Choose the number below that represents the digit in the hundreds place of the number 365

Answer:

a. For the function:

f(x) = { sin x/3, if x ≤ π

{ x√3/2π, if x > π

I. To find lim f(x) as x approaches π from the negative side, we need to evaluate f(x) for values of x that are slightly less than π. In this case, since sin(x/3) is a continuous function, we can simply evaluate it at x = π:

lim f(x) as x approaches π- = f(π-) = sin(π/3) = √3/2

II. To find lim f(x) as x approaches π from the positive side, we need to evaluate f(x) for values of x that are slightly greater than π. In this case, we can simply evaluate the other part of the piecewise function at x = π:

lim f(x) as x approaches π+ = f(π+) = π√3/2π = √3/2

III. To find lim f(x) as x approaches π, we need to check whether the left-hand and right-hand limits are equal. In this case, since both the left- and right-hand limits exist and are equal, we have:

lim f(x) as x approaches π = √3/2

b. For the function:

f(x) = (x^2 - 36)/√(x^2 - 12x + 36)

I. To find lim f(x) as x approaches 6 from the negative side, we need to evaluate f(x) for values of x that are slightly less than 6. In this case, we can substitute x = 6 - h, where h is a positive number approaching zero, to get:

lim f(x) as x approaches 6- = lim f(6 - h) as h approaches 0

Substituting x = 6 - h into the function, we get:

f(6 - h) = [(6 - h)^2 - 36]/√[(6 - h)^2 - 12(6 - h) + 36]

= [h^2 - 12h]/√[h^2]

Simplifying the numerator and denominator separately, we get:

f(6 - h) = h(h - 12)/|h|

Since h approaches 0 from the positive side, we have:

lim f(6 - h) as h approaches 0+ = lim h(h - 12)/h as h approaches 0+ = lim (h - 12) as h approaches 0+ = -12

II. To find lim f(x) as x approaches 6 from the positive side, we need to evaluate f(x) for values of x that are slightly greater than 6. In this case, we can substitute x = 6 + h, where h is a positive number approaching zero, to get:

lim f(x) as x approaches 6+ = lim f(6 + h) as h approaches 0

Substituting x = 6 + h into the function, we get:

f(6 + h) = [(6 + h)^2 - 36]/√[(6 + h)^2 - 12(6 + h) + 36]

= [h^2 + 12h]/√[h^2]

Simplifying the numerator and denominator separately, we get:

f(6 + h) = h(h + 12)/|h|

Since h approaches 0 from the positive side, we have:

lim f(6 + h) as h approaches 0+ = lim h(h +

Step-by-step explanation:

Answer:

  -64

Step-by-step explanation:

Undo the cube root by cubing both sides.

  (∛x)^3 = (-4)^3

  x = -64

The statements DF=EG, EF=DG and ∠DEG ≅ ∠FGE are true for parallelogram DEFG.

a quadrilateral is a four-sided polygon, having four edges and four corners.

DEFG is a parallelogram.

A parallelogram is a simple quadrilateral with two pairs of parallel sides.

The opposite or facing sides of a parallelogram are of equal length and the opposite angles of a parallelogram are of equal measure.

DF=FG is a true statement.

The diagonal passing through a parallelogram are equal in length.

EF=DG is a true statement

The opposite sides of a parallelogram are equal.

∠DEG ≅ ∠FGE are congruent angles.

Because the opposite angles of a triangle are equal in meausure.

Hence, the statements DF=EG, EF=DG and ∠DEG ≅ ∠FGE are true for parallelogram DEFG.

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Answer:height = 5 inches  and the base = 10 inches.

Step-by-step explanation:

The answer, based on the information provided, fractional exponents will be 3.

A product in which the same integer is used repeatedly as a factor is represented by a number elevated to a power. The exponent provides the power, and the integer is referred to as the base. The exponent indicates the number of factors, while the base is the repeating factor (the multiplied number).

That number will be the outcome! One of the simplest exponent laws is this one. You'll see that this rule doesn't merely apply to numerical data. We might, for example, elevate a statistic to the initial power.

\(=3^{\frac{1}{4} }\times3^{\frac{1}{4} }\times3^{\frac{1}{4} }\times3^{\frac{1}{4} }\\=3^{\frac{1}{4}+{\frac{1}{4}+{\frac{1}{4}+{\frac{1}{4}\\\\=3^{1} \\=3\)

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The dairy farmer should use 1330 pounds of the 70% protein supplement and 570 pounds of the 20% protein ratio to make a 1900-pound high-grade 55% protein ration.

To determine the amounts of the 70% protein supplement and the 20% protein ratio needed to make a 1900-pound high-grade 55% protein ration, we can set up a system of equations.

Let's assume x represents the pounds of the 70% protein supplement and y represents the pounds of the 20% protein ratio.

The total weight equation is given by:

x + y = 1900

The protein content equation is given by:

(0.70x + 0.20y) / 1900 = 0.55

Simplifying the second equation, we get:

0.70x + 0.20y = 0.55 × 1900

0.70x + 0.20y = 1045

Now, we can solve this system of equations to find the values of x and y.

Rearrange the first equation to solve for x:

x = 1900 - y

Substitute this expression for x in the second equation:

0.70(1900 - y) + 0.20y = 1045

1330 - 0.70y + 0.20y = 1045

1330 - 0.50y = 1045

-0.50y = 1045 - 1330

-0.50y = -285

y = -285 / -0.50

y = 570

Now substitute this value of y back into the first equation to find x:

x + 570 = 1900

x = 1900 - 570

x = 1330

Therefore, the dairy farmer should use 1330 pounds of the 70% protein supplement and 570 pounds of the 20% protein ratio to make a 1900-pound high-grade 55% protein ratio.

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Answer:

I will need to buy 22.5 pounds of turkey and pay $23.63

Step-by-step explanation:

Proportions

Each person is planned to eat 2 x 3/8 pound servings of turkey for thanksgiving dinner. This means each person will eat

\(2\cdot\frac{3}{4}=\frac{3}{2}\)

pounds of turkey.

There are going to be 15 people at the dinner, thus the total turkey needed is:

\(15\cdot\frac{3}{2}=22.5~pounds\)

The turkey costs $1.05 per pound, thus the total cost is

22.5*$1.05 = $23.63

I will need to buy 22.5 pounds of turkey and pay $23.63

Answer:

1. No

2. 90 and 180

3. 9

4. 150 as consecutive angles

5. 73

6. x+x+2x+2x = 180

6x = 180

x = 30

7. 3x+2y+24=180

3x+2y +24=180

3x+2y=180-24

3×32 +2y= 156

y=60/2

y=30

when, y=24

3x+2y+24=180

3x+2×24-180-24

3x=-156-48

x=108/3

x=34.444

Answer:

  499.338 feet

Step-by-step explanation:

You want to know the distance traveled by an object in 25 seconds when its velocity is described by 20+5cos(t) feet per second.

The distance an object travels is the integral of its velocity. For the given velocity and time period, the distance is ...

  \(\displaystyle d=\int_0^{25}{v(t)}\,dt=\int_0^{25}{(20+5\cos(t))}\,dt=(20t+5\sin(t))|_0^{25}\\\\d=500+5\sin(25)\approx\boxed{499.338\quad\text{feet}}\)

The distance traveled in 25 seconds is 499.33 feet.

It is required to find the distance traveled in 25 seconds.

The distance of an object can be defined as the complete path travelled by an object .Distance is a scalar quantity that refers to "how much ground an object has covered" during its motion.

Given:

We have to find the distance , we will integrate v(t) from 0 to 25 second.

Consider an object traveling at constant velocity v = k. Then, each second, it travels k feet, so after t seconds, the distance traveled is k*t.

Now, suppose its speed increases by 1 feet/sec . So, estimate for distance traveled after t seconds is

1 + 2 + 3 + 4 + ... + t = t(t+1)/2, or approximately 1/2 t^2.

According to given question we have

Given a velocity function v, the distance s is figured by taking the integral. In this case,

v = 20 + 5 cos(t)

s = 20t + 5 sin(t) from 0 to 25

= s(45)-s(0)

s(0) = 0

so, the distance is

s(25) = 20*25 + 5sin(25)

= 500 -0.661

=499.33 feet.

Therefore, the distance traveled in 25 seconds is 499.33 feet.

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The value of the composite function (f o g)(3) is 1603

The functions are given as

f(x) = 3x² - 7x - 3

g(x) = -4x - 10

Next, calculate (f o g)(x) using

(f o g)(x) = f(g(x))

So, we have

(f o g)(x) = 3(-4x - 10)² - 7(-4x - 10) - 3

Substitute 3 for x.

So, we have

(f o g)(3) = 3(-4 x 3 - 10)² - 7(-4 x 3 - 10) - 3

Evaluate

(f o g)(3) = 1603

Hence, the value of the composite function (f o g)(3) is 1603

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Answer:

the area of the triangle is 36

The four main principles of randomized experiments are:

True, True, False, True, and True

1. True: Confounding variables can make it harder to draw conclusions from a study because they can obscure the effect of the treatment being studied. Confounding variables are extraneous factors that can affect the outcome of the study and mimic or mask the effect of the treatment being studied.

2. True: In a randomized experiment, the treatment and control groups are designed to be as similar as possible in terms of all relevant factors, except for the treatment itself. This helps to ensure that any observed differences between the groups can be attributed to the treatment being studied, rather than to other factors that might affect the outcome.

3. False: Observational studies are generally considered to be less reliable than randomized experiments because they are subject to a number of biases that can affect the results. For example, observational studies often involve selection bias, in which certain groups are more likely to be included in the study, and measurement bias, in which the measurements used in the study are not accurate or reliable.

4. True: The four main principles of randomized experiments are:  

5. True: In a double-blind study, neither the investigators nor the subjects know who is receiving which treatment. This helps to reduce the potential for bias and increase the reliability of the results, by ensuring that neither the investigators nor the subjects can influence the outcome of the study based on their knowledge of the treatment assignments.

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The binomials (x - 3) and (x - 10) are factors of the trinomial x² - 13x + 30.

To determine which binomial is a factor of the trinomial x² - 13x + 30, we need to factorize the trinomial completely.

In this case, we need to find two binomials in the form (x - a)(x - b) that satisfy the equation:

(x - a)(x - b) = x² - 13x + 30

So, (x - 3)(x - 10) = x² - 13x + 30.

Therefore, the binomials (x - 3) and (x - 10) are factors of the trinomial x² - 13x + 30.

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Answer:

what it is language

Step-by-step explanation:

Answer:

51%

Step-by-step explanation:

the answer is the answer because it's the answer (ФДФ)

The length of the other leg for triangle BCD will be 13.86cm.

From the triangle BCD is a right triangle. The length of the hypotenuse is 19 centimeters and the length of one of the legs is 13 centimeters.

The Pythagoras theorem states that the sum of two squares equals the squared of the longest side. The Pythagoras theorem formula is given as

H² = P² + B²

Let the unknown sides be x. Then we have,

19² = 13² + x²

361 = 169 + x²

x² = 361 – 169

x² = 192

 x = 13.856 ≈ 13.86 cm

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The triangle BCD is a right triangle. The length of the hypotenuse is 19 centimeters. The length of one of the legs is 13 centimeters.

What is the length of the other leg?

Answer:

Amount to deposit= $26799.0

Step-by-step explanation:

Amount A = $60,000

Years t = 8 years,

Rate R = 9% .

A= p(1+r/n)^(nt)

60000= p(1+0.09/9)^(9*9)

60000= p(1+0.01)^(81)

60000= p(1.01)^81

60000= p(2.23888)

60000/2.23888= p

26799.1138= p

P= $26799.0

Amount to deposit= $26799.0

To be able to have $60,000 after 8 years at a rate of 9% per annum, the amount to deposit today is $30,111.98

You can solve this using the Future Value formula which is:

Future value = Present value x ( 1 + rate)^ number of years

You have everything except the present value so solve for it:

60,000 = PV x ( 1 + 9%)⁸

60,000 = PV x 1.9925626416901921

PV = 60,000 / 1.9925626416901921

PV = $30,111.98

In conclusion, you should deposit $30,111.98 today.

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By using the concept of dilation factor, length of BC obtained is 3 units

What is dilation factor?

Dilation is a transformation which changes the size of a figure by a certain factor.

That factor is called the scale factor

In the figure, A'B'C'D' is the image of ABCD under dilation with a scale factor of 3

A'B'C'D' is the dilated figure

Length of B'C' = 9 units

Length of BC = \(9 \div 3\) = 3 units

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Complete Question

The figure has been attached here

Answer:

33.4

Step-by-step explanation:

tanα = \(\frac{opp}{adj}\)→\(tan 50^{o} = \frac{x}{28}\)

x = 28 tan 50° = 33.4

Answer:

The value of missing x = 33.37 units

Step-by-step explanation:

Given

Ф = 50°

We know that

tan Ф = opposite/adjacent

Here:

opposite = x

adjacent = 28

so

tan Ф = opposite/adjacent

tan 50 = x/28

x = 28 × tan 50

  =33.37

Therefore, the value of missing x = 33.37 units.

The gradient of the line joining the points (1,-1) and (4,9) is 10/3, while the gradient of the line joining (5,1) and (2,-2) is 1. The x-intercept of the equation 3y = 2x - 2 is 1, and the y-intercept is -2/3. These calculations follow the formula for gradient and the methods for finding intercepts in linear equations.

1) To find the gradient of a line joining two points, you can use the formula: gradient = (change in y)/(change in x).
Given the points (1,-1) and (4,9), the change in y is 9 - (-1) = 10 and the change in x is 4 - 1 = 3.
Therefore, the gradient of the line joining these points is 10/3.
2) Similarly, to find the gradient of a line joining two points (5,1) and (2,-2), we can use the same formula. The change in y is -2 - 1 = -3 and the change in x is 2 - 5 = -3.
Therefore, the gradient of the line joining these points is -3/-3 = 1.
3) To find the x-intercept, we set y to 0 and solve for x.
Given the equation 3y = 2x - 2, if we substitute y with 0, we have 3(0) = 2x - 2, which simplifies to 0 = 2x - 2.
To solve for x, we can add 2 to both sides: 0 + 2 = 2x - 2 + 2, which gives us 2 = 2x.
Dividing both sides by 2, we get x = 1.
Therefore, the x-intercept of the equation 3y = 2x - 2 is 1.
To find the y-intercept, we set x to 0 and solve for y.
Using the same equation, if we substitute x with 0, we have 3y = 2(0) - 2, which simplifies to 3y = -2.
To solve for y, we can divide both sides by 3: (3y)/3 = (-2)/3, which gives us y = -2/3.
Therefore, the y-intercept of the equation 3y = 2x - 2 is -2/3.
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C. The Roth IRA reduces the tax burden because its taxes are calculated in a lower bracket.

In a traditional IRA, contributions may be tax-deductible in the year they are made, but withdrawals in retirement are taxed as ordinary income. This means that the $1000.00 investment in a traditional IRA would be taxed at the investor's ordinary income tax rate when it is withdrawn in retirement. If the investor's ordinary income tax rate is 12%, then the tax burden on the $1000.00 investment in a traditional IRA would be $120.00.

In a Roth IRA, contributions are not tax-deductible, but withdrawals in retirement are tax-free. This means that the $1000.00 investment in a Roth IRA would be taxed at the investor's ordinary income tax rate when it is made, but it would not be taxed when it is withdrawn in retirement. If the investor's ordinary income tax rate is 10%, then the tax burden on the $1000.00 investment in a Roth IRA would be $100.00.

Overall, the tax burden on the $1000.00 investment in a Roth IRA is lower than the tax burden on the same investment in a traditional IRA because the taxes on the Roth IRA are calculated in a lower bracket (10% vs 12%).

\(f(x)=x\) for \(x\leq0\), therfore \(f(0)=0\).

the first domain is true for f(0) so we substitute value of x in the first function

\(f(x) = x \\ f(0) = 0\)

Triangle ABC and ADE are similar triangles

Similar triangles have the same corresponding angle measures and proportional side lengths.

This means that for two triangles to be similar, the corresponding angles must be equal and the ratio of corresponding sides of similar triangles are equal.

