what is the total amount that First Consumer Bank will receive after lending Jane $7,000 for three years at an interest rate of 5 percent, compounded annually

Answer:

5.2

Step-by-step explanation:

Construct an altitude. Using the Pythagorean theorem, the height is [tex]\sqrt{6^2-3^2} \approx 5.2[/tex]

Answer: 40%

Step-by-step explanation:

The best estimate of the average change in mood rating linked with an additional hour spent playing sports is 1.5 points, according to the presented linear function.

Modeling a linear function involves:

y = mx + b

The slope, or m, measures how quickly y changes when x changes by one.

The value of y at x = 0 is represented by the y-intercept, or b.

In the given problem

The amount of time they invested in sports is x.

Their mood score is y.

The required equation is ,

y =1.5 + 5

Given that the slope is m = 1.5, the best estimate of the average change in mood rating resulting from an extra hour spent playing sports is 1.5 points.

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Answer:

103.98cm

Step-by-step explanation:

14 + 14 = 28

20 + 20 = 40

(14(3.14)) / 2+ 14 = 35.98cm

40 + 28 + 35.98 = 103.98cm

The local maxima is(1,0) , local minima is indefinite and the saddle point is (1,0).

As per given in the question ,

f(x,y)=[x2+1 ]

          [-2y   ]

The critical points are therefore (1,0) and (1,0).

The Hessian is currently

∇²f(x,y)=[−2x     0

               0     −2]

2 and 2 are the eigenvalues of the function 2f(1,0).

As a result, (1,0) is a saddle point and 2f(1,0) is indefinite.

Two and two are the eigenvalues of 2f(1,0).

As a result, (1,0) is a maximum and 2f(1,0) is negative definite.

Critical point: If f (p) = 0, then a point p U is f's critical point.

In light of this, the tangent plane to z = f when f is differentiable (x) at (p, f (p)) is horizontal.

Theorem: Assume that f exists and possesses a local extremum at position p. Then, p is a f critical point, with the result that f (p) = 0.

Example: Take into account f (x, y) = x 2 y 2. Once again demonstrating that (0, 0) is the only crucial point of f, fx = 2x = 0 and fy = 2y = 0

However, (0, 0) is not a f local maxima.

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Answer: X = 5

Step-by-step explanation:

4x - 2 = 18

    +2    +2

4x = 20

/4     /4

x = 5

4(5) -2 =18

20 - 2 =18

18=18

1/34 is the probability of cards are not returned to the deck.

What does the math term "probability" mean?

Simply put, probability measures how probable something is to occur. We can discuss the probabilities of various outcomes, or how likely they are, whenever we are unsure of how an event will turn out.

                                   Statistics is the study of events subject to probability.

A = the first card of ace.

B = Drawing two ace from a standard deck

P(AB) = ²C₄ / ²C₃₂

P(A) = ¹C₄ ¹C₅₁ / ²C₃₂

P(B/A) =P(AB)/P(A)

           = ²C₄ /  ²C₃₂ *  ²C₃₂ /  ¹C₄ ¹C₅₁

            = ²C₄ /¹C₄ ¹C₅₁

             = 1/2 * 17

             = 1/34

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The answer for all 3 of the boxes is 3. The number of observations for each class interval of a variable is shown in group frequency distributions.

DISTRIBUTION OF GROUPED FREQUENCIES

The greatest score is H, while the lowest is L.

By dividing the range by a number of groupings or classes, you can estimate the class width w.

Establish the class intervals.

Add up the scores for each period in the appropriate number.

The shopping time (in minutes) of the nine shoppers are:

15, 16, 18, 20, 22, 25, 27, 28, 29 (just to make it easier to read, I rearranged  everything from least to greatest.)

We can see, that 3 shoppers shopped for 15-20 minutes.

And, 3 shoppers shopped for 21-26 minutes.

And finally, 3 shoppers shopped for 27-32 minutes.

So the answer for all 3 of the boxes is 3.

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The approximate percentage of women with platelet count between 3 and 4.1 is 350

We should know that platelet deals the cells that are found in our body which assemble together when they discover bad blood in the cells.

The range of women is given as 3-4.1

The average of the women is [tex]\frac{3+4.1}{2}=\frac{7.1}{2}[/tex]

Simplifying the expression we have

= 3.5

The appromimate percentage is 3.1*100=350 women

In conclusion the approximate percentage of women with blood platelet is 350 women

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1. Which equation represents a line that has a slope of 2 and passes through the origin?

A y=2x

B. y=x+2

C. y x

D. y=-x

2. A regular jeepney ride costs $12.00 for the first 4 km, and each additional km adds P1.50 to the fare. Which of the following can be used to compute a regular fare (F), in pesos, for a 6-km nde?

A. F = 12(7)

B. F=12(7)+1.50

C.=12(150)+7

D.=12+2(1.50)

3. A regular jeepney ride costs P12.00 for the first 4 km, and each additional km adds P1.50 to the fare. How much is the regular fare for a 6-km ride?

A. P15

B. P13.50

C. P14.50

D. P16

4.Which equation represents a vertical line?

A. y =2x

B. x = 2

C. y = 3

D. y = -x​

There are 15 two-point questions and 5 four-point questions.

What is an expression?

Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication and division.

Let x be two-point questions and y be four-point questions. We know that there are 20 questions so the number of two-point questions plus the number of four-point questions equals 20. So x + y = 20. We also know that the total number of points is 50, so 2x + 4y = 50.

Solving the system:

1) x + y = 20

2) 2x + 4y = 50

Isolate x in 1) to get x = 20-y, then plug into 2)

2(20-y) + 4y = 50

2y=10  

y = 5,

It means that there are 5 four-point questions. Plug y = 5 into either equation to get x = 15 so there are 15 two-point questions.

x + y = 20

x + 5 = 20

x = 15

Hence, there are 15 two-point questions and 5 four-point questions.

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Answer:

Step-by-step explanation:

the test ha 65 questions worth points and 5 questions worth 4 points

The 3 to the power of three halves equal to square root of 27 sqrt(27).

What is the square root?

A square root of a number x is a number y such that y² = x; in other words, a number y whose square is x. For example, 4 and −4 are square roots of 16, because 4² = ² = 16.

A square root is a number that can be multiplied by itself to give the original number.

3 to the power of 3/2 is equal to the square root of 3 to the power of 3, which is equal to the square root of 27. The square root of 27 is approximately 3.872983346207417.

To calculate this value, you can use a calculator or you can use the following formula:

3^(3/2) = sqrt(3^3) = sqrt(27) = 3.872983346207417

Hence, the 3 to the power of three halves equal to square root of 27 sqrt(27).

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12: This one if fairy simple: all you need is a line that is not parallel to the line provided, and combined with it, it will provide a solution that's on that line. For example:

y = 2x

x - y = 10

13: Just find two lines that cross (6, -4).

You can use point-slope form:

y - y1 = m(x-x1)

y + 4 = m(x - 6)

then choose two equations with different m's

y = 2(x-6) - 4

y = 3(x-6) - 4

14:

Line one has a slope of two and an intercept at y=0 so it is y = 2x

Line two has a slope of one and an intercept at y=-1 so it is y = x - 1

To find the solution of the system, substitute y:

2x = x - 1

x = -1

Then plug back in:

y = 2 * -1 = -2

So the solution is: (-1, -2)

Answer:24.90

Step-by-step explanation: My brain

Answer:

Step-by-step explanation:

The slope of a line is defined as the change in y-coordinate divided by the change in x-coordinate between two points on the line. In this case, the change in y-coordinate between the two points is -11 - (-1) = -10, and the change in x-coordinate is 0 since both points have the same x-coordinate. Therefore, the slope of the line that passes through the points (-8, -1) and (-8, -11) is -10/0, which is undefined.

The solution to the given inequality 2(2.1z + 4.5) < 21.6 to solve for the unknown value of z is z < 3

Inequality refers to a statement that is of two quantities in which one is specifically less than (or greater than) another.

The symbols of inequality includes;

2(2.1z + 4.5) < 21.6

open parenthesis

4.2z + 9 < 21.6

substract 9 from both sides

4.2z < 21.6 - 9

4.2z < 12.6

divide both sides by 4.2

z < 12.6 / 4.2

z < 3

Hence, z < 3 satisfies the value of z in the inequality 2(2.1z + 4.5) < 21.6

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Using the table we find the constant of proportionality  is 15/8

The ratio that establishes a proportionate link between any two given values is referred to as the constant of proportionality. There are also other names for the constant of proportionality, such as constant ratio, constant rate, unit rate, constant of variation, and even rate of change.

Here,

Since from the table we have to find the constant of proportionality

So, the values of ounces of milk(x) are

30,45

and the values of amount of truffle(y) are

16,24

So for finding the constant of proportionality We take 2 cases,

a)Taking first values of x & y

x/y=30/16

x/y=15/8

b)Taking secondary values of x & y

x/y=45/24

x/y=15/8

Therefore the constant of proportionality  is 15/8

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Answer:

Soft tacos are $1.25 each, while double deckers are $2.5 each.

(I didn't have time for a step by step explanation at the moment)

Sorry

Ummi's quotients in this situation represent the unit rates of the advertisement

You will not be able to draw a straight line through the points

From the question, we have the following quotients parameters that can be used in our computation:

2.90/10 = 0.29/1 3.48/12 = 0.29.1 4.48/16 = 0.28.1

These can be rewritten as

2.90/10 = 0.29/1

3.48/12 = 0.29/1

4.48/16 = 0.28/1

The quotients mean that

Unit rate = Total amount spent/Number of adverts

So, the quotient expressions represent the unit rate

Recall that

2.90/10 = 0.29/1

3.48/12 = 0.29/1

4.48/16 = 0.28/1

The values of the quotients are not equal

This means that it is not possible to draw a straight line through the points

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Answer:

93.2° (nearest tenth)

Step-by-step explanation:

[tex]\boxed{\begin{minipage}{7.6 cm}\underline{Sine Rule} \\\\\\$\dfrac{\sin A}{a}=\dfrac{\sin B}{b}=\dfrac{\sin C}{c} $\\\\\\where:\\ \phantom{ww}$\bullet$ $A, B$ and $C$ are the angles. \\ \phantom{ww}$\bullet$ $a, b$ and $c$ are the sides opposite the angles.\\\end{minipage}}[/tex]

From inspection of the given triangle:

Substitute the values into the sine rule to find the measure of angle C:

[tex]\implies \dfrac{\sin B}{b}=\dfrac{\sin C}{c}[/tex]

[tex]\implies \dfrac{\sin 38^{\circ}}{9}=\dfrac{\sin C}{11}[/tex]

[tex]\implies \sin C=\dfrac{11\sin 38^{\circ}}{9}[/tex]

[tex]\implies C=\sin ^{-1} \left(\dfrac{11\sin 38^{\circ}}{9}\right)[/tex]

[tex]\implies C=48.80523914...^{\circ}[/tex]

Interior angles of a triangle sum to 180°.

[tex]\implies A+B+C=180^{\circ}[/tex]

[tex]\implies A+38^{\circ}+48.80523914...^{\circ}=180^{\circ}[/tex]

[tex]\implies A=93.19476086...^{\circ}[/tex]

Therefore, the size of angle A is 93.2° (nearest tenth).

Answer:

  19 units

Step-by-step explanation:

You have midline LM marked as 6x+1 and parallel baseline IJ marked as -6x+56 in triangle IJK. You want to know the length of LM.

The midline of a triangle is half the length of the parallel base:

  LM = 1/2(IJ)

  6x +1 = 1/2(-6x +56) . . . . . substitute expressions

  6x +1 = -3x +28 . . . . . . . simplify

  9x = 27 . . . . . . . . . . . . sdd 3x-1

  x = 3

Now, we can find LM:

  6x +1 = 6(3) +1 = 19

The measure of LM is 19 units.

Answer:

  ±{1, 2, 3, 6, 9, 18}

Step-by-step explanation:

You want the possible rational zeros of f(x)= x^3-6x^2+6x-18.

The rational root theorem tells you the possible rational zeros are of the form ...

  ±{divisors of the constant term} / {divisors of the leading coefficient}

Here, the leading coefficient is 1, so its only divisor is 1.

The constant term is 18, and its divisors are 1, 2, 3, 6, 9, 18.

The possible rational roots are ±{1, 2, 3, 6, 9, 18}.

__

Additional comment

A graph shows the only real root is between 5 and 6, so none of the roots are rational.

Answer:

$84.50

Step-by-step explanation:

Add the amounts:

$63.48 + $52.02 = $115.50

Two $100 bills add to $200.

To find the change, subtract the total cost from the amount of money handed over.

$200 - $115.50 = $84.50

Molly should give him $84.50. Thus option B is the correct answer.

The change given must be equal to the balance left after deducting the price of the goods from the total money received.

In this case,  

Price of goods = Price of DVD player + Price of five DVDs

                         = $63.48 + $52.02

                         =$115.50

Total Money Received = 2 x $100 = $200

Therefore, Change = Total Money Received - Price of goods

                                = $200 - $115.50

                                = $84.50

Answer:

a. 240pieces

b. 4800+ 10x

Step-by-step explanation:

a. 40÷4=10, 120÷5=24, 10×24=240

b. (240×20)+ (x×10)= 4800+ 10x ===> x is the number of cars

Answer:

[tex]\begin{gathered} \sf - 21 \div (2 - 5) + ( - 14) + 6 \times (8 - 4 \times 3) = \\\sf- 21 \div (2 - 5) + ( - 14) + 6 \times (8 - 12) = \\ \sf- 21 \div( - 3) + ( - 14) + 6 \times ( - 4) = \\ 7 + ( - 14) +( - 24) = \\ \sf 7 - 14 - 24 = \\ \sf - 7 - 24 = \\ \sf \green{ - 31}\end{gathered}[/tex]

When we solve combined calculations, we must first separate into terms when there is an addition or a subtraction.

Then, we solve the operations respecting the hierarchical order of the operations:

If the calculation has grouping signs, they must be solved in the following order:

Merry Christmas and Happy New Year

Answer:

negative 36

Step-by-step explanation:

You will useva method known as BODMAS its a principle of combined operations like the one above in mathematics.

B-brackets

O-Of (multipliction) ;commonly used when fractions are involved

D- division

M- multiplication

A- addition

S- subtraction

Working out:

first we will solve the brackets then rewrite the question with the answer obtained

-2-5=-7

8-4×3= minus 4

new question :

-21÷-7+-14+6×minus 4

Next is division since there is no of

-21÷-7=3

Negative divided by negative equals positive

3+minus 14 +6×minus 4

Now do multiplication 6×minus 4= minus24

3+ minus 14+minus 24=minus 36

255 biology and 192 sociology textbooks were sold in a week.

Each term in a linear equation has an exponent of 1, and when this algebraic equation is graphed, it always produces a straight line. It is called a "linear equation" for this reason.

While the graph of a linear equation with two variables, x and y, creates a straight line, the graph of a linear equation with just one variable, x, forms a vertical line that is parallel to the y-axis.

Step 1:

Let x be the number of biology textbooks and y be number of sociology textbooks.

x + y = 447 ------(1)

x - y = 63 ------(2)

Step 2:

Adding (1) and (2), we get

2x = 510

x = 255

Step 3:

Subtracting (1) from (2), we get

2y = 384

y = 192

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The solution to the expression 2 1/2 + 3 1/5 x 5 5/8 is 223/2

fractions are represented as a numerical value, which defines a part of a whole. A fraction can be a portion or section of any quantity out of a whole, where the whole can be any number, a specific value, or a thing.

2 1/2 + 3 1/5 x 5 5/8 can be solved by converting all the mixed fraction to improper fraction

2 1/2 = 5/2

3 1/5 = 16/5

5 5/8 = 45/8

which reduces it to

5/2 + 45/8 x 16/5

using BODMAS we taking care of the multiplication section first

45/8 x 16/5 = 18

5/2 + 18

18 can be writen as a fraction which is 36/2

5/2 + 36/2 = 41/2

in conclusion the simplified form of the expression is 41/2

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The values of x and y for fig. 1) is 5/4 and 4/7, for fig. 2) x = 15, y = 4 and for fig. 3) x = 3 and y = 2

Thales's Theorem or Basic Proportionality Theorem states that if a line is drawn parallel to one side of a triangle intersecting the other two sides in distinct points, then the other two sides are divided in the same ratio.

Given are three figures of triangles,

Figure 1)

5/x+5 = 8/10

50 = 40+8x

x = 5/4

y = 7/7+y = 8/10

70 = 56 +8y

y = 4/7

Figure 2)

12/12+y = 18/18+6

12/12+y = 18/24

48 = 36 +3y

y = 4

12/4 = x/5

x = 15

Figure 3)

y/4 = 1.5/3

y = 2

x/6 = 1.5/3

x = 3

Hence, the values of x and y for fig. 1) is 5/4 and 4/7, for fig. 2) x = 15, y = 4 and for fig. 3) x = 3 and y = 2

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Answer: To find the value of f(5), we need to substitute 5 for x in the expression f(x) = 8x+5. This gives us:

f(5) = 8*5+5 = 45

So, the value of f(5) is 45.