Harry needs wood pieces to complete a project in woodshop class. He needs six pieces of wood that have a length of two and five eighths feet and three pieces of wood that are one and one fifth feet. What is the total amount of wood that Harry will need for the project?

nineteen and seven twentieths feet
three and 5 over 6 feet
three and 1 over 7 feet
two and one fifth feet

Answer: $8.70

Step-by-step explanation: $3.48 x 2 for the 2 pounds. You divide 3.48/2 to get the half pound. 3.48 x 2 = 6.96. 3.48/2=1.74.  1.74 + 6.96 = $8.70

Answer:

Step-by-step explanation:

$3.48 x 2 for the 2 pounds. You divide 3.48/2 to get the half pound. 3.48 x 2 = 6.96. 3.48/2=1.74.  1.74 + 6.96 = $8.70

The amount of money accumulated after 18 years at compound interest is  $192429.71 . At 65 there will be $1412484.01 in the account.

Compound interest, also known as interest on principal and interest, is the practice of adding interest to the principal amount of a loan or deposit.

The compounding interest formula when there are annual contributions is:

[tex]A=P(1 + r)^Y + c[ ((1 + r)^Y - 1) / r ][/tex]

Where P is the principal amount which is 4500,

r is 8.3% = 0.083

Y is the number of years which is 18 .

and C is the annual contributions which is equal to P

Therefore:

[tex]A=4500(1 + 0.083)^{18} + 4500[ ((1 + 0.083)^{18} - 1) / 0.083 ]\\\\A=192429.71[/tex]

Hence the amount of money in the account is $192429.71

Now the principal is  $192429.71 and the rate is 0.083 , now it is a  compound interest and time is 65 - 40 = 25 years.

[tex]A = P(1+0.083)^{25}[/tex]

[tex]A = 192429.71(1+0.083)^{25}\\\\A= 1412484.01[/tex]

Hence the total money accumulated is $1412484.01

c) Total money put in the account = 3000 × 18 = 54000

Difference =  $1412484.01 - $ 54000 = $ 1358484.01

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(a) the domain of f would be an interval (−3,6]

(b) the range of f would be an interval (−6,3]

(c) the zero(s) of f are x = −0.5 and x=6.

(d) the value of f(-3.5) would be 2

(e) the intervals at (−3,3) which f is increasing

(f) the intervals at (3,6] which f is decreasing

(g) the values are (−3,−0.5] for which f(x) ≤0

(h) x = 3 which is a relative maximum point

(i) the value of x is 3 for which f(x) = 3

(j) the function would be positive if f(0)

The domain of the function includes all possible x values of a function, and the range includes all possible y values of the function.

The domain of the function shown in the graph is given by the set of values x that has a point on the graph.

In other words, by launching the graph onto the x-axis we will cover the interval (−3,6]

The range of the function shown in the picture is given by the set of values y that has a point on the graph.

In other words, by launching the graph onto the y-axis we will cover the interval (−6,3]

The zeros of the function are the x-intercepts of the function, so the zeros are x = −0.5 and x=6.

The value of f(-3.5) is given by the y- coordinate of the point of intersection of the graph with the vertical line x=-3.5 So, f(-3.5)≈2.

The function is increasing whenever the y- coordinate increases if we trace the graph in the direction of positive x values.

So, the graph is increasing on (−3,3), where x=3 corresponds to the x- coordinate of the turning point on the graph.

The function is decreasing whenever the y- coordinate decreases if we trace the graph in the direction of positive x values.

So, the graph is decreasing on (3,6].

The values of x where f(x) ≤0, correspond to the points where the graph is below the x-axis, so the values of x for which f(x) ≤0 are (−3,−0.5].

The relative maxima or minima are the x-coordinate points where the continuous function has a turning point, like x=3 which is a relative maximum point

.

There are no relative minimum points for the given function.

The value of x for f(x)=3 is the x- coordinate of the point of intersection of the graph with the horizontal line y=3

So, x≈3.

we will determine the  y = coordinate of the point of intersection of the graph with the vertical line

x=0, which is above 2, so f(0) is positive.

Therefore, the domain of the function is interval (−3,6], and the range of the function is interval (−6,3].

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4) m∠BAD=30° (angle subtraction postulate)

5) m∠B=45° (sum of angles in a triangle)

Answer:

Step-by-step explanation:

You want to know which trig functions on the given list have a value of zero.

