A model rocket is launched with an initial upward velocity of 126. The rocket's height (in feet) after seconds is given by the following. Find all values of for which the rocket's height is 50 feet.

Anna is a sales person who has jobs this week in cities within North Carolina and South Carolina. On a map, these two cities are 50 centimeters apart. The map uses a scale of 2 centimeters = 4 kilometers. What is the actual distance between these cities?

Applying the Rule of Three that allows you to solve problems based on proportions.

Distance of the two cities= 50 cm

The map uses a scale of 2 centimeters = 4 kilometers.

Answer: The actual distance between these cities is 100 km

Answer: 0.876, 9.123

Step-by-step explanation:

The function is \(y=-x^2+10-8\)

It meets the ground level when \(y\) is 0

\(\Rightarrow -x^2+10x-8=0\\\Rightarrow x^2-10x+8=0\\\\\Rightarrow x=\dfrac{10\pm \sqrt{(-10)^2-4(1)(8)}}{2}\\\\\Rightarrow x=\dfrac{10\pm \sqrt{68}}{2}\\\\\Rightarrow x=5\pm \sqrt{17}\\\Rightarrow x=0.876,\ 9.123\)

Thus, it touches the ground at two points given above

The values of the constants m and c include the following:

m = -1.3

c = 7.1

In Mathematics and Geometry, the slope-intercept form of the equation of a straight line is given by this mathematical equation;

y = mx + c

Where:

Since the point P(-7, 2) is mapped onto P' (3, -11) by the reflection y = mx + c, we can write the following system of equations;

2 = -7m + c    ...equation 1.

-11 = 3m + c    ...equation 2.

By solving the system of equations simultaneously, we have:

2 = -7m - 3m - 11

11 + 2 = -10m

13 = -10m

m = -1.3

c = 7m + 2

c = 7(-1.3) + 2

c = -7.1

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Answer:

Probability that the difference in the mean BMI (men-women) for 45 women and 50 men selected independently and at random will exceed 2.1 = 0.2451

Step-by-step explanation:

The central limit theorem helps us to obtain the mean and the standard deviation of any sampling distribution.

Given that the sample was obtained from a normal distribution or an approximately normal distribution & it was obtained using random sampling techniques with each variable independent of one another and with each sample with adequate sample size,

Mean of sampling distribution (μₓ) = Population mean (μ)

Standard deviation of the sampling distribution = σₓ = (σ/√N)

where σ = population mean

N = Sample size

For the 45 women

μₓ = μ = 23.1

σₓ = (σ/√N) = (3.7/√45) = 0.552

For the 50 men

μₓ = μ = 24.7

σₓ = (σ/√N) = (3.3/√50) = 0.467

To find the probability that the difference in the mean BMI (men-women) for 45 women and 50 men selected independently and at random will exceed 2.1, we need to combine the distributions.

New distribution = (BMI of men) - (BMI of women) = x = X₁ - X₂

When independent distributions are combined, the combined mean and combined variance are given through the relation

Combined mean = Σ λᵢμᵢ

(summing all of the distributions in the manner that they are combined)

Combined variance = Σ λᵢ²σᵢ²

(summing all of the distributions in the manner that they are combined)

λ₁ = 1, λ₂ = -1

μ₁ = 24.7, μ₂ = 23.1

σ₁ = 0.467, σ₂ = 0.552

Combined mean = (Mean of men) - (Mean of women) = 24.7 - 23.1 = 1.6

Combined Variance = (1²×0.467²) + [(-1)²×(0.552²)] = 0.522793

Combined standard deviation = √0.522793 = 0.723

Probability that the difference in the mean BMI (men-women) for 45 women and 50 men selected independently and at random will exceed 2.1 = P(x > 2.1)

Note that the resulting distribution from the combination of distributions is still a normal distribution since the distributions combined were normal distributions too.

Hence, we first normalize or standardize 2.1

The standardized score for any value is the value minus the mean then divided by the standard deviation.

z = (x - μ)/σ = (2.1 - 1.6)/0.723 = 0.69

To determine the required probability

P(x > 2.1) = P(z > 0.69)

We'll use data from the normal distribution table for these probabilities

P(x > 2.1) = P(z > 0.69) = 1 - P(z ≤ 0.69)

= 1 - 0.7549

= 0.2451

Hope this Helps!!!

Answer:

hi

Step-by-step explanation:

Answer

Slope between two given points (1,3) and (2,7) is

m=  

2−1

7−3

​  

=4

Then perpendicular slope is m  

1

​  

=  

4

−1

​  

The line equation with this slope is given by

y=  

4

−1

​  

x+c.......(1)

Now, the above line passes through the point (−4,−3)

⇒−3=  

4

−1

​  

×(−4)+c

⇒c=−4

Therefore required line is 4y+x+16=0 (Substitute  

′

c  

′

 in (1) and simplify)

Answer:

1) The factors of  \(x^2-3x+2=0\) are \(\mathbf{(x-1)(x-2)=0}\)

Option C is correct.

3) The factors of  \(x^2+2x-8=0\) are \(\mathbf{(x-2)(x+4)=0}\)

Option B is correct.

Step-by-step explanation:

1) Factor : \(x^2-3x+2=0\)

For factoring we need to break the middle term, such that there sum is equal to middle term of expression and product is equal to product of first and last term.

The middle term : -3x

We can break them as (-2x)( -x)

Solving:

\(x^2-3x+2=0\\x^2-2x-x+2=0\\x(x-2)-1(x-2)=0\\(x-1)(x-2)=0\)

So, factors of  \(x^2-3x+2=0\) are \(\mathbf{(x-1)(x-2)=0}\)

Option C is correct.

3) Factor: \(x^2+2x-8=0\)

For factoring we need to break the middle term, such that there sum is equal to middle term of expression and product is equal to product of first and last term.

The middle term : 2x

We can break them as (4x)( -2x)

Solving

\(x^2+2x-8=0\\x^2+4x-2x-8=0\\x(x+4)-2(x+4)=0\\(x-2)(x+4)=0\)

So, factors of  \(x^2+2x-8=0\) are \(\mathbf{(x-2)(x+4)=0}\)

Option B is correct.

Answer:

\(134.56\)

Step-by-step explanation:

Break 11.6 into addenda.

\((11 + 0.6)\)

Apply the binomial expansion method.

\((11 + 0.6)(11 + 0.6)\)

\(11 {}^{2} = 121\)

\(2(11)(0.6) = 13.2\)

\(0.6 {}^{2} = 0.36\)

Add them all up and you get.

\(134.56\)

Answer:

209.25

Step-by-step explanation:

Calculate the areas of the triangle, rectangle, and half circle, then add them together:

triangle = 1/2bh = 1/2(6)(10) = 30

rectangle = bh = (14)(10) = 140

half circle = 1/2πr² = 1/2(3.14)(5)² = 39.25

radius = r = D/2 = 10/2 = 5

Total area = 30 + 140 + 39.25 = 209.25

Answer:

209.25 ft²

Step-by-step explanation:

To find the total area of the figure you have to add the areas of the triangle, rectangle and the semi circle.

Area of the triangle.

\( \sf \: A = \frac{1}{2} \times base \times height \\ \sf \: A = \frac{1}{2} \times 6 \: ft \times10 \: ft \\ \sf \: A = \frac{1}{2} \times 60 \: {ft}^{2} \\ \sf \: A =30 \: {ft}^{2} \)

Area of the rectangle.

\(\sf \: A =length \times width \\ \sf \: A =14 \: ft \times 10 \: ft \\ \sf A =140 \: {ft}^{2} \)

Area of the semi circle.

\( \sf \: A = \frac{1}{2} \pi {r}^{2} \\ \sf \: A = \frac{1}{2} \times \pi \times ( \frac{10}{2}) ^{2} \\ \sf \: A = \frac{1}{2} \times \pi \times {5}^{2} \\ \sf \: A = \frac{1}{2} \times \pi \times 25 \\ \sf \: A = \frac{1}{2} \times 3.14 \times 25 \\ \sf \: A = \frac{1}{2} \times 78.5 \\ \sf \: A = 39.25 {ft}^{2} \)

Add up all the areas to find the total area.

\( \sf \: Total \: Area = 30 {ft}^{2} + 140 {ft}^{2} + 39.25 {ft}^{2} \\ = 209.25 {ft}^{2} \)

The equation for the line of best fit from the given data, will be y = 2.12 x + 4.42.

The line of best fit would be the line that has an equal number of points above it, as the number of points beneath it.

Going by this definition, two points that would be on the line are (6, 17) and ( 7, 19 ).

The slope of this line would be:

= ( Y2 - Y1 ) / ( X 2 - X1)

= ( 19 - 17 ) / (7 - 6 )

= 2.12

The y intercept would be:

y = mx + c

19 = 2.12 (7 ) + c

c = 4.42

The equation of the  line of best fit is then :
y = 2.12 x + 4.42

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we need to substitute t=5

The George's height after 5 seconds was 960

28. t = I / (Pr)

29. y = -(3x / 5) + (15 / 5)

30. y = -3/5 x + 3

31. y = -3/5 * -1 + 3 = 3 + 3/5 = 3.6

32. 2 tablespoons per serving

33. $0.92 per slice

34. 5 tablespoons

35. 45% (159 / 350 = 0.45 and 0.45 * 100 = 45)

Simple interest is a method of calculating the interest charge on a loan or deposit based on a constant interest rate and the original principal amount. The formula for simple interest is I = Prt, where P is the principal amount, r is the interest rate as a decimal, t is the time period in years, and I is the interest amount. In simple interest, the interest amount is calculated only on the original principal, not on any accumulated interest from prior periods.

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Answer:

dose in MCG = 10.2 mcg

Total volume to be sent home = 1.836 ml (1836μl)

Step-by-step explanation:

weight of patient = 680g

dosage in mcg of medication = 15mcg/kg

This means that

for every 1kg weight, 15mcg is given,

since 1kg = 1000g, we can also say that for every 1000g weigh, 15mcg is given.

1000g = 15mcg

1g = 15/1000 mcg = 0.015 mcg

∴ 680g = 0.015 × 680 = 10.2 mcg

Dosage in MCG = 10.2 mcg

Next, we are also told ever ml volume of the drug contains 50 mcg weight of the drug (50mcg/ml). This can also be written as:

50mcg = 1 ml

1 mcg = 1/50 ml = 0.02 ml

∴ 10.2 mcg = 10.2 × 0.02 = 0.204 ml

since the medication is to be taken TID (three times daily) for 3 days, the total number of times the drug is to be taken = 9 times.

therefore, the total volume required = 0.204 × 9 = 1.836 ml (1836 μl)

The equation which describes the relationship between the side length and shaded area of the quilt is y=0.5x²

Side length, x = 1,3,4,5,8

Shaded Area, y = 0.5, 4.5, 8, 12.5, 32

The relationship can be modeled as a quadratic function. Using a graphing calculator for the quadratic function written in the form y = ax² + bx + c

a = 0.5 ; b = 0 ; c = 0

Therefore, the quadratic function can be written as y = 0.5x²

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Navern's manufacturing cycle efficiency (MCE) for its elevators is: 41.4%

The formula for obtaining the manufacturing cycle efficiency is value-added time divided by the production cycle time * 100. In the data given, the process and inspection times qualify as a value-added time

Process time = 23 days

Inspection time = 13 days

Value added time = 23 + 13 = 36days

The production cycle time = Move time + process time + queue time + inspection time + wait time

= 22 + 12 + 23 + 13 + 17 days

= 87 days

So, the manufacturing efficiency time = 36/87 * 100

= 41.4%

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To simplify the expression (2x-3)(5x^2-2x+7), we can use the distributive property.

First, multiply 2x by each term inside the second parentheses:

2x * 5x^2 = 10x^3

2x * -2x = -4x^2

2x * 7 = 14x

Next, multiply -3 by each term inside the second parentheses:

-3 * 5x^2 = -15x^2

-3 * -2x = 6x

-3 * 7 = -21

Combine all the resulting terms:

10x^3 - 4x^2 + 14x - 15x^2 + 6x - 21

Now, combine like terms:

10x^3 - 19x^2 + 20x - 21

So, the simplified expression is 10x^3 - 19x^2 + 20x - 21.

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By using  Matrix method it denotes that the equations are consistent and have a single solution.

Matrix method, we will use the formula, \(X=A^{-1} B\) where,

\(\[{\rm{X}} = \left[ {\begin{array}{*{20}{l}}x\\y\\z\end{array}} \right]\]\)

\(\[{A^{ - 1}} = \frac{{adjA}}{{|A|}}\]\)

\(\[{\rm{B}} = \left[ {\begin{array}{*{20}{c}}{33}\\{ - 26}\\{23}\end{array}} \right]\]\)

So, we will have to find \(A^{-1}\), for that, we will first find the determinant of matrix A, that is |A|, then we will find the cofactors of matrix A, take its transpose, and that will be Adj A.

Therefore, we will be able to get the inverse of matrix A using

\(A^{-1}\) =Adj A|A|

and hence We then substitute all the obtained values of \(A^{-1}\) and B in the main formula and do necessary calculations to get the value of x, y and z accordingly.

Complete step-by-step answer:

It is given in the question that, we have to solve the system of equations,

2x-y+4z=33

X+2y-3z=−26

-5x−3y+5z=23

Applying the matrix approach.

Therefore, the first step is to convert the supplied equations into matrix form. Thus, it can be expressed as follows.

\(\[\left[ {\begin{array}{*{20}{c}}2&{ - 1}&4\\1&2&{ - 3}\\{ - 5}&{ - 3}&5\end{array}} \right]\left[ {\begin{array}{*{20}{l}}x\\y\\z\end{array}} \right]\]\[\)\(= \left[ {\begin{array}{*{20}{c}}{33}\\{ - 26}\\{23}\end{array}} \right]\)

\(\[|{\rm{A}}| = \left[ {\begin{array}{*{20}{c}}2&{ - 1}&4\\1&2&{ - 3}\\{ - 5}&{ - 3}&5\end{array}} \right]\]\)

= 2(10+9) + 1(5-15) + 4(-3+10)

= 38-10+28

=56

Since we have |A|≠0.

Hence, it denotes that the equations are consistent and have a single solution.

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Step-by-step explanation:

a probability is always the ratio

desired cases / totally possible cases

let's relist the 10 names, as there was some "mixing" going on in your text :

Dorothy

Anthony

Harold

Margaret

Tiffany

Nancy

Angela

Paul

Patrick

Jeremy

so, whatever happens, the totally possible cases are 10 (as we are only taking about these 10 names, no other name can suddenly appear in all the scenarios).

in each scenario one student is randomly chosen.

a) the probabilty to pick a student with name ending "k".

we look through the list and find only 1 student, whose name ends with "k" : Patrick.

that means the number of desired cases is 1.

and the probabilty is therefore

1/10 = 0.1

b) the probability to pick a student with name beginning "C".

we look and look and look. none of the 10 names start with a "C".

that means the number of desired cases is 0.

and the probabilty is

0/10 = 0

c) the probability that the name of the picked student contains "m" or "M".

we find 2 names : Margaret and Jeremy.

that means that the number of desired cases is 2.

and the probabilty is therefore

2/10 = 1/5 = 0.2

d) in how many ways can we pick 7 elements out of 10, when the sequence of the pulled 7 elements does not matter (e.g. ... Nancy, Paul ... is the same as ... Paul, Nancy, ...). and no student can be pulled more than once (no repetitions).

that means we have to calculate the combinations of 7 items out of 10 without repetition :

C(10, 7) = 10! / (7! × (10-7)!) = 10! / (7! × 3!) =

= 10×9×8 / (3×2) = 5×3×8 = 120

there are 120 possibilities to build the math club.

e) now we pick 4 students out of 10. but as we give them prices based on ranking, the sequence matters (e.g. Nacy first, Paul second is different to Paul first, Nancy second).

but we still have no repetition, as nobody can win more than one price.

that means we need to calculate the permutations of 4 items out of 10 without repetition :

P(10, 4) = 10! / (10-4)! = 10! / 6! = 10×9×8×7 = 5,040

there are 5040 different ways to distribute the 4 prices among the 10 students.

Step-by-step explanation:

6.5%÷100×277

=13×277÷20

=180.05

=180

Answer:

r = 15

Step-by-step explanation:

That's my answer hope it helps brainliest my answer please that's correct

Answer:

r=15

Step-by-step explanation:

hope it helps you bro

Answer:

Standard complex form 3/13 + 11/13i

Step-by-step explanation:

not sure  if this helps

The volume of the rectangular pyramid is 64 cubic feet.

