I need help with the answer please :)

Answer:

a)

[tex]\boxed{22}\\\\\boxed{19} - \boxed{7} = \boxed{12}[/tex]

b)

[tex]\boxed{ 243}\\\\\boxed{117} - \boxed{44} = \boxed{73}[/tex]

Step-by-step explanation:

The easiest way is to convert each base 5 number in each expression to base 10, perform the calculations and then convert from base 10  back to base 5.

a) 34₅ - 12₅

34₅ = (3 x 5¹ + 4 x 5⁰) = (3 x 5) + (4 x 1) = 15 + 4 = 19₁₀

12₅ = (1 x 5¹ + 2 x 5⁰) = (1 x 5) + (2 x 1) = 5 + 2 = 7₁₀

There are online calculators to do this job so no one really goes through this exercise by hand

Conversion from base 10 to base 5 is rather more complex process of repeatedly dividing by 5 noting the quotients and remainders of each division and working backward through the remainders

Again online calculators are available to ease your pain of doing this

Let's illustrate with a number like 123₁₀

123÷ 5 : Quotient: 24;    Remainder: 3
24 ÷ 5:   Quotient 4   ;    Remainder: 4

4 ÷ 5 :    Quotient 0   ;    Remainder: 4

Since quotient is 0, we stop

Going from bottom to top the remainders are 4, 4, 3 so 443 is the equivalent in base 5

We can check
443₅ = (4 x 5² + 4 x 5¹ + 3 x 5⁰) = 100 + 20 + 3 = 123₁₀

I am simply going to use a calculator to convert from base 10 to base 5

Final result

34₅ - 12₅ = 19₁₀ - 7₁₀ = 12₁₀

12₁₀ = 22₅

Answer

34₅ - 12₅ = 22₅
19₁₀ - 7₁₀ = 12₁₀

b)
432₅ - 134₅

432₅ = (4 x 5²) + (3 x 5¹) + (2 x 5⁰)

= 4 x 25 + 3 x 15 + 2 x 1

= 117₁₀

134₅ = (1 x 5²) + (3 x 5¹) + (4 x 5⁰)

= 25 + 15 + 4

= 44₁₀

So the equivalent computation in base 10 is
117₁₀ - 44₁₀ = 73₁₀

73₁₀ = 243₅

Answer:
432₅ - 134₅ = 243₅

117₁₀ - 44₁₀ = 73₁₀

Note I have been using 5 not five for the subscript. The final answer asks you only to enter the numbers in the boxes so it does not matter

The conversions of the number bases gives;

a)  12 ten

b)  73 ten

We have to note that the number base is the ground work upon which we can be able to perform mathematical operations. We know that in this case, we would have to change the numbers from base five to base 10.

For the first problem, we have;

34 five = 19 ten

12 five = 7 ten

We then have;

19 - 7 = 12 ten

For the second problem;

432 five = 117 ten

134 five = 44 ten

Then;

117 - 44 = 73 ten

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Answer:

D. x < 1

is correct answer

Answer:

100-170 bpm

Step-by-step explanation:

Answer:

40 dollars per hour

The composite function c(x) = 0.8x - 3, and the cost of a $30 item would be $21.

When the output of one function is given to the input of another function they are called composite functions.

In (fog)x which is [f{g(x)}] here the out of the function g(x) is the input of the function f(x).

Let, 'x' be the original cost of the item.

A store offers a 20% discount on all items,

So, f(x) = [(100 - 20)/100]×x.

f(x) = (80/100)×x.

f(x) = 0.8x.

Again, you also have a $3 coupon.

Let, g(x) = x - 3.

Now, The composition of the functions f(x) and g(x) is f(x) + g(x) = C(x).

C(x) = 0.8x - 3.

Now, The cost of an item is $30.

Therefore, C(30) = 0.8×30 - 3.

C(30) = 24 - 3.

C(30) = 21.

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The mean of the sampling distribution of sample means is (21.515, 23.485).

Normal distribution, also known as the Gaussian distribution, is a probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean.

Given that a study A study on the latest fad diet claimed that the amounts of weight lost by all people on this diet had a mean of 22.5 pounds and a standard deviation of 5.9 pounds

Sampling is done for 72 people

According to central limit theorem if random samples are taken for large sizes, the sample mean would follow a normal distribution with mean = population mean.

Hence expected mean value of the sampling distribution = 22.5 ±margin of error provided samples are drawn at random

Here, 1+72% =1.72

Margin of error = 1.72(5.9/√106) =0.985

Hence mean of sample would lie between

(22.5-0.985, 22.5+0.985)

= (21.515, 23.485)

Therefore, the mean of the sampling distribution of sample means is (21.515, 23.485).

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The value of angle ∠DEC  = 60 degree.

In the given the figure , m∠BAC = 64° and m∠CBA = 56°.

A triangle is a polygon with three sides and three vertices and three angles.

WE are given that AB || CD

Let BC be the transversal , then ∠CBA = ∠DCB (by alternate opposite angles)

∠DCB = 56 degree

As we know the sum of opposite interior angle sis equal to exterior angle therefore, ∠ ECB = 120 degree

∠DCE = 120-56 = 64 degree

BC || DE

∠EDC = ∠DCB = 56 degree (By alternate opposite angles)

The Sum of all the interior angles of a triangle is equal to 180 degree.

56 +64+∠DEC = 180

∠DEC  = 60 degree.

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Answer:

5 units^2

Step-by-step explanation:

Answer: 31

Step-by-step explanation:

You need to find the perimeter of something, you just add the numbers of the sides.

6 + 9 = 15

15 + 5 = 20

20 + 3 = 23

23 + 5 = 28

28 + 3 = 31

Perimeter = 31 in.

A perimeter of any shape is just the total length of all its sides. In other words, is the distance around the edge of the shape.

Perimeter = 5 in + 3 in + 5 in + 9 in + 6 in + 3 in = 31 in.

Perimeter = 31 in.

Answer:

10 4/6 = 10 2/3

Step-by-step explanation:

dude this is easy and not for college but thanks anyway

Answer:

Independent variable: The variable that is changed or manipulated in an experiment to observe its effect on the dependent variable. Example: The number of hours of studying (Independent variable) and the test score (Dependent variable)

Dependent variable: The variable that is being measured or observed in an experiment. Its value is dependent on the independent variable. Example: The temperature of water (Independent variable) and the volume of the water (Dependent variable)

Answer:

y=5x

Here y is dependent variable because it's depend on x but x is not depend on any other variable. So, it's independent variable.

The solutions for the equation |z+7|=|z-4| general is z = -7/2 and z = 11/2.

To solve the equation |z + 7| = |z - 4|, we consider two cases:

z + 7 = z - 4

z + 7 = -(z - 4)

In the first case, solving for z we get:

z + 7 = z - 4

11 = -4

z = -7/2

In the second case, solving for z we get:

z + 7 = -(z - 4)

z + 7 = -z + 4

2z = 11

z = 11/2

So, the solutions are z = -7/2 and z = 11/2.

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The fraction which is closest to 1/2 is, 3/8. So option B is correct

Fraction is a mathematical term, which represents the portion or sub-parts of the whole thing. Basically, It has two parts: numerator and denominator.

Numerator is a number which lies on the top side, it indicates the number of equal parts taken and denominator is on the bottom side, it indicates the equal parts of the whole number.

Given that,

A fraction number 1/2

In decimal form = 0.5

Closest fraction number = ?

Most closest number is that number from which we subtract the given number and the magnitude of result we get is very less,

Lets take, A fraction 1/6

In decimal form it can written as,  0.167

Difference 1 =  0.5 - 0.167

                  =   0.333

Similarly, For numbers 3/8, 3/4, -1/2

Difference 2 =  0.5 - 0.375  = 0.125

Difference 3 =  0.5 - 0.75  = -0.25

Difference 4 =  0.5 - (-0.5)  =  1.0

It can be seen that,

Magnitude of difference in case of 3/8 is very less

Hence, the closest number is 3/8

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A vehicle owner wants to calculate the total cost of his 2007 jeep compass with a MSRP of $18366. His monthly loan payment is $312.54 for 5 yrs after he puts down a $2000 payment.

a) T(m) = 312.54m + 2000

b) $20,752.4 is the total cost of the car.

c) he wound up shelling out almost $2,700 extra in interest.

The sum of money that has to be paid each week or month to fulfil the loan's requirements. This may be calculated using an amortisation table based on the principal, loan period, and interest rate.

Home purchase loans, vehicle loans, personal loans, and several student loans are typical examples. You may borrow and pay back money again using revolving loans. Secured loans, like house loans, are the least expensive loans in India. Although the utilisation is limited, they have low interest rates. For instance, you are only eligible for a house loan if you are purchasing a home.

Let,

m = number of months he has made payments on the car

T(m) = total amount paid after m months

a)

The states that he makes a loan payment of $312.54 every month.

It also states that he made a $2,000 down payment.

Thus, T(m) = 312.54m + 2000

This means that at m = 0 months, the total paid is just the down payment ($2,000), which makes sense.

After 1 month (m = 1), the total is the down payment plus 1 month's payment of $312.54.

b)

The loan amount is for 5 years.

Since there are 12 months in a year, that's a total of 12 × 5 = 60 payments he'll be making.

So, the total cost of the car will be figured out when m = 60.

T(60) = (312.54 × 60) + 2000 = $20,752.4

c)

The interest paid will be the total amount he's paid on the car minus the MSRP (i.e. how much it would have cost if he had just paid cash upfront).

Interest paid = Total Paid - MSRP = $20,752.4 - $18,366.00 = $2,386.4

For paying off the car in small increments over a long period of time,

he wound up shelling out almost $2,700 extra in interest.

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Answer:

Step-by-step explanation:

Slope intercept form is

[tex]y=mx+b[/tex]

Start with your equation and move y terms to one side and all other terms to the other side:

[tex]1-x-2y=-6[/tex]

[tex]1-x+6=2y[/tex]

Combine numbers:

[tex]7-x=2y[/tex]

Divide both sides by 2

[tex]\frac{7}{2} - \frac{x}{2} =y[/tex]

Write y on the left hand side and put the rest of the equation in standard slope intercept form:

[tex]y=-\frac{1}{2}x+\frac{7}{2}[/tex]

This is slope intercept form with m = -1/2 and b =7/2

Answer:

1/2

Step-by-step explanation:

On the clock from 3 to 9, the hour hand turns clockwise 1/2 of the revolution. On the clock from 4 to 7, the hour hand turns clockwise 1/4 of the revolution

Answer:

84

Step-by-step explanation:

Number of skiers = Number of athletes * Fraction of skiers
= 240 * 7/20
= 84 skiers

Answer:

84

Step-by-step explanation:

240/20=12

12*7=84

The panel of the window is 3.15 ft width.

A rectangle is a closed 2-D shape, having 4 sides, 4 corners, and 4 right angles (90°). The opposite sides of a rectangle are equal and parallel.

Given that, Rachel's bedroom window is rectangular with an area of 81.9 square feet, and the panel is 26 feet long

We need to find the width of the window,

Let the width be w

Area of a rectangle = width × length

81.9 = w × 26

w = 81.9 / 26

w = 3.15

Hence, the panel of the window is 3.15 ft width.

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The probability that a randomly selected password has no digits is 10.24%.

Probability can be defined as the ratio of the number of favourable outcomes to the total number of outcomes of an event.

Given that, a seven-character database password is formed from 10 digits and 26 upper-case letters.

Number of characters in passwords: 7

The possible number of ways to formed the first value of passwords is sum of 26 (upper letters) and 10 (0 to 9 numbers).

The required number of possible passwords is 36⁷

= 78364164096

Favorable out comes is 26⁷

= 8031810176

Now, probability of an event = 8031810176/78364164096

= 0.1024

= 10.24%

Therefore, the probability that a randomly selected password has no digits is 10.24%.

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Answer:

The ratio for 63 inches to 4 yards is 1:16. To calculate this, divide 63 inches by 4 yards, which is equal to 48 inches per yard. Therefore, the ratio for 63 inches to 4 yards is 1:16.

The domain of function U(x) = x √(1-x²/a²) is x = a or x = 0. The function of U(x) is an odd function. When a = 1, the plot function is as the attached graph below. The optimum point of the function is x = 1/2 a.

The domain of function U(x) can be find by making U(x) equals to 0:

U(x) = x √(1 - x²/a²) = 0

U(x) = √x² - x⁴/a² = 0

U(x) = x - x²/a = 0

x - x²/a = 0

ax - x² = 0

x² - ax = 0

x (x - a) = 0

x = 0 or x = a

The function of U(x) is an odd function because its biggest order is 2.

If a = 1, then the value of U(x) would be:

U(x) = x √(1 - x²/a²)

U(x) = x √(1 - x²/1)

U(x) = x - x²

x = a = 1

U(x) = 1 - 1

U(x) = 0

The graph is as attached below

The critical point of U(x) function can be determined by differentiate the function equals to 0.