Sine

The sine function is zero at x=0 and multiples of π.

Cosine

The cosine function is zero at x = π/2 and for odd multiples of π.

Tangent

The tangent function is zero at x=0 and multiples of π. It is zero in the same places the sine function is zero.

These values are zero:

These function values are something different:

Answer:

40

Step-by-step explanation:

For this equation, all we do is simply plug in the values.

-4 (c) (a)

-4 (-5) (2)

-4*-5*2

Now, multiply, and you get your answer.

-4 * -5 = 20

20 * 2 = 40

40 is your answer

Answer:

242

Step-by-step explanation:

Based on the calculation below, the net income would have been 13,475 if income tax expense had been 23%.

The net income when the tax rate is 23% can be calculated as follows:

Income before tax = Income tax expenses at 25% tax rate / Tax tax rate = 4,375 / 25% = 17,500

Net income at 23% tax rate = Income before tax * (100% - Tax rate of 23%)

Net income at 23% tax rate = 17,500 * (100% - 23%)

Net income at 23% tax rate = 17,500 * 77%

Net income at 23% tax rate = 13,475

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Answer:

d = -12

Step-by-step explanation:

[tex]3i-4-di = -4-11i+2i\\3i-4-di = -4-9i\\3i-\left(4-di\right)-3i = -4-9i-3i\\-\left(4-di\right)=-4-12i\\\frac{- 4 - di}{-1} = -\frac{4}{-1}-\frac{12i}{-1}\\\frac{-\left(4-di\right)}{-1}\\= \frac{\left(4-di\right)}{1}\\=4-id\\=\frac{- 4 - 12i}{-1}\\=-\frac{- 4-12i}{1}\\=-( - 4)-( - 12i)\\=-\left(-4\right)-\left(-12i\right)\\= 4 + 12i\\4-(id) = 4 + 12i\\4 - id - 4 = 4 + 12i - 4\\- id=12i\\\frac{-id}{-i} = \frac{12i}{-i}\\\frac{id}{i}\\= d\\- \frac{12i}{i}\\= - 12[/tex]

6x³ + 2x² + 3x - 4 is not exactly divisible by x² + 3x - 4.

Given,

The expression : 6x³ + 2x² + 3x - 4

We have to divide the given expression by x² + 3x - 4.

Let's take 6x³ + 2x² + 3x - 4 as p(x) and x² + 3x - 4 as g(x).

If p(x) is divisible by the factors of g(x), then p(x) is divisible by g(x).

So, let's factorize  x² + 3x - 4

x² + 3x - 4 = (x - 1) (x + 4)

Now,

p(x) = 6x³ + 2x² + 3x - 4

By using remainder theorem,

If p(1) = 0 and p(4) = 0, then p(x) is divisible by g(x).

So,

p(1) = 6 × 1³ + 2 x 1² + 3 x 1 -4

p(1) = 6 + 2 + 3 - 4

p(1) = 11 - 4

p(1) = 7

Next,

p(4) = 6 x 4³ + 2 x 4² + 3 x 4 - 4

p(4) = 6 x 64 + 2 x 16 + 12 - 4

p(4) = 384 + 32 + 12 - 4

p(4) = 424

Here, p(1) and p(4) is not 0.

So, p(x) is not divisible by g(x).

That is, 6x³ + 2x² + 3x - 4 is not exactly divisible by x² + 3x - 4.

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The z-score of the value is -0.79

The given parameters are

Value = 86

Mean = 101

Standard deviation = 19

The z-score of the value is calculated using

z= (Value - Mean)/Standard deviation

This gives

z = (86 - 101)/19

Evaluate

z = -0.79

Hence, the z-score of the value is -0.79

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Answer:

Step-by-step explanation:

Using scientific notation, The value of  8x10⁹ is 8000000000

In scientific notation, the correct format is an x 10 b, where an is an integer or decimal number whose absolute value is more than or equal to one and less than ten, or 1 |a| 10. In order for the scientific notation to be mathematically identical to the original number, b must be a power of 10.

The given problem is written in scientific notation,

The multiplication of the given number will be-

8x10⁹ = 8000000000

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Answer:

The mapping diagram above represents a function since there is one number in Set A (the input) where there is only one mapping to Set B (the output).

