Round the following number as indicated 106,513

Answer:

32ft

Step-by-step explanation:

The approximate probability that the driver will be fined is 0.25.

If the driver of a truck loaded with 900 boxes of books will be fined if the total weight of the boxes exceeds 37,350 pounds, then the weight of each box of book must not exceed 41.5 pounds.

37,350 pounds / 900 boxes = 41.5 pounds

Suppose that distribution of the weight is a normally distributed set of data, given the mean and standard deviation, the probability can be determined by solving the z-score and using the z-table.

First, solve for the z-score using the formula below.

z-score = (x – μ) / σ

where x = individual data value = 41.5

μ = mean = 41.1

σ = standard deviation = 6

z-score = (41.5 - 41.1) / 6

z-score = (0.4) / 6

z-score = 0.06667

Find the probability that corresponds to the z-score in the z-table. (see attached images)

at z = 0.06667,     p = 0.7472

Since the fine will be given if the load exceeds 41.5, we have to consider the values greater than 41.5. Subtract the answer from 1.

probability = 1 - 0.7472 = 0.25

Hence, the approximate probability that the driver will be fined is 0.25.

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We are given that Jane used 200 minutes and the cost was $75, and also she used 680 minutes and the cost was $195. To determine a function of the cost "C" as a function of the minutes "x" we will assume that the behavior of this function is that of a line. Therefore, the function must have the following form:

Where "m" is the slope and "b" the y-intercept. We will determine the slope using the following formula:

Where:

Are points in the line. The given points are:

Substituting in the formula for the slope we get:

Solving the operations we get:

Now we substitute in the formula for the line:

Now we determine the value if "b" by substituting the first point. This means that when C = 200, x = 75.

Solving the product:

Now we subtract 18.75 from both sides:

Therefore, the formula of the cost is:

Part B. We are asked to determine the cost is there is a consumption of 323 minutes. To do that we will substitute in the formula for "C" the value of x = 323.

Solving the operations we get:

Therefore, the cost is $262.

Answer:

Step-by-step explanation:

We will make use of algebra here.

First of all, we know that the monthly fee will be the same throughout all the months.
So, let's consider that cost to be the yet-to-find constant: \(a\).

A charge is accumulated for every minute on the call, so let's consider that minutely charge to be the constant: \(b\).

\(x\) is the number of minutes spent on the call.
So, the total charge after talking for \(x\) minutes would be:

\(b \times x\\=bx\)

The monthly cost is the sum of the monthly fee and the total charge.

So, if this is represented mathematically, we get:

\(C(x)= a+bx\)

A piece of information that we have is that, after calling for 200 minutes (which means \(x=200\)), the monthly cost ( \(C(x)\) ) would be $75.

Upon substituting these values in the equation we found above, we get:

\(C(x)=a+bx\\\\75=a+200b\)

Similarly, we have another piece of information, which states that calling for 680 minutes (\(x=680\)) produced a monthly cost of $195.

Upon substituting these values in the equation we found above, we get:

\(C(x)=a+bx\\\\195=a+680b\)

And, thus we have found a system of equations:

 \(a+200b=75\\a+680b=195\)

For the first equation, let's make \(a\) the subject:

\(a+200b=75\\\\a+200b-200b=75-200b\\\\a=75-200b\)

Substitute this expression for \(a\) into the second equation:

\(a+680b=195\\\\75-200b+680b=195\\\\75+480b=195\)

Find the value of \(b\) using this equation:

\(75+480b=195\\\\75+480b-75=195-75\\\\480b=120\\\\\frac{480b}{480}=\frac{120}{480}\\\\b=\frac{1}{4}\)

Insert the value for \(b\) into the expression for \(a\):

\(a=75-200b\\\\a=75-200(\frac{1}{4})\\\\a=75-50\\\\a=25\)

Since we have the values for the constants \(a\) and \(b\), we can complete the function/equation  \(C(x)\):

\(C(x)=a+bx\\\\C(x)=25+\frac{1}{4}x\)

So, the answer for (A) is:

\(C(x)=25+\frac{1}{4}x\)

For (B), we have to find the monthly bill/cost ( \(C(x)\) ) when 323 minutes have been spent on calling.

So, we just have to substitute \(x\) for 323, since \(x\) represents the number of minutes spent on calling:

\(C(x)=25+\frac{1}{4}x\\\\C(x)=25+\frac{1}{4}(323)\\\\C(x)=25+80.75\\\\C(x)=100.75\)

The answer for (B) is \(\$100.75\)

Answer:

ordered pairs: (3,0) (6,0) (9,0)

slope : 0

Step-by-step explanation:

Hey There!

So if you graph a line that has a horizontal line then the slope is going to be 0

If you look at the graph i put an example with three points

Answer:

Answer

5.0/5

Step-by-step explanation:

Answer:

A. 2 units

Step-by-step explanation:

took the test and got it right

The radius of the circle is r = 2 units

A circle is a closed figure in which the set of all the points in the plane is equidistant from a given point called “center”. Every line that passes through the circle forms the line of reflection symmetry. Also, the circle has rotational symmetry around the center for every angle

The circumference of circle = 2πr

The area of the circle = πr²

where r is the radius of the circle

The standard form of a circle is

( x - h )² + ( y - k )² = r²,

where r is the radius of the circle and (h,k) is the center of the circle.

The equation of circle is ( x - h )² + ( y - k )² = r²

For a unit circle , the radius r = 1

x² + y² = r² be equation (1)

Now , for a unit circle , the terminal side of angle θ is ( cos θ , sin θ )

Given data ,

Let the equation of the circle be represented as A

Now , the value of A is

( x - 7 )² + ( y - 10 )² = 4

The equation ( x - 7 )² + ( y - 10 )² = 4 represents a circle in standard form, where the center of the circle is located at the point (7, 10) and the radius is the square root of the number on the right side of the equation

Taking the square root of 4, we find that the radius of the circle is 2 units

Hence , the radius is r = 2 units

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The difference between the linear and projectile motion is that "Linear-motion" refers to motion of object in a "straight-line", while "projectile-motion" refers to motion of an object that is thrown into air, in a curved path.

In linear motion, the object moves along a straight line, with its velocity and acceleration aligned in the same direction. The object's speed and direction may change, but its motion remains linear.

In projectile motion, the object moves along a curved path under the influence of gravity. The object is launched into the air with an initial velocity, and then gravity causes it to follow a parabolic path until it lands back on the ground. The motion of the object is influenced by both its initial velocity and the force of gravity.

In both linear and projectile motion, the "horizontal-component" of velocity will usually remain constant because there is no external force acting on the object in horizontal direction, and thus no acceleration.

Therefore, the object will continue to move at a constant velocity in the horizontal direction, as long as there is no external force acting on it.

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Answer:

\(a=3, b=2\)

Step-by-step explanation:

Using the remainder theorem,

\(b^2-ab+3=1 \implies b^2-ab+2=0 \\ \\ 2a-b=4 \implies b=2a-4 \\ \\ \therefore (2a-4)^2-a(2a-4)+2=0 \\ \\ 4a^2+16-16a-2a^2+4a+2=0 \\ \\ 2a^2 - 12a+18=0 \\ \\ a^2-6a+9=0 \\ \\ (a-3)^2=0 \\ \\ a=3 \\ \\ \therefore 2(3)-b=4 \implies b=2\)

Answer:

Triangle ABC ~ DAC

Step-by-step explanation:

If you would like a full explanation let me know and I'll try my best.  

ABC ~ DAC

Step-by-step explanation:

yw

Answer:

Step-by-step explanation:

Answer:

52 grams to ounces = 1.8304 ounces

Step-by-step explanation:

Formula: for an approximate result, divide the mass value by 28.35

Brainliest please! I am so close to getting my next rating! I would really appreciate it, and it would make my day! Thank you so much, and have a wonderful rest of your day!

Answer:

52 grams to ounces = 1.8304 ounces

Step-by-step explanation:

Hope this helps :)

Answer:

\(x = \frac{-7 +\sqrt{489} }{2}\)

\(x = \frac{-7 - \sqrt{489} }{2}\)

Step-by-step explanation:

2x² +21x-61 = (x+7)²

expand

2x² + 21x - 61 = x² + 14x +49

move everything to one side

x² + 7x - 12 = 0

use quadratic formula

\(x = \frac{-b +- \sqrt{b^{2}-4ac } }{2a}\)

plug in the values

\(x = \frac{-7 +- \sqrt{7^{2}-4(1)(-110) } }{2(1)}\)

solve

\(x = \frac{-7 +- \sqrt{49-4(1)(-110) } }{2}\)

\(x = \frac{-7 +- \sqrt{49 + 440 } }{2}\)

\(x = \frac{-7 +- \sqrt{489} }{2}\)

7.54 and 0.46 are the solutions to the given quadratic equations

Given the quadratic equation below:

x^2-18x+8=0

We need to determine the solutions to the given quadratic expression. Using the general formula below:

x = -b±√b²-4ac/2a

From the equation

a = 1

b = -18

c = 8

Substitute

x = 18±√18²-4(1)(8)/2(1)
x= 18±√324-32/2

x =18± 17.08/2

x = 35.08/2 and 0.92/2

x = 17.54 and 0.46

Hence the two solutions to the given quadratic equation are 17.54 and 0.46

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a) the probability of drawing a face card is 3/13. b) , the probability of not drawing a black face card is 1/2. c) the probability of drawing a heart or a queen is 4/13.

A) To find the probability of drawing a face card (a jack, queen, or king), we need to determine the number of favorable outcomes (face cards) and divide it by the total number of possible outcomes (52 cards in a deck).

Number of favorable outcomes = 12 (4 jacks + 4 queens + 4 kings)

Total number of possible outcomes = 52

Probability of drawing a face card = Number of favorable outcomes / Total number of possible outcomes

                               = 12 / 52

                               = 3 / 13

Therefore, the probability of drawing a face card is 3/13.

B) To find the probability of not drawing a black face card, we need to determine the number of favorable outcomes (non-black face cards) and divide it by the total number of possible outcomes (52 cards in a deck).

Number of favorable outcomes = 12 (4 jacks + 4 queens + 4 kings)

Total number of possible outcomes = 52

Since there are 26 black cards in the deck, the number of non-black cards is 52 - 26 = 26.

Probability of not drawing a black face card = Number of favorable outcomes / Total number of possible outcomes

                                          = 26 / 52

                                          = 1 / 2

Therefore, the probability of not drawing a black face card is 1/2.

C) To find the probability of drawing a heart or a queen, we need to determine the number of favorable outcomes (hearts + queens) and divide it by the total number of possible outcomes (52 cards in a deck).

Number of favorable outcomes = 16 (13 hearts + 3 other queens)

Total number of possible outcomes = 52

Probability of drawing a heart or a queen = Number of favorable outcomes / Total number of possible outcomes

                                       = 16 / 52

                                       = 4 / 13

Therefore, the probability of drawing a heart or a queen is 4/13.

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Answer:

LSA = 56.5 cm²

Step-by-step explanation:

LSA = 2πrh

LSA = 2π(3)(3)

LSA = 56.5 cm²

Answer:

false

Step-by-step explanation:

Answer:

-33/4 ft/s

Step-by-step explanation:

\(x^2+y^2=2500 \\ \\ 2x \frac{dx}{dt}+2y \frac{dy}{dt}=0 \\ \\ x\frac{dx}{dt}+y \frac{dy}{dt}=0 \\ \\ (30)(11)+40 \frac{dy}{dt}=0 \\ \\ \frac{dy}{dt}=-\frac{33}{4}\)

We use ANOVA to test for differences between population means by examining the amount of variability between the samples relative to the amount of variability within the samples. Hence, it is TRUE

The statistical analysis tool known as analysis of variance (ANOVA) divides the observed aggregate variability present in a data set into two categories: systematic variables and random components. The random factors have no statistical impact on the presented data set, whereas the systematic factors do. The ANOVA test is used by analysts to ascertain how independent factors in a regression analysis affect the dependent variable.

ANOVA basically stands for analysis of the variance.

Hence, according to above statements, given fact is true.

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As r is reflexive, symmetric, and transitive, we can conclude that it is an equivalence relation on z2.

The set of ordered pairs of integers z2 = {(a, b)} is the set of elements whose first element is a and whose second element is b, where a and b are integers.

Suppose a = b = 0; therefore, we have z2 = {(0, 0)}. This is the only element in the set z2.

Let us define r on z2 by saying that (a, b) r (c, d) if and only if ad = bc.

To show that r is an equivalence relation on z2, we must show that r is reflexive, symmetric, and transitive.

Reflexivity:If we take (a, b) from z2, then we must show that (a, b) r (a, b) i.e., ab = ba. This is true since multiplication is commutative.

Symmetry:Suppose (a, b) r (c, d) i.e., ad = bc.

Then (c, d) r (a, b) i.e., ba = dc.

We can observe that if ab = 0 or cd = 0, then ab = dc = 0, and the symmetry property holds.

If ab ≠ 0 and cd ≠ 0, then we can rearrange the equation as: ad = bc. Thus, we can write d/c = b/a, which shows that (c, d) and (a, b) are related.

Transitivity:Let (a, b) r (c, d) and (c, d) r (e, f). This means that ad = bc and cf = de.

If we multiply the two equations, we obtain adcf = bcde. We can rearrange the terms and get abcf = bdef.

Since f ≠ 0, we can cancel it out and obtain abce = bcde.

We can cancel b from both sides and get ae = cd.

This shows that (a, b) r (e, f), which means that r is transitive.

Since r is reflexive, symmetric, and transitive, we can conclude that it is an equivalence relation on z2.

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Base on the given quadrilateral GHIJ and RQPS, the measure of m<Q is 91°.

The sum of interior angles in a quadrilateral is equal to 360°

From quadrilateral GHIJ

<G = 360° - (<J + <I + <H)

<G = 360° - (55° + 81° + 91°)

<G = 360° - 227°

<G = 133°

Since GHIJ ~ RQPS.

So,

<J ~ <S = 55°

<G ~ <R = 133°

<H ~ <Q = 91°

<I ~ <P = 81°

Therefore, the missing angle in quadrilateral GHIJ is 133°.

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The system of equations is:

x + y = 10

4x + 3y = 36

The solution is x = 6 and y = 4.

A)

Let's define the variables:

We can write the system of equations:

x + y = 10

4x + 3y = 36

Isolate x on the first equation to get:

x = 10 - y

Replace that in the other one:

4*(10 - y) + 3y = 36

40 - 4y + 3y = 36

40 - y = 36

40 - 36 = y

4 = y

And thus, the value of x is:

x = 10 - y = 10 - 4 = 6

They bought 6 cheese wafers and 4 chocolate ones.

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Step-by-step explanation:

when 22 is divided by 2345

Then

22/2345

= 0.0093816631

Answer:

22÷2355? or 2345 ÷ 22

Step-by-step explanation:

22÷ 2345 =0.00093

but, 2345 ÷22= 106.590

263,334 $ much they will pay in interest over the life of the loan.

With a balloon mortgage of 30/5, Twyla and Tony will make regular payments for 5 years before making the bulk balloon payment with 25 years left to go.

Considering the $389,00 mortgage loan value

4.85% interest rate

The interest on the loan over its whole term must be calculated, as requested.

We will compute interest by adding up all of the consistent payments made over the course of the five years prior to the balloon payment and deducting them from the $389,900 mortgage loan.

The formula for constant payments :

A= P×r×r(1+r)^n/(1+r)^n-1

Where A= constant/monthly payments

r= interest rate on the mortgage loan

n= number of payments = 30×12= 360

P= mortgage loan given

A= $389900×0.0485×0.0485(1+0.0485)^360/(1+0.0485)^360-1

=$389900×0.0485×1231340.79/25388468.94

=$389900×0.0485×0.04850

A= $917.142

Payment for five years(with interest)= $917.142×60= $55028.52

Calculate balloon payment:

FV= PV(1+r)^n - P((1+r)^n-1/r)

Where FV= future value of balloon payment

PV= initial loan given

r= interest rate on loan

n= number of payments

P= monthly payments

Substitute:

FV= $389900(1+0.0485/12)^60-917.142((1+0.0485/12)^60-1/0.0485/12)

=$389900×1.2738-917.142(0.2738/0.004041)

=$389900×1.2738-917.142×67.756

= 496654.62-62141.87

FV = $434512.75

Therefore total payment made with interest over the life of the loan= balloon payment+ constant payments for five years= $434512.75+$55028.52

=263,334

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Answer:

201

Step-by-step explanation:

As we can see, the line is continuous, and the area is below the line, therefore, we can conclude that the inequality is given by:

Answer:

The answer is in the picture

To satisfy the conditions that the mode is larger than the median, and the median is larger than the mean, one possible set of frequencies is 1 person chooses 1, 3 people choose 2, 4 people choose 3, 1 person chooses 4 and 11 people choose 5 This results in a mode of 5, a median of 4, and a mean of approximately 3.75.

Since we are given that the mode is larger than the median, that means that at least 11 people must choose the same number. Let's assume that 11 people choose the number 5.

Now, since the median is larger than the mean, we want to make sure that the remaining 9 people choose numbers that are smaller than 5. If they all choose 1, 2, or 3, then the median will be 3, which is larger than the mean. Therefore, we need to make sure that at least one person chooses 4.

So one possible set of frequencies could be

1 person chooses 1

3 people choose 2

4 people choose 3

1 person chooses 4

11 people choose 5

This set of frequencies gives us a mode of 5 (since 11 people choose 5), a median of 4 (since the middle value is 4), and a mean of

(11 + 32 + 43 + 14 + 11*5) / 20 = 3.7

Since the median is larger than the mean, this set of frequencies satisfies all the given conditions.

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Let:

a = ounces of 72% alcohol solution

b = ounces 9% alcohol solution

c = ounces Final mixture:

so:

She needs to add 6 oz of 9% alcohol solution to create the desired mixture

Lohi Corp.'s expected capital gains yield over the next year is 0.48%.

To determine the price of lohi corp., we need to calculate the present value of its future dividends. First, we estimate that the company will skip the next three annual dividends. This means that we will start receiving dividends from the fourth year. The first dividend to be paid is $1.00, and subsequent dividends will grow at a constant rate of 6 percent per year. The required rate of return on lohi corp. is 14 percent per year. This is the rate of return that investors expect to earn from investing in the company.

To calculate the price of Lohi Corp., we need to use the dividend discount model (DDM). The DDM formula is:

Price = Dividend / (Required rate of return - Dividend growth rate)

In this case, we know that Lohi Corp. will skip its next three annual dividends and then resume paying a dividend of $1.00. The dividend growth rate is 6% per year, and the required rate of return is 14% per year.

First, let's calculate the present value of the future dividends:

PV = (1 / (1 + Required rate of return))^1 + (1 / (1 + Required rate of return))^2 + (1 / (1 + Required rate of return))^3

PV = (1 / (1 + 0.14))^1 + (1 / (1 + 0.14))^2 + (1 / (1 + 0.14))^3

PV = 0.877 + 0.769 + 0.675

PV = 2.321

Next, let's calculate the price:

Price = (Dividend / (Required rate of return - Dividend growth rate)) + PV

Price = (1 / (0.14 - 0.06)) + 2.321

Price = (1 / 0.08) + 2.321

Price = 12.5

Therefore, the price of Lohi Corp. should be $12.50.

To calculate the expected capital gains yield over the next year, we need to use the formula:

Capital gains yield = (Dividend growth rate) / (Price)

Capital gins yield = 0.06 / 12.5

Capital gains yield = 0.0048

Convert to percentage:

Capital gains yield = 0.0048 * 100

Capital gains yield = 0.48%

Therefore, Lohi Corp.'s expected capital gains yield over the next year is 0.48%.

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Lohi Corp.'s expected capital gains yield over the next year is 0.48%.

To determine the price of lohi corp., we need to calculate the present value of its future dividends. First, we estimate that the company will skip the next three annual dividends. This means that we will start receiving dividends from the fourth year. The first dividend to be paid is $1.00, and subsequent dividends will grow at a constant rate of 6 percent per year. The required rate of return on lohi corp. is 14 percent per year. This is the rate of return that investors expect to earn from investing in the company.

To calculate the price of Lohi Corp., we need to use the dividend discount model (DDM). The DDM formula is:

\(Price = Dividend / (Required rate of return - Dividend growth rate)\)

In this case, we know that Lohi Corp. will skip its next three annual dividends and then resume paying a dividend of $1.00. The dividend growth rate is 6% per year, and the required rate of return is 14% per year.

First, let's calculate the present value of the future dividends:

\(PV = (1 / (1 + Required rate of return))^1 + (1 / (1 + Required rate of return))^2 + (1 / (1 + Required rate of return))^3\)

\(PV = (1 / (1 + 0.14))^1 + (1 / (1 + 0.14))^2 + (1 / (1 + 0.14))^3\)

\(PV = 0.877 + 0.769 + 0.675\)

PV = 2.321

Next, let's calculate the price:

\(Price = (Dividend / (Required rate of return - Dividend growth rate)) + PV\)

\(Price = (1 / (0.14 - 0.06)) + 2.321\)

Price = (1 / 0.08) + 2.321

Price = 12.5

Therefore, the price of Lohi Corp. should be $12.50.

To calculate the expected capital gains yield over the next year, we need to use the formula:

\(Capital gains yield = (Dividend growth rate) / (Price)\)

\(Capital gins yied = 0.06 / 12.5\)

Capital gains yield = 0.0048

Convert to percentage:

Capital gains yield = 0.0048 * 100

Capital gains yield = 0.48%

Therefore, Lohi Corp.'s expected capital gains yield over the next year is 0.48%.

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