of angle sector -

(144/96) × 80

1.5 × 80

120

Therefore, money for food was GH¢ 120.00.

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Problem 22

The smaller inner circle has a radius of r = 5. That will be plugged into the circumference formula below.

C = 2pi*r

C = 2pi*5

C = 10pi

This is the exact distance around the circle in terms of pi. Think of it like the amount of fencing you need to enclose the circle.

If you want an approximate perimeter, then use something like pi = 3.14

So 10pi = 10*3.14 = 31.4 cm is the approximate perimeter aka circumference of the smaller circle.

-------------

The larger circle is the same idea. The radius is r = 5+5 = 10 cm

C = 2pi*r

C = 2pi*10

C = 20pi .... exact circumference

C = 20*3.14

C = 62.8 ... approximate circumference

Use more decimal digits of pi to get a more accurate value.

===================================================

Problem 23

The smaller circle has a diameter of 9 ft, which means the radius is r = 9/2 = 4.5 ft

C = 2pi*r

C = 2pi*4.5

C = 9pi .... exact circumference

C = 9*3.14

C = 28.26 .... approximate circumference

The units of the circumference are in feet

-------------

The larger circle has radius r = 4.5+2.5 = 7 ft

C = 2pi*r

C = 2pi*7

C = 14pi .... exact circumference

C = 14*3.14

C = 43.96 .... approximate circumference

===================================================

Problem 24

The larger circle has radius 22. This radius is the diameter of the smaller circle.

So the smaller circle has radius 22/2 = 11

C = 2pi*r

C = 2pi*11

C = 11pi .... exact circumference

C = 11*3.14

C = 34.54 .... approximate circumference

The circumference units are "meters".

-------------

Now onto the larger circle

C = 2pi*r

C = 2pi*22

C = 44pi .... exact circumference

C = 44*3.14

C = 138.16 .... approximate circumference

The probability that a student rides a bike to school, given that the student's school has a crossing guard is given by 0.25.

For two events A and B, we have:

Probability that event A or B occurs = Probability that event A occurs + Probability that event B occurs - Probability that both the event A and B occur simultaneously.

We know that;

For two events A and B:

The chain rule states that the probability that A and B both occur is given by:

⇒ P (A∩B) = P (A) P (B|A) = P (B) P (A|B)

You can remember this fact by using a trick that when A is on left, it is behind B in next term P(A) P(B|A)

And when B is on left, then it is behind A in next term P(B)P(A|B)

P(A|B) = Probability that A will happen given B has already happened.

P(B|A) = Probability that B will happen given A has already happened.

Using those above stated rules, we have

Let the event A be that a student rides bike to school.

Let the event B be that the student's school has a crossing guard

Then we are given that:

P(A) = P{rides bike to school}) = 0.14

P(B) = P{has crossing guard}) = 0.48

P{rides bike and crossing guard}) = 0.12

We have to find P(a student rides a bike to school, given that the student's school has a crossing guard) = P(A | B)

From the chain rule of probability, we have;

⇒ P (A ∩ B) = P (B) P (A |B)

⇒ 0.12 = 0.48 × P (A|B)

⇒ P (A|B) = 0.12 / 0.48

⇒ P (A|B) = 0.25

Thus, The probability that a student rides a bike to school, given that the student's school has a crossing guard is given by 0.25.

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Answer:

Step-by-step Explaination:

Area of base section of prism = area of square

Area of square = a²

side = 14 unit

=> (14)²

=> 196 unit square

Answer: a) To calculate the total rate of return if Josh invests the same amount in each company, we need to add up the individual rates of return from each company and divide by the number of companies.

The total rate of return for the four companies is: (7.62% + -4.17% + -0.83% + 3.70%) / 4 = 2.52%

So the total rate of return if Josh invests the same amount in each company is 2.52%.

b) To calculate the total rate of return if Josh invests three times as much in Stiller Co. as in the other companies, we need to multiply the rate of return for Stiller Co. by 3 and add it to the rates of return for the other companies.

The total rate of return for the four companies is: (-4.17% x 3) + 7.62% + -0.83% + 3.70% = -7.32%

So the total rate of return if Josh invests three times as much in Stiller Co. as in the other companies is -7.32%.

It's important to note that the answer may change if the investment amount on each company is different.

Step-by-step explanation:

When a fifth degree polynomial with a root of multiplicity 3 at x = 2, and a root of multiplicity to at x = -3. The polynomial can be written in the form

Each zero's multiplicity is the quantity that indicates how frequently its corresponding factor appears. In other words, the powers are the multiplicities.

The polynomial is expressed as  y = (x - 2) ^a (x - b)^c

for x = 2, x - 2, and the multiplicity is 3 hence

(x - 2)³

for x = -3, x + 3 and the multiplicity is will be 2 hence

(x + 3)²

Because of this we can say that

a = 3, b = -3 and c = 2

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Answer: We can use the distributive property to write an expression that shows how many bracelets were in each box.

Let b be the total number of bracelets that Sidney made.

The number of bracelets in each box can be represented as:

b/4

This expression means that Sidney divided the total number of bracelets she made, represented by b, by 4, the number of gift boxes.

So, the total number of bracelets in each box is b/4 bracelets.

Step-by-step explanation:

We come to the conclusion that if the scale factor from S to M is 3/2, the scale factor from M to S must be 2/4.

Assume we have a figure S. If we apply a stretch of scale factor K to our figure S, we may say that all of figure S's dimensions have been multiplied by K.

Following the stretch, we will have a bar of length M, such that:

M = S*K

If the scale factor is 3/2, the following scenario arises:

M = (3/2)*S

In the relationship mentioned above, S can be separated out as follows:

(2/3)*M = S

We now have an equation (similar to the first one).

As of right now, the scaling factor from M to S is 2/3, according to an equation (like the first one).

After that, we draw the conclusion that if the scale factor from S to M is 3/2, the scale factor from M to S must be 2/4.

The complete question is,

Scale factor is 3/2 for the range of S to M. How many are there in the scale from M to S?

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The division of the value 8.8x10^9 and 2.2 x10^-3 in standard form is 4*10^12.

The concept that will be used here is division. One of the four fundamental arithmetic operations, or how numbers are combined to create new numbers, is division. The other operations are multiplication, addition, and subtraction.

Division in mathematics is the process of dividing an amount into equal parts. For instance, we may split a group of 20 people into four groups of 5, five groups of 4, and so on.

To simplify the values 8.8x10^9/2.2 x10^-3, the we can write as

8.8/2.2 *10^9*10^3

=4*10^12

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complete question:

simplify 8.8x109/2.2 x10-3