It has been shown that angles in ABC and ADE are equal.

To show that the ratio of corresponding sides are equal

6/12 = 8/16 = 10/20

The ratios all give a value of 1/2

Therefore we can say that the triangles ABC and ADE are similar.

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Answer:

a= 5

Step-by-step explanation:

3 (a-7)= 14-4a -Remove Parentheses

3a-21=14-4a -Move the terms

3a+4a=14+21 -Collect like terms

7a=35 -Divide both sides

a=5 - Solution

Answer: 3 mph

Step-by-step explanation:

1. 1/2 mph for 1/2 an hour as they said, meaning that they would've walked for 3 miles kn an hour.

2. 4 and 1/2 miles.

3 + 1 2/4. = 4 1/2

3. 1 3/4 hours.

3 + 2.25 = 5.25

3 x .75 = 2.25

3 miles per hour.

Answer:

52.5 inch square

Step-by-step explanation:

Area of pentagon: A = 1/2 × p × a;

where 'p' is the perimeter of the pentagon and 'a' is the apothem of the pentagon.

A = 1/2 x (6 x 5) x 3.5 = 1/2 x 30 x 3.5 = 15 x 3.5 = 52.5

The area of the regular pentagon with apothem 3.5 and side 6 is 52.5

In Mathematics, a pentagon is a polygon with 5 sides. A pentagon can be classified as a regular pentagon and irregular pentagon. When all the sides and the angles of a pentagon are of equal measure, then it is called a regular pentagon.

Given the question, we need to find the area of the regular pentagon with apothem 3.5 and side 6.

In order to find the area, the formula to calculate the area of the regular pentagon is given by:

\(\text{Area of pentagon} =\sf \huge \text(\dfrac{5}{2}\huge \text) \times s \times a\)

Now,

\(\text{Area of pentagon} =\sf \huge \text(\dfrac{5}{2}\huge \text) \times s \times a\)

\(\text{Area of pentagon} =\sf \huge \text(\dfrac{5}{2}\huge \text) \times 6 \times 3.5\)

\(\text{Area of pentagon} =52.5\)

Therefore, the area of the regular pentagon with apothem 3.5 and side 6 is 52.5

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Step-by-step explanation:

we would have needed only one corresponding side length. because for similar triangles all corresponding lines (like sides but also heights and so on) would be related in size by using the same scaling factor.

going from the large to the small triangle : what do I need to multiply the large side length with to get the small one ?

27 × x = 9

x = 9/27 = 1/3

that is the scale factor.

Answer: (3,-3)

Step-by-step explanation:

The correct option is not available among the choices provided (A. 49.4, B. 39.5, C. 55.2, D. 50.45).

To find the measure of angle A in triangle ABC using the Law of Sines, we can use the formula:

sin(A)/a = sin(B)/b = sin(C)/c

Given that a = 14, b = 17, and c = 22, we can substitute these values into the formula:

sin(A)/14 = sin(B)/17 = sin(C)/22

To find angle A, we need to solve for sin(A) and then take the inverse sine (arcsin) of that value.

First, let's find sin(B) using the given information:

sin(B)/17 = sin(A)/14

sin(B) = (17 * sin(A))/14

Next, let's find sin(C):

sin(C)/22 = sin(A)/14

sin(C) = (22 * sin(A))/14

Since the sum of angles in a triangle is 180 degrees, we can calculate angle C:

angle C = 180 - angle A - angle B

Now, we can substitute the expressions for sin(B) and sin(C) into the equation:

(22 * sin(A))/14 = (17 * sin(A))/14 + sin(B)

To solve for sin(A), we can multiply both sides of the equation by 14:

22 * sin(A) = 17 * sin(A) + 14 * sin(B)

22 * sin(A) - 17 * sin(A) = 14 * sin(B)

5 * sin(A) = 14 * sin(B)

sin(A) = (14/5) * sin(B)

Finally, we can take the inverse sine (arcsin) of sin(A) to find the measure of angle A:

A = arcsin((14/5) * sin(B))

Now, since the values of angles B and C are not provided, it is not possible to directly determine the measure of angle A using the given information.

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