U(x) = x - x²/a

U'(x) = 1 - [(2ax - 0)/a²] = 0

U'(x) = 1 - 2x/a = 0

2x/a = 1

x = 1/2 a --> optimum point

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The domain of the function is x < a

Given that

U(x) = x√(1 - x²/a²) where a > 0

Set the radicand greater than or equal to 0

1 - x²/a² > 0

So, we have

1 > x²/a²

Rewrite as

x²/a² < 1

This gives

x² < a²

Take the square roots

x < a

This represents the domain

We have

U(x) = x√(1 - x²/a²) where a > 0

For even function;

U(x) = U(-x)

For odd function

U(-x) = -U(x)

So, we have

U(-x) = -x√(1 - (-x)²/a²)

U(-x) = -x√(1 - x²/a²) ---- not an even function because U(x) ≠ -U(x)

U(x) = x√(1 - x²/a²) ---- an odd function because U(-x) = -U(x)

Hence, it is neither

See attachment

The critical points are points where the function is defined and its derivative is zero or undefined

We have

U(x) = x√(1 - x²/a²)

a = 1

U(x) = x√(1 - x²)

Using a graphing tool, we have the critical points to be

x = ±1 and x = ±1/√2

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Answer:

To find the total number of players participating in the event, we need to find the total number of players for each sport, then add those values together.

Step 1: Find the number of players for each sport based on the ratio:

Football players: 5 : 3 : 4 = 5 * 36 players / (5 + 3 + 4) = 60 players

Volleyball players: 36 players

Basketball players: 4 : 3 : 5 = 4 * 36 players / (5 + 3 + 4) = 48 players

Step 2: Find the total number of players:

60 players + 36 players + 48 players = 144 players

Answer:

144 players participated in the event.

Triangle congruence is proved by a sequence of reflections and translations.

A translation in math moves a shape left or right and/or up or down. The translated shapes look exactly the same size as the original shape, and hence the shapes are congruent to each other. They just have been shifted in one or more directions.

Given that, ∆ABC has vertices at A(11, 6), B(5, 6), and C(5, 17).

By using distance formula, distance =√(x₂-x₁)²+(y₂-y₁)²

AB = 6 units   BC = 11 units AC = 12.53 units

∆XYZ  X(-10, 5), Y(-12, -2), and Z(-4, 15)

XY = 7.14 units   YZ = 18.79 units XZ = 11.66 units

∆MNO  M(-9, -4), N(-3, -4), and O(-3, -15).

MN = 6 units   NO = 11 units MO = 12.53 units

∆JKL  J(17, -2), K(12, -2), and L(12, 7).

JK = 5 units   KL = 9 units JL = 10.30 units

∆PQR  P(12, 3), Q(12, -2), and R(3, -2)

PQ = 5 units   QR = 9 units PR = 10.30 units

So, we have the ∆ABC and the ∆MNO  

With all three sides equal are congruent  

We have the ∆JKL  and the ∆PQR

with all three sides equal are congruent  

Two plane figures are congruent if and only if one can be obtained from the other by a sequence of rigid motions (that is, by a sequence of reflections, translations, and/or rotations).

1) If ∆MNO by a sequence of reflections and translation, it can be obtained ∆ABC, then ∆MNO ≅ ∆ABC  

a) Reflection (On x-axis)

The coordinate notation for the Reflection is (x,y)→(x,-y)

∆MNO  M(-9, -4), N(-3, -4), and O(-3, -15).

M(-9, -4)→ M1(-9,4)

N(-3, -4)→ N1(-3,4)

O(-3,-15)→ O1(-3,15)

B) Reflection (y-axis)

The coordinate notation for the Reflection is (x,y)→(-x,y)

In ∆M'N'O', M'(-9, 4), N'(-3, 4), and O'(-3, 15).

M'(-9, -4)→M"(9,4)

N'(-3, -4)→N"(3,4)

O'(-3,-15)→O"(3,15)

C) Translation

The coordinate notation for the Translation is (x,y)→(x+2,y+2)

∆M"N"O", M"(9,4), N"(3,4), and O"(3, 15).

M"(9, 4) → A(11,6)

N"(3,4)→B(5,6)

O"(3,15)→C(5,17)

So, we have ∆ABC,  A(11, 6), B(5, 6) and C(5, 17)

From ∆MNO to ∆M'N'O' reflection, from ∆M'N'O' to ∆M"N"O" reflection, and from ∆M"N"O" to ∆ABC its translation.

2)If ∆JKL, by a sequence of rotation and translation

We obtained ∆PQR

So, ∆JKL ≅ ∆PQR  

D) Rotation 90 degree anticlockwise

The coordinate notation for the Rotation is (x,y)→(-y, x)

In ∆JKL, J(17, -2), K(12, -2), and L(12, 7).

J(17, -2)→J'(2,17)

K(12, -2)→K'(2,12)

L(12,7)→L'(-7,12)

E) Translation:

The coordinate notation for the translation is (x, y)→ (x+10, y-14)

Then, ∆J'K'L' has vertices J'(2, 17), K'(2, 12), and L'(-7, 12).

J'(2, 17)→P(12,3)

K'(2, 12)→Q(12,-2)

L'(-7, 12)→R(3,-2)

So, ∆PQR has P(12, 3), Q(12, -2) and R(3, -2)

From ∆JKL to ∆J'K'L' its rotation and from ∆J'K'L' to ∆PQR its translation.

Therefore, ∆JKL ≅ ∆PQR  

Hence, triangle congruence is proved by a sequence of reflections and translations.

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The surface area of the composite bin can be found using the expression  6·5 + 4·5 + 3·5 + 5·5 + 2·[3·4 + (1/2)·(3·4)]

Please find attached the drawing of the net of the composite bin, created with MS Word

The surface area of a composite figure can be found finding the sum of the individual exposed surface area of the composite figure.

Please find attached the possible drawing of the diagram in the question, created with MS Word

The possible complete expression in the question, obtained from a similar, online question, is presented as follows;

6·5 + 4·5 + 3·5 + 5·5 + 2·[3·4 + (1/2)·(3·4)]

The surface area of the figure consists as follows;

Two trapezoidal faces (in front and on the rear

Four rectangular faces, orthogonal to the trapezoidal faces

Please find attached the net of the composite bin created with MS Word

The area of the trapezoidal faces = (3 + 6)×4/2 = ((1/2)·(3·4) + ((1/2)·(6·4))

((1/2)·(3·4) + ((1/2)·(6·4)) = ((1/2)·(3·4) + (3·4)

((1/2)·(3·4) + ((3·4)) = 3·4 + (1/2)·(3·4)

Therefore, the area of the two trapezoidal faces = 2 × (3·4 + (1/2)·(3·4))

The area of the four rectangular faces are;

Face              [tex]{}[/tex]                  Area

Orthogonal rear face = 6 × 5

Orthogonal front face = 3 × 5

Face at the bottom of the figure = 4 × 5

The slant face at the top = 5 × 5

The area is therefore;

The surface area of the composite bin, A, is therefore;

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The value of x in the equation x^x = 4^(x + 16) is 16

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

x^x = 4^(x + 16)

Take the logarithm of both sides

So, we have

xlog(x) = (x + 16)log(4)

At this point, we make use of a graphing calculator

From the calculator, we have

x = 16

Hence, the solution is x = 16

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Answer:

A. -infinity < x < +infinity

Step-by-step explanation:

the domain is the interval or set of all valid x (function input) values.

The value of the angle ∠I = 13

An isosceles triangle in geometry is one with at least two sides that are of equal length. Both having exactly two sides of equal length and having at least two sides of equal length are acceptable specifications, with the latter version containing the equilateral triangle as an exception. The faces of bipyramids, the golden triangle, the isosceles right triangle, and some Catalan solids are all examples of isosceles triangles.

in this figure, it is an isosceles triangle as two sides of the triangle are equal.

given in the ΔGHI is an isosceles triangle.

So the other two angles will be 13

Hence The value of the angle ∠I =13°

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The given  expression √(a³-7)+ | b |, when a = 2 and b = -4, the value of the expression is, 5

An expression is a sentence with at least two numbers or variables having mathematical operation. Math operations can be addition, subtraction, multiplication, division.

For example, 2x+3

Given that,

The expression,

√(a³-7) + | b |

where, a = 2

b = -4

Now, by putting values of a and b in the given equation,

⇒ √(a³-7) + | b |

⇒ √(2³-7) + | -4 |

For whatever value of x, |x| will give always positive value

So, now it can be further written as,

⇒   1  + 4

⇒   5

Hence, the value is 5

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