Step-by-step explanation:

For each number in set A, there is one mapping from set A (input) to set B (output), so the mapping represents a function.

NB. The relation is a function IF AND ONLY IF each input value has only 1 output value.

Using proportions, it is found that the total amount of cement, sand, and gavel required is of 55.2 cubic yards.

A proportion is a fraction of a total amount, and the measures are related using a rule of three. Due to this, relations between variables, either direct(when both increase or both decrease) or inverse proportional(when one increases and the other decreases, or vice versa), can be built to find the desired measures in the problem, or equations to find these measures.

The decimal equivalent to the mixed number 1 1/2 is given by:

1 + 1/2 = 1 + 0.5 = 1.5.

1.5 times 36.8 cubic yards is:

1.5 x 36.8 = 55.2.

The total amount of cement, sand, and gavel required is of 55.2 cubic yards.

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Answer:

$4,872.00

Step-by-step explanation:

Convert 8% into a decimal and multiply

$60,900.00 x 0.08 = $4,872.00

The domain of f(x) is all real numbers & satisfies function f(x+1)=2f(x).

For  x∈(0,1], the function f(x)=x(x-1). For value x∈(-[tex]\infty[/tex],m], f(x)≥[tex]\frac{-8}{9}[/tex]. What is the value of m?​

the smallest value m=[tex]\frac{7}{3}[/tex].

Given that, for x∈(0,1], f(x)=x(x-1)

Let's plot this function

We'll go from 0 to 1 and let's graph what this function is look like

f(x)=x(x-1) will be a parabola and it's going to go between the points (0,0) and (1,0).

Will graph it in figure1 we can see.

The minimum value of this parabola is right in the middle and it is

f(0.5)=-0.25

Now, let try and graph the function in the other intervals

We know f(x+1)=2f(x)

Now we can evaluate couple of points

f(0+1)=2f(x)

f(0.5+1)=2f(0.5)

f(1+1)=2f(1)

And we quickly deduce that the graph in(1,2] is twice the height of the graph in (0,1].

We will graph a parabola in figure 2 we can see.

This parabola is going to have a graph of 2 between its twice as tall and this can be multiplied by the quantity of (x-1) multiplied by the quantity of (x-2).

It is 2(x-1)(x-2).

We graph next interval twice the height of the graph in the interval from 2 to 3. We can see the graph in figure3.

This parabola will have an equation 4 times the quantity of (x-2) and (x-3).

We can also shift this graph to the left and it going to be half the height.

Looking at this graph we want f(x)≥[tex]\frac{-8}{9}[/tex].

In the 3 interval from 2 to 3 its going to intersect .

we want to look for the points where f(x)≥[tex]\frac{-8}{9}[/tex].

We are looking for m which f(x)≥[tex]\frac{-8}{9}[/tex].

parabolas equation =[tex]\frac{-8}{9}[/tex].

4(x-2)(x-3)=[tex]\frac{-8}{9}[/tex]

[tex]x^{2} -5x+6=\frac{-2}{9} \\(x-\frac{7}{3})(x-\frac{8}{3})=0\\ x= \frac{7}{3},\frac{8}{3}\\\\[/tex]

Therefore, We will take the smallest value m=[tex]\frac{7}{3}[/tex].

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Answer:

1×32

2×16

4×8

8×4

16×2

32×1

Step-by-step explanation:

This question about arranging pictures is just trying to get you to explore the factors of 32, maybe for practicing the math ideas of factoring, or area, or max/min, or matrices.

Think of what numbers go into 32:

1, 2, 4, 8, 16, 32

Pair them up!

1×32 and 32×1 will look differently if they are pictures on a wall. So we'll list them separately. Then there's also 2×16 and 16×2, and 4×8 and 8×4.

The angle of elevation of the sun from the ground to the top of a tree is 36°.

We are given that:

The sun from the ground to the top of a tree when a tree that is 10 yards tall casts a shadow 14 yards long.

Now by using the trigonometric identity .

tan θ = P / B

As figure is  given below .

AB =  Perpendicular = 10 yards

BC =  Base = 14 yards

Putting all the values in the trigonometric identity .

tan θ = 10 / 14

θ = 36°

Therefore, the angle of elevation of the sun from the ground to the top of a tree is 36°.

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The percentage of the actual salary that actual mortgage is is 30%.

Percentage is the fraction of an amount that is expressed as a number out of hundred. Percentage is a measure of frequency. The sign used to show percentage is %.

In order to transform a number into a percentage, express it as a fraction of a total amount and multiply by 100. So, actual mortgage would be divided by actual budget, the fraction would then be multiplied by 100.

Percentage of actual salary that is actual mortgage  = (actual mortgage / actual salary) x 100

(1080 / 3600) x 100 = 30%

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The values of x in the inequalities are x< -2 and x < 4

Given the inequalities;

To determine the value of x for each, we have;

-3x + 2 < 8

collect like terms

-3x < 8 - 2

-3x < 6

Make 'x' the subject

x < 6/ -3

x< -2

1/2x - 5 < -3

Find the Lowest common multiple

x - 10 / 2 < -3

cross multiply

x - 10 < -3 × 2

x - 10 < -6

collect like terms

x < - 6 + 10
x < 4

Thus, the values of x in the inequalities are x< -2 and x < 4

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1. The experiment conducted by Tom is wrong because of the following:

2. The independent variable is the IQ test while the dependent variables are the IQ scores of the four boys and girls.  The constant is the number of testers. There is no control.

3. To improve the experiment, Tom needs to increase the sample sizes of boys and girls to at least 50 boys and 50 girls to make the generalization reasonable.  He should obtain the IQ scores of girls as a control to compare the IQ scores of boys.

An experiment is a scientific study conducted to support or refute a hypothesis.

An experiment involves observations and actions performed to solve a problem or make a discovery.

Thus, Tom's experiment should be improved with research methodologies.

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Mediante el uso de porcentajes, concluimos que la clase tiene una población total de 30 estudiantes.

En este problema tenemos a 12 estudiantes procedentes de una clase que participan en un evento cultural de su escuela y también se conoce que equivalen al 40 por ciento de su clase. El total de estudiantes de la clase se obtiene al dividir el número de estudiantes por el porcentaje:

x = 12 / 40 %

x = (12 · 100) / 40

x = 30

La clase tiene una población total de 30 estudiantes.

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The smaller number is 3496

The difference between the two numbers is 2030

The sum of the two numbers is 9022

Given no.

5526,3496

The difference between the two numbers is 5526-3496=2030

The sum of the two numbers is 5526+3496=9022

The process of combining two or more objects is known as addition. The procedure of determining the sum of two or more integers in mathematics is known as addition. It is a basic mathematical operation that we all employ on a daily basis. When we work with money, compute our shopping bills, or calculate the time, we employ addition frequently.

Addition is a mathematical procedure that is used to add numbers. The sum of the provided numbers is the outcome of adding the supplied numbers. For instance, if we add 2 and 3, (2 + 3), the result is 5. We used the addition function on two integers, 2 and 3, to produce the sum, 5.

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Answer:

c.x=9sr=95

THATS THE ANSWER PO.

The value of the variable x will be 88. Then the length of the side RS will be 84.

A triangle is a three-sided polygon with three angles. The angles of the triangle add up to 180 degrees.

If two triangles are similar, then the ratio of the corresponding sides will remain constant.

Triangle BCD has the following side lengths: BC = 60, CD = 50.

Triangle RST has the following side lengths: RS = 11x-4, ST = 70.

The triangle BCD and RST are similar triangles. Then we have

RS / ST = BC / CD

11x - 4 / 70 = 60 / 50

11x - 4 = 84

11x = 88

x = 8

Then the length of the side RS will be

RS = 11x - 4

RS = 11 × 8 - 4

RS = 88 - 4

RS = 84

The value of the variable x will be 88. Then the length of the side RS will be 84.

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The value of x should be 20 for the line l to be parallel to the line m

Parallel lines are those lines that are equidistant from each other and never meet.

Parallel lines cut by a transversal, forms different angle relationship like alternate angles, corresponding angles, etc.

Therefore, for the line l to be parallel to the line m, the angles formed are corresponding angles.

Corresponding angles are equal.

Therefore,

3x - 20 = 2x + 10

3x - 2x = 10 + 20

x = 20

Therefore, the value of x should be 20 for the line l to be parallel to the line m.

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Answer:

Step-by-step explanation: