Shirley assumes that none of the marks had rubbed off between Monday and Tuesday.
(b) If Shirley's assumption is wrong, explain what effect this would have on your answer
to part (a).

The solution to the system of equation {x + y = 1, 3x - y = 7 } using augmented matrices is ( 2,-1 ).

Given the system of equation in the question;

x + y = 1

3x - y = 7

First, we write the system of equation in matrix form.

[tex]\left[\begin{array}{ccc}1&1&1\\3&-1&7\\\end{array}\right][/tex]

Next, we find the reduced row echelon form

Row operation R₂ = R₂ - 3R₁ to make the entry at 2, 1 a 0.

[tex]\left[\begin{array}{ccc}1&1&1\\3-3*1&-1-3*1&7-3*1\\\end{array}\right] \\\\\left[\begin{array}{ccc}1&1&1\\0&-1\4&4\\\end{array}\right][/tex]

Next, multiply each element of R₂ by -1/4 to make the entry at 2, 2 a 1.

[tex]\left[\begin{array}{ccc}1&1&1\\-\frac{1}{4}*0 &-\frac{1}{4}*-4 &-\frac{1}{4}*4 \\\end{array}\right] \\\\\left[\begin{array}{ccc}1&1&1\\0&1&-1\\\end{array}\right][/tex]

Now, perform the operation, R₁ = R₁ - R₂, to make the entry at 1,2 a 0.

[tex]\left[\begin{array}{ccc}1-0&1-1&1+1\\0&1&-1\\\end{array}\right] \\\\\left[\begin{array}{ccc}1&0&2\\0&1&-1\\\end{array}\right][/tex]

Using the result from the matrix, x = 2 and y = -1.

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The volume of the cylinder is 502.4m³

Volume of the cylinder:

Volume of the cylinder can be calculated by the product of the area of base and height.

For any cylinder with base radius ‘r’, and height ‘h’, the volume will be base times the height.

V = πr²h cubic units.

Given,

A cylinder with radius r and height h is inscribed in a cone with radius of 4m and height of 10m.

Here we need to find the volume of the cylinder,

We know that the values of,

Radius = 4m

height = 10m.

Now we have to apply the value on the formula, then we get,

V = π x (4)² x 10

Apply the value of π as 3.14 then we get,

V = 3.14 x 16 x 10

V = 502.4

Therefore, the volume of the cylinder is 502.4 m³.

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Answer:

18 pi

Step-by-step explanation:

2xpixr d divided by 2 equals 9 pi x 2 x 9 =18

The population of the city in 5 years is 3430386 as the population is increasing 10% per year

What is percentage and how to calculate?

Percentage is the ratio which can be expressed as fraction of 100. And to calculate percentage we multiply by 100.

We are given that population of a city is 2130000

And the population is increasing at a rate of 10%

We are asked to find the population after 5 years

The equation can be given as (1.1)^x*2130000

We put x =5

We get

[tex](1.1)^5*2130000\\1.61051*2130000\\=3430386[/tex]

Hence the population will be 3430386 after 5 years at a rate of 10% increase per year

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By using the graph we can see:

First, we want to find the value of x such that the graph touches (intercepts) the x-axis.

On the graph, we can see that it intercepts the x-axis at x = 0, so that is the x-intercept.

Now we want to find f(-2), this is the value of the function when x = -2, to find that we first need to find x = -2 in the horizontal axis.

f(-2) = 4

Now we want to find the value of x such that:

f(x) = 2

so now we need to find 2 in the vertical axis. we can see that the function is equal to 2 for x = -1.3 (approximation).

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Answer:The total cost is $41.04

Step-by-step explanation:

No, there is nothing wrong in the research that is done by the head of the institution. He said correct that the mean age of the full time students has declined.

Given above that a university's director of institutional research thought that the average age of full-time students was lowering. The average age of a full-time student in 1995 was 27.4 years old.

He registered all 4934 pupils for this and the average age was 27.1 years.

The fact that the inquiry concerns the average age of a full-time student makes this situation ideal. This is a trustworthy approach when the mean is calculated after accounting for all full-time students at the university.

Given that this is a left-tailed test, the hypothesis is also correct.

He rejected the null hypothesis because p = 0.0020.05.

The average age did decrease, in conclusion. The situation is ideal.

Therefore his hypothesis is absolutely correct. There is nothing wrong with it.

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Answer:

(xy-6)(y-3)

Step-by-step explanation:

i don't know if you needed this, but if you need this i can explain step by step

xy(y-3)-6(y-3). we take the common ones out and than simplify as:. (xy-6)(y-3)

The value of x is 6 degrees.

It is given in the question that:-

HI is parallel to JK and FG is the transversal intersecting HI at L and JK at M.

∠LMK = 115 degrees

∠MLI = (8x + 17) degrees

We have to find the value of x.

We know that,

Angles on the same side of the transversal sum up to 180 degrees.

Hence, we can write,

∠LMK + ∠MLI = 180 degrees.

115 + (8x + 17) = 180 degrees

8x + 132 = 180 degrees

8x = 180 - 132

8x = 48 degrees

x = 48/8 degrees

x = 6 degrees

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Answer:

[tex]P'(-6,4)[/tex]

Step-by-step explanation:

P(x,y) -> rotate 90 degrees -> P'(-y,x)

P'(-6,4)

:]

(Brainliest would be greatly appreciated :] )

If the equation be [tex]$300000=\frac{300\left(1+\frac{0.0375}{12}\right)^{(12 t)}}{\left(\frac{0.0375}{12}\right)}$$[/tex]then the value of t = 30.43236.

Let the equation be

[tex]$300000=\frac{300\left(1+\frac{0.0375}{12}\right)^{(12 t)}}{\left(\frac{0.0375}{12}\right)}$$[/tex]

Multiply both sides by 0.0375 / 12, and we get

[tex]$300000 \cdot \frac{0.0375}{12}=\frac{300\left(1+\frac{0.0375}{12}\right)^{12 t}}{\frac{0.0375}{12}} \cdot \frac{0.0375}{12}$$[/tex]

Simplifying the above equation, we get

[tex]$\frac{1875}{2}=300\left(1+\frac{0.0375}{12}\right)^{12 t}$$[/tex]

Switch sides of the equation,

[tex]$300\left(1+\frac{0.0375}{12}\right)^{12 t}=\frac{1875}{2}$$[/tex]

Divide both sides by 300, and we get

[tex]$\frac{300\left(1+\frac{0.0375}{12}\right)^{12 t}}{300}=\frac{\frac{1875}{2}}{300}$$[/tex]

Simplifying the above equation, we get

[tex]$\left(1+\frac{0.0375}{12}\right)^{12 t}=\frac{25}{8}$$[/tex]

Apply exponent rules, then

[tex]$12 t \ln \left(1+\frac{0.0375}{12}\right)=\ln \left(\frac{25}{8}\right)$$[/tex]

Solving the above equation, then

[tex]$12 t \ln \left(1+\frac{0.0375}{12}\right)=\ln \left(\frac{25}{8}\right): \quad t=\frac{\ln \left(\frac{25}{8}\right)}{12 \ln \left(\frac{12.0375}{12}\right)}$[/tex]

[tex]$t=\frac{\ln \left(\frac{25}{8}\right)}{12 \ln \left(\frac{12.0375}{12}\right)}$$[/tex]

simplifying the above value of t, we get

t = 30.43236.

If the equation be [tex]$300000=\frac{300\left(1+\frac{0.0375}{12}\right)^{(12 t)}}{\left(\frac{0.0375}{12}\right)}$$[/tex]then the value of t = 30.43236.

Therefore, the value of t = 30.43236.

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We want to find where to put the parentheses on each expression to make the expression true.

First, we identify the symbols +, x, / and - to identify the pairs of numbers. For example, in the expression

we have two symbols (+, *).

Now, this would give us two pairs of expression where we can put the parentheses. That is, one possibility per symbol. So we have

and

Now, let us try the first choice. Remember that first we have to evaluate what is inside the parentheses. This would give us

which coincides to the value we wanted.

In the second case, we have the following symbols / and -

This would give us two pairs for grouping, namely

and

as before, we will first evaluet the first option

If we try the second option, we woud get

which would give us the correct value.

As per the Simple interest concept, at 7% of rate the remainder of the money need to be invested so that the two investments together yield at least $1620 in yearly​ interest.

Simple interest.

Simple interest is calculated by multiplying the daily interest rate by the principal by the number of days that elapse between payments.

Given,

A financial planner has a client with 16000​$ to invest.

Here we need to calculate the rate does the remainder of the money need to be invested so that the two investments together yield at least $1620 in yearly​ interest when he invests $10,000 with the annual simple interest 12%.

Let us consider R represents the rate that remainder of money needs to be invested

Here we know that, $10,000 is invested at 12%

So, according to the formula the interest at 12% is evaluated as,

=> $10,000 * 0.12 * 1 = $1200

And the remaining $6000 is invested at R%

Then the interest at R%=$6000 * R * 1 = $6000R

Now we need to find that the two investments together need to yield at least $1620, so our equation to solve is:

$1620 = $1200 + $6000R

Now, we have to subtract $1200 from both sides, then we get,

$1620 - $1200=$6000R

Then collect similar terms

$420=$6000R

Now, divide both sides by $6000

R=0.07 or 7%

Therefore, the answer is 7%.

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Answer:

Step-by-step explanation:

Givens

OF =     RF

OU = UR

Draw a line from U to F

UF = UF                              Reflexive property.

Solution

ΔOUF = ΔRUF                    SSS

<O = < R                              Congruent parts are congruent when the triangles are congruent.

pls tell me u understand the drawing

Answer: Carlos started with 38 comic books.

Step-by-step explanation:

33 - 14 = 19

19 x 2 = 38

SOLUTION

Solve the inequality.

divide both sides by -4

then the  generator is the element which can generate whole set

therefore U(49) has 12 generator

What is meant by cyclic group?

A cyclic group is a group that can be generated by a single element. (the group generator). Cyclic groups are Abelian.

the group u(49) is cyclic. using only the sage commands described previously, use sage to find a generator for this group.

elements of U(49) are {1,2,3,5,,7,11,,13,17,19,23,29,31,37,39,,41,47}

then the  generator is the element which can generate whole set

therefore U(49) has 12 generator

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Answer: It is impossible for two obtuse angles to be a straight angle

Step-by-step explanation:

Definition of a straight angle: An angle that is exactly 180 degrees

Definition of obtuse angle: An angle that is more than 90 degrees

1)  X = obtuse angle

x > 90

Set minimum to test:

x = 91

2) Set up the question

(<= less than or equal to)

2x <= 180

3) Sub the first equation

2(91) <= 180

182 <= 180

4) Answer the question

It is impossible for two obtuse angles to be a straight angle

The sequence of numbers, 7, 10, 17, 27, 44, 71, 115... in which each new term is given by the sum of the previous two terms, gives the sum of the first 10 terms as 1,265

A number sequence consists of a listing of numbers that are connected to each other by a rule.

The given sequence is presented as follows;

7, 10, 17, 27, 44, 71, 115..., [tex] a_{10}[/tex]

From the given sequence, we have;

a_n = a_{(n-1)} + a_{(n-2)}

The first 10 terms of the sequence is therefore;

7, 10, 17, 27, 44, 71, 115, (71+115), (115+(71+115)), ((71+115)+(115+(71+115)))

Which gives;

7, 10, 17, 27, 44, 71, 115, 186, 301, 487

The sum of the first 10 terms of the sequence is therefore;

7 + 10 + 17 + 27 + 44 + 71 + 115 + 186 + 301 + 487 = 1265

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The rational number of 7¹/₃  as; a/b where a and b are integers.

A rational number is defined as any number that can be written as a fraction, where both the numerator (the top number) and the denominator (the bottom number) are integers, and the denominator is not equal to zero

Now, we are given the fraction as; 7¹/₃

This given number is expressed as a mixed fraction and so we convert it to improper fraction to get; 22/7

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Answer:

David's orchid: 20 +x

Pam's orchid: 25 + 0.75x

Step-by-step explanation:

Framing linear equations:

Cost of first 10 pounds = 10 * 2 = $ 20

Let the weight of additional apples picked = x pounds

Cost of 'x' pounds = 1 * x = $ x

Total cost = cost of first 10 pounds + cost of additional 'x' pounds

                = 20 + x

                     Entry fee = $ 10

Cost of first 10 pounds = 10 * 1.50 = $ 15

      Cost of 'x' pounds = 0.75*x = 0.75x

Total cost = Entry fee + cost of first 10 pounds + cost of additional 'x' pounds

                = 10 + 15 + 0.75x

                = 25 + 0.75x

Answer:

w - 20

Step-by-step explanation:

Remove the parenthesis by multiplying each term of (w + 5) by (-4)

-4(w + 5) + 5w = -4*w + 5*(-4) + 5w

                       = -4w - 20 + 5w

                       = -4w + 5w - 20

        Combine like terms. Like terms have same variable with same power.

                       = w - 20

The number of millionaires Los Angeles should have will be equal to 5,065 millionaires.

Proportion may be defined as part or share of a complete unit compared with respect to the whole unit. A proportion is basically the equality of ratios. Two different ratios can be treated as equals if they are in proportion to each other. Now, the number of millionaires in Los Angeles will be equal to the Proportion of Millionaires in Dubai multiplied by the Population of Los Angeles that is

= 0.00124 × 4,085,014

= 5,065 millionaires

The Data and Calculations will be given as:

City                Millionaires     Population      Proportion

Los Angeles    11,560              4,085,014        0.00283 (11,560/4,085,014)

Casablanca     6,900              3,752,357        0.00184 (6,900/3,752,357)

Berlin               6,750              3,562,038         0.00189 (6,750/3,52,038)

Dubai               3,570              2,878,344         0.00124 (3,570/2,878,344)

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Complete Question:

City Millionaires Population

Los Angeles 11,560 4,085,014

Casablanca 6,900 3,752,357

Berlin

6,750

3,562,038

Dubai

3,570

2,878,344

Consider the chart of Millionaires and Population. If Los Angeles were

proportional to Dubai with respect to population, how many millionaires

should we expect Los Angeles to have? Round your answer to a whole number.

The probability of a simple event to occur is this:

In the question given, the favorable outcomes are either 8 or diamond.

In a deck of cards, there are 13 diamond cards and 4 eights however one of the diamond cards is also 8. Therefore, total favorable outcome is 13 + 4 - 1 = 16.

Of course, the total number of possible outcomes is 52. So, the probability of getting an eight or a diamond is:

The probability, in fraction, is 4/13.

In decimal form, it is 0.3077.

In percentage form, it is 30.77%

Answer:

2 points

Step-by-step explanation:

According to the graph, the parabola has two x-intercept, where is (0,-2) and (0,-8).

The minimum sample size of the given condition is 89.

In given condition,

For 95% confidence level, critical value of z is z* = 1.96

The margin of error given is E = 1

Standard deviation ( α ) = 4.8

Final required sample size is;

n = [tex](\frac{z*\alpha }{E} )^{2}[/tex]

  = [tex](\frac{1.96 * 4.8}{1} )^2[/tex]

  = 88.51

n  ≅ 89

The minimum sample size of the given condition is 89.

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Step-by-step explanation:

Since right angles are 90°

11 = 90°

12 = 90°

13 = 90°