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Half of Maria's boxes were destroyed in a fire. She bought seven more boxes.
Write an expression to show how many boxes she started with, b.

The height of the building is calculated as; 14.725 m

We are given;

Horizontal component of velocity; vₓ = 6.45 m/s * cos 45 = 4.56 m/s

Horizontal distance from base of building = 10.3 m

Now,

Total time of flight = Horizontal distance ÷ Horizontal component of velocity

Total time of flight = 10.3  ÷ 4.56

Total time of flight = 2.259 sec.

Now;

Vertical component of velocity; v_y = 6.45 * sin 45  = 4.56 m/s

Time taken to reach maximum height = Vertical component of velocity  ÷ g = 4.56  ÷ 9.81 = 0.465 sec.

Time taken to reach ground from maximum height is;

= 2.259 - 0.465

= 1.794 sec.

Maximum height from ground = ¹/₂gt² = ¹/₂ * 9.81 * 1.794² = 15.786 m

Thus;

Maximum height from the top of building = 0.5 * 9.81 * 0.465² = 1.061 m

Total height of the building

= 15.786 - 1.061

= 14.725 m

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The length of ET and the length of RT to the nearest tenth will be 268.3 units and 198.7 units, respectively.

The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.

RECT is a square (not drawn to scale).

RA = 13² - 3x - 3  

AC = x(x + 2)

The diagonals of the square will be RC and ET. And "A" is the intersection point. Then the equation is given as,

RA = AC

13² - 3x - 3 = x(x + 2)

169 - 3x - 3 = x² + 2x

x² + 5x - 166 = 0

x = [- 5 ± √(5² - 4 × 1 × (-166))] / (2 × 1)

x = 10.62, -15.62

Then the length of AC is given as,

AC = 10.62 (10.62 + 2)

AC = 134.13 units

The diagonals of the square are congruent. Then we have

ET = RC

ET = 2 AC

ET = 2 x 134.13

ET = 268.3 units

Then the length RT is given as,

RT = ET / √2

RT = 198.7 units

The length of ET and the length of RT to the nearest tenth will be 268.3 units and 198.7 units, respectively.

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2 cos 35 sin 67 can be expressed as the sum of sin(102) and -sin(32).

To express 2 cos 35 sin 67 as a sum, we can use the trigonometric identity for the product of two sine or cosine functions.

Specifically, the identity states that 2 cos A sin B can be written as

sin(A + B) + sin(A - B).

Applying this identity, we have:

2 cos 35 sin 67 = sin(35 + 67) + sin(35 - 67)

Simplifying the expressions inside the sine functions:

sin(102) + sin(-32)

Since the sine function is an odd function,

sin(-x) = -sin(x),

so we can rewrite the equation as:

sin(102) - sin(32)

Therefore, 2 cos 35 sin 67 can be expressed as the sum of sin(102) and -sin(32).

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Answer:

your answer is correct.

Step-by-step explanation:

The resultant equation is 28x + 14 + 3 = -67 which could represent the first step of solving for x.

The equation is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are equal.

The equation is given in the question as follows:

7 (4x+2) + 3 = -67

We have to determine the resultant equation that could represent the first step of solving for x.

As per the question, we have

⇒ 7 (4x+2) + 3 = -67

Apply the distributive property of multiplication,

⇒ 7 × 4x + 7 × 2 + 3 = -67

⇒ 28x + 14 + 3 = -67

Therefore, the resultant equation will be 28x + 14 + 3 = -67.

Hence, the correct answer would be an option (D).

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Answer:

composite

Step-by-step explanation:

Answer:

50 is composite

Step-by-step explanation:

it is even:)

The ratio which is equivalent to 30:20 is option C, 3:2.

Suppose the  real measurements were "a" and "b"

Then their ratio will be formed as

\(\dfrac{a}{b} = \dfrac{p \times x}{q \times x} = \dfrac{p}{q}\)

where is a common factor (not 1)? This shows that to get the real measurements from the given ratio, we need to assume to have some factor possibly canceled from both the numerator and the denominator.

Thus, a = px, b = qx

We have given that a 2-column table has 2 rows. Column 1 is labeled

The Total with entries 30, and 15. Column 2 is labeled Red with entries 20, and 10.

Given ratio is 30:20

Or

3:2

Therefore, we can conclude that the ratio which is equivalent to 30:20 is option C, 3:2.

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Answer:

that my answer

brainlist me

The decimal calculation for Arturo's is 18.97, Bonnie's is 20.51, Courtney's is 31.42, Dawson's is 35.00.

Measurement is the process of assigning a numerical value to a physical quantity, such as length, weight, temperature, or time. Measurements are used to quantify and compare different aspects of the world around us, and they play a crucial role in many areas of science, engineering, and everyday life.

Measurements can be made using a variety of tools and techniques, ranging from simple rulers and scales to sophisticated scientific instruments. The accuracy and precision of a measurement depend on many factors, including the quality of the measuring instrument, the skill of the person making the measurement, and the conditions under which the measurement is taken.

In order for measurements to be meaningful and useful, they must be expressed in units that are well-defined and universally accepted. The International System of Units (SI) is the most widely used system of units in the world, and it is based on seven fundamental units of measurement, including the meter for length, the kilogram for mass, the second for time, and the kelvin for temperature.

Student           Measurement (yards)    Decimal Calculation

Arturo           6√28                            18.97

Bonnie           8√17                            20.51

Courtney   10π                            31.42

Dawson           3.5√100                    35.00

To calculate the decimals, we can use a calculator to evaluate the square roots and π, and then multiply by the given constant factor, and round the result to the nearest hundredth yard.

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The complete question is:

Since the y-intercept of the line is (0,1) and the line passes through the point (2,4) which is also satisfied by the equation of the line, the given equation represents the graph of the line.

The slope-intercept form of a line is y = mx +c where m is the slope of the line and c is the y-intercept.

The given equation of the line is y = (3/2)x + 1.

To find the y-intercept of the line, substitute x = 0 into the given equation,

y = (3/2)(0) + 1

y = 1

Note that the y-intercept of the graph of the line is also 1.

The graph of the line passes through points (2,4).

To verify whether the equation satisfies the coordinates of (2,4) or not, substitute the coordinates of the point into the given equation:

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

4 =4

The equation is true.

Hence, it can be said that the given equation represents the graph of the line.

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Answer:

I need more information

Step-by-step explanation:

Answer:

9x - 2x + 62 = 9x + 24

Number of correct answer each obtained = 19

Step-by-step explanation:

Given that:

Number of correct answers = x

POINTS for correct answers = 9

POINTS for incorrect answers = - 2

SCHOOL A:

Number of correct answers = x

Number of incorrect answers = x

Initial point = 62

Initial point + 9(number of correct answers) + - 2(number of incorrect answers)

62 + 9x - 2x

SCHOOL B :

Number of correct answers = x

Number of incorrect answers = 0

Initial point = 24

Initial point + 9(number of correct answers) + - 2(number of incorrect answers

24 + 9x

Since they end up tied :

School A = School B

62 + 9x - 2x = 24 + 9x

9x - 2x + 62 = 9x + 24

Number of correct answers gotten :

9x - 2x + 62 = 9x + 24

7x + 62 = 9x + 24

7x - 9x = 24 - 62

-2x = - 38

x = 19

Hence, Number of correct answers each obtained = 19

The equation is correct, and the value on both sides of the equation is 40.

To verify if the equation 90 × 4/9 = 40 is true, we can perform the calculation on both sides and compare the results.

On the left side of the equation:

90 × 4/9 = (90 × 4) / 9 = 360 / 9 = 40

On the right side of the equation:

40

Both sides of the equation evaluate to 40, which means they are equal. Therefore, the equation 90 × 4/9 = 40 is indeed true.

In summary, the equation is correct, and the value on both sides of the equation is 40.

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The following is deduced from the equation f(x)=(x - 1)^3 + 5

Horizontal shift: 1 left

Vertical shift: 5 down

Vertical stretch factor: 1

Vertical compression factor: 1

Axis of reflection: -x + 6

Domain: all real numbers

Range: all real numbers

Inflection Point: (1, 5)

The vertical stretch factor is a term used in mathematics to describe the transformation that changes the height of a graph while leaving the horizontal axis unchanged. In other words, it's a factor by which the y-values of a function are multiplied to produce a new, stretched or compressed version of the original graph.

The stretch factor is usually represented by the symbol "k". For example, if the equation of a function is y = f(x), then the equation of its vertically stretched image would be y = k * f(x). A positive value of k stretches the graph upward, while a negative value of k compresses the graph downward. If k > 1, the graph is stretched vertically; if 0 < k < 1, the graph is compressed vertically; if k = 1, the graph remains unchanged.

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Answer will be 27.

Given,

3√81

Now, to solve the expression the squares of whole numbers and square roots for some numbers must be known.

For example, squares of

1² = 1

2² = 4

3² = 9

4² = 16

5² = 25

6² = 36

7² = 49

8² = 64

9² = 81
10² = 100

Square roots,

√100 = 10

√81 = 9

√64 = 8

√49 = 7

√36 = 6

√25 = 5

√16 = 4

√9 = 3

√4 = 2

√1 = 1

Now ,

3√81 = 3× 9

= 27.

Thus the value is 27.

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The total value of the loan with quarterly compounded interest is approximately $45,288.38, while the total value of the loan with monthly compounded interest is approximately $45,634.84. The difference in total interest accrued is approximately $346.46.

Part A: To determine the total value of the loan with quarterly compounded interest, we can use the formula for compound interest:

A = P(1 + r/n)^(nt),

where:

A is the total value of the loan,

P is the principal amount (initial loan amount),

r is the interest rate (in decimal form),

n is the number of times interest is compounded per year,

and t is the number of years.

Given:

P = $20,000,

r = 9% or 0.09,

n = 4 (quarterly compounding),

t = 10 years.

Substituting the values into the formula, we have:

A = 20000(1 + 0.09/4)^(4*10).

Calculating this value, we find:

A ≈ $45,288.38.

Therefore, the total value of the loan with quarterly compounded interest is approximately $45,288.38.

Part B: To determine the total value of the loan with monthly compounded interest, we follow the same formula but with a different value for n:

n = 12 (monthly compounding).

Substituting the values into the formula, we have:

A = 20000(1 + 0.09/12)^(12*10).

Calculating this value, we find:

A ≈ $45,634.84.

Therefore, the total value of the loan with monthly compounded interest is approximately $45,634.84.

Part C: The difference between the total interest accrued on each loan can be calculated by subtracting the principal amount from the total value of each loan.

For the loan with quarterly compounding:

Total interest = Total value - Principal

Total interest = $45,288.38 - $20,000

Total interest ≈ $25,288.38.

For the loan with monthly compounding:

Total interest = Total value - Principal

Total interest = $45,634.84 - $20,000

Total interest ≈ $25,634.84.

The difference between the total interest accrued on each loan is approximately $346.46.

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Answer:

your answer would be 697

Answer:

answer below:)

Step-by-step explanation:

There are 5280 feet in one mile. So, half a mile is equal to 0.5 x 5280 = 2640 feet.

Answer:

384 cubic inches

Step-by-step explanation:

first find the volume of the fish tank by multipying the length, width, and height.

v=lwh

 =(16in)(4in)(12in)

 = 768 cubic inches (This answer is equal to the volume of the entire fish tank, however we need to find how much water half the tank can hold. To figure this out, we need to divide 768 by 2. And you should get 384 cubic inches)

Answer:

384

Step-by-step explanation:

took the quiz

Answer:

244.8

Step-by-step explanation:

If we divide a number by 10, we are moving the decimal place on value to the left.

The decimal place is currently here:

2448.000

So moving it left one gets us:

244.8000

Hope this helped!

We conclude that after 7/4 years the value of the jet ski is $4,784

The value of the jet ski is given by the exponential equation:

f(t) = 8,500*(0.72)^t

Where t is the time in years, to get the value of the jet ski after 7/4 years, we just need to evaluate the above function in t = 7/4, where evaluating means that we need to replace the variable t by the given number, then we will get:

f(7/4) = 8,500*(0.72)^(7/4) = 4,783.55

If now we need to round it to the nearest dollar, then we round upwards to 4,784

In this way, we conclude that after 7/4 years the value of the jet ski is $4,784

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The mean, median and range of the given data are respectively; 49, 48 and 3.

Formula for mean is;

Mean = Total sum/sample size

Total sum = 48 + 51 + 48 + 48 + 50

Total sum = 245

Sample size = 5

Mean = 245/5

Mean = 49

To get the median, we arrange in ascending order and pick the mid term.

48, 48, 48, 50, 51

Median is mid term which is 48.

Range is difference between highest and lowest term.

Range = 51 - 48

Range = 3

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Answer:

$7.5

Step-by-step explanation:

3/.4

Answer: 7

Step-by-step explanation:

The percentage of students who play a sport but do not like physical education = 16%

The correct answer is an option (B)

The complete two way frequency table for given situation would be,

                                                    Play a Sport  Do not Play a Sport    Total

Like Physical Education                    150                 72                          222

Do Not Like Physical Education        28                 164                         192

Total                                                    178                 236                        414

Now we find the percentage of students who play a sport, and  do not like physical education.

The total number of students who play sport.

n = 178

And the number of students who play a sport but do not like physical education are 28.

Using percentage formula, the required percentgae would be,

P = 28/178 × 100

P = 15.73%

P ≈ 16%

Therefore, the correct answer is an option (B)

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Find the complete question below.

Answer:

The answer is C: the ranges of g(x) and f(x) are the same, and their domains are also the same.

Step-by-step explanation:

Just took the test on edge!! :)

Option C The ranges of g(x) and f(x) are the same, and their domains are also the same is correct.

What is domain?

List of values of x an equation can satisfy is called Domain.

What is range?

List of values y the function can generate is called range

For example, f(x)=x

it can satisfy real domain i.e. x∈R

and range is R

g(x) = 3 x + 6 - 8 and f(x) = 3x

Domain for both the function is R

Both the function can satisfy all the real numbers, so its range is also R.

Therefore,Option C The ranges of g(x) and f(x) are the same, and their domains are also the same is correct.

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Answer:

Step-by-step explanation:

If we assume the length and width are integer numbers of centimeters, we can look at the factors of 330:

  330 = 1×330 = 2×165 = 3×110 = 5×66 = 6×55 = 10×33 = 11×30 = 15×22

The factors in this last pair differ by 7, so represent the width and length of the rectangle.

The rectangle's length and width are 22 cm and 15 cm, respectively.

The sec 132 degrees 15 minutes in degrees is approximately -1.638 degrees.

The secant function, denoted as sec(x), is a trigonometric function that is defined as the reciprocal of the cosine function, cos(x).

In other words,

sec(x) = 1 / cos(x)

The secant function is defined for all values of x except for those where the cosine function is equal to zero, which corresponds to the values x = (2n+1)π/2 where n is an integer. At these points, the secant function is undefined.

To convert sec(132 degrees 15 minutes) to degrees, we first need to convert the angle to decimal degrees.

We know that 1 degree is equal to 60 minutes, so 15 minutes is equal to 15/60 = 0.25 degrees.

Therefore, the angle 132 degrees 15 minutes is equal to 132 + 0.25 = 132.25 degrees.

Now we can find the secant of this angle:

sec(132.25 degrees) = 1/cos(132.25 degrees) ≈ -1.638

So the answer is approximately -1.638 degrees.

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Answer:

300 cm cubed or 300 cm^3

Step-by-step explanation:

(b x h ) / 2 = Area of triangle

5 x 12 = 60

60 / 2 = 30

Because it is a prism, the cross-sectional area is the same throughout the prism. Therefore, you just need to multiply the area by the height/width, which is 10cm.

30 x 10 = 300 cm cubedor 300 cm^3

Answer:

1/2BA*2+l*w

1/2*12*5*2+10*13+12*10+10*5

=360cm

a) The probability of a student living within walking distance of campus is 0.1521.

To find the probability of a student living within walking distance of the campus, we can use the formula for conditional probability:

P(A and B) = P(A) * P(B|A).

For this situation, An is "living within walking distance to campus" and B is "living with parents."

Thus, P(A and B) = (0.23)(0.67) + (0.06)(0.33) = 0.1521.

Hence, the probability of a student living within walking distance of campus is 0.1521.

b)  The probability given a student living within walking distance of campus they experience with their parents is 0.67.

To find the probability given a student day to day routines within walking distance to campus they experience with their parents, we can use the formula for conditional probability:

P(A|B) = P(A and B)/P(B).

In this situation, A is "living with parents" and B is "living within walking distance to campus."

Thus, P(A|B) = P(A and B)/P(B) = (0.23)(0.67)/0.1521 = 0.67.

Subsequently, the probability gave a student living within walking distance of campus experience with their parents is 0.67.

c) Living with parents and living within walking distance are independent events.

To decide whether living with parents and living within walking distance are independent events, we can analyze P(A|B) with P(A).

On the off chance that P(A|B) = P(A), the events are independent. For this situation, P(A|B) = 0.67 and P(A) = 0.67, so living with parents and living within walking distance are independent events.

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