A pyramid with a rectangular base is known as a rectangle pyramid. When viewed from the bottom, this pyramid seems to be a rectangle. As a result, the base has two equal parallel sides.

The apex, which is located at the summit of the pyramid's base, serves as its crown. Right or oblique pyramids can be seen in rectangular shapes. If it is a right rectangular pyramid, the peak will be directly over the base's center; if it is an oblique rectangular pyramid, the apex will be angled away from the base's center.

The volume of a rectangular pyramid is given as:

V = (l)(b)(h) / 3

V = (6)(8)(4) / 3

V = 192 / 3

V = 64 cubic feet.

Hence, the volume of the rectangular pyramid is 64 cubic feet.

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The correct question is:

Discuss measures that can be taken to develop the spirit of hard work

The value of \(log_35 \times log_{25}9\) is 1.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

\(log_35 \times log_{25}9\)

\(log_ab = \frac{logb}{loga}\)

So,

= log 5 / log 3 x log 9 / log 25

= log 5 / log 3 x log 3² / log 5²

\(logm^n = n~logm\)

So,

= log 5 / log 3 x log 3² / log 5²

= (log 5 / log 3) x (2 log 3 / 2 log 5)

= (log 5 / log 3) x (log 3 / log 5)

= 1

Thus,

1 is the value.

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Answer:

a

Step-by-step explanation:

Answer:

C, the only info for the question is about yourself which is a survery question

Step-by-step explanation:

The asterisk (*) represents the vertex of the angle, the initial side is the positive x-axis, and the terminal side is the red line segment that forms an angle of 8/3 π with the positive x-axis.

What is the standard position of angles?

Standard position simply means that the vertex of the angle is at the origin of the circle and that one ray of the angle is on the positive x-axis. The other ray of the angle is placed at the angle measure formed by traveling counter-clockwise along the circle.

To draw an angle in standard position with measure 8/3 π, follow these steps:

Start with the positive x-axis.

Counterclockwise, rotate the initial side of the angle until it coincides with the positive x-axis.

Starting from the initial side on the positive x-axis, rotate the terminal side of the angle in a counterclockwise direction until the angle measures 8/3 π.

The resulting angle will have a measure of 8/3 π and will look like the following:

       |

       |

--------*-----------

       |

       |

Here, the asterisk (*) represents the vertex of the angle, the initial side is the positive x-axis, and the terminal side is the red line segment that forms an angle of 8/3 π with the positive x-axis.

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The quantity of each colour beads that are in the necklace include the following:

Purple beads = 56

Purple beads = 56silver beads = 24

A ratio is defined as the mathematical expression that shows the number of times one value is contained in another value.

The number of purple beads = 14

The number of silver beads ,= 6

The total quantity of beads = 80

Therefore the total combination = 14+6 = 20

For purple beads = 14/20 × 80/1

= 1120/20 = 56

For silver beads = 6/20×80/1

= 480/20= 24

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The formula to calculate the confidence interval is

Where

We can calculate the sample proportion by

The parameters are

Using an online calculator, the z-score for a 90% confidence interval is 1.645.

Therefore, we can calculate P to be:

Hence, we can calculate calculate the confidence interval by substituting the values

Therefore, the lower limit of the confidence interval is

The lower limit of the confidence interval is 1.6072

Therefore, the upper limit of the confidence interval is

Therefore, the upper limit of the confidence interval is 1.6828

Answer:

To find the total distance, we need to add up the distance the student ran in the first 5 days and the distance the student ran in the next 5 days.

Distance for the first 5 days = 3 1/2 miles/day × 5 days = 17.5 miles

Distance for the next 5 days = 4 1/4 miles/day × 5 days = 21.25 miles

Total distance = Distance for the first 5 days + Distance for the next 5 days

Total distance = 17.5 miles + 21.25 miles

Total distance = 38.75 miles

Therefore, the student ran a total of 38.75 miles during these 10 days.

Answer:

1.056

Step-by-step explanation:

Because 2 4/5+ 3/5= 3 1/5

3 1/5 as a decimal is, 3.2

3.2× .33= 1.056

Answer:

3

Step-by-step explanation:

Answer:

3

Step-by-step explanation: