A quarterback rushed 32 yards in one game. What is the number of feet the quarterback rushed in one game

The solution to the linear system is c = -6 and d = 3.

To solve the linear system using the elimination strategy, we can eliminate one variable by adding or subtracting the equations. Let's solve the first linear system:

(1) 12c + 28d = 12

(2) -20c + 16d = 168

To eliminate one variable, we can multiply equation (1) by 5 and equation (2) by 3, which will result in opposite coefficients for 'c'. This will allow us to eliminate 'c' when adding the equations together:

(1) 60c + 140d = 60

(2) -60c + 48d = 504

Now, we can add the equations:

(60c + 140d) + (-60c + 48d) = 60 + 504

188d = 564

d = 564/188

d = 3

Substituting the value of 'd' back into equation (1):

12c + 28(3) = 12

12c + 84 = 12

12c = 12 - 84

12c = -72

c = -72/12

c = -6

The solution to the linear system is c = -6 and d = 3.

Now let's analyze the second linear system:

(1) 7x - 3y = 43

(2) 7x - 3y = 13

By comparing the two equations, we can see that they have the same coefficients for both 'x' and 'y', and the constant terms on the right side are different. This means the lines represented by the equations are parallel and will never intersect.

The linear system has no solution.

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9514 1404 393

Answer:

  A.  3

Step-by-step explanation:

"3 percent tip" means the tip is 3% of the cost of whatever product or service is being tipped. The tip is 3% of the cost of the pizza.

Answer:

\(\Huge \boxed{\boxed{\bf{Volume = 848.23 cm^3}}}\)

Step-by-step explanation:

To calculate the volume of a cone with a height of 10 cm and a diameter of 18 cm, we can use the formula:

\(\LARGE \boxed{\tt{V = \frac{1}{3} \times \pi \times r^2 \times h}}\)

➤V = volume

➤r = radius

➤h = height

Since the diameter is 18 cm, the radius is half of that, which is 9 cm. Now, we can plug in the values:

The volume of the cone is \(\tt{270\pi \approx 848.23 \texttt{ cm}^3}\)

__________________________________________________________

Answer:

7^15

Step-by-step explanation:

7^5^3 = 7^(5*3) = 7^15

Answer:

b

Step-by-step explanation:

Answer:

B

Step-by-step explanation: I took it on a test and got it right

Answer:

a. 0.52 = 52% probability that Linda gives the correct answer to a question.

b. 0.7692 = 76.92% probability that Linda knows the answer

Step-by-step explanation:

Conditional Probability

We use the conditional probability formula to solve this question. It is

\(P(B|A) = \frac{P(A \cap B)}{P(A)}\)

In which

P(B|A) is the probability of event B happening, given that A happened.

\(P(A \cap B)\) is the probability of both A and B happening.

P(A) is the probability of A happening.

In this question:

Event A: Supplies the correct answer:

Event B: Knows the answer

A. What is the probability that Linda gives the correct answer to a question?

0.4(knows the answer)

1/5 = 0.2 of 1 - 0.4 = 0.6(guesses the answer). So

\(P(A) = 0.4 + 0.2*0.6 = 0.52\)

0.52 = 52% probability that Linda gives the correct answer to a question.

B. What is the conditional probability that Linda knows the answer, given that she supplies the correct answer?

Intersection of events A and B is knowing the answer and giving the correct answer, which means that \(P(A \cap B) = 0.4\)

The desired probability is:

\(P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{0.4}{0.52} = 0.7692\)

0.7692 = 76.92% probability that Linda knows the answer

Answer:

A) 10

Step-by-step explanation:

3(8)(5) / 6(2) = 120/12 which equals 10

Answer: A = 10

Step-by-step explanation:

substitute the value of the variable into the equation and simplify

Hope this helps !

Answer:

Step-by-step explanation:

Let,

The req. number be = x

So,

Two - thirds of the number

\( = \frac{2}{3} x\)

Then, it is reduced by 13

\( = \frac{2}{3} x - 13\)

After that,

The req. result we get is = 7

Therefore,

By the problem,

\( = > \frac{2}{3} x - 13 = 7\)

\( = > \frac{2}{3} x = 7 + 13\)

\( = > \frac{2}{3}x = 20\)

\( = > \frac{2}{3} x \times \frac{3}{2} = 20 \times \frac{3}{2} \)

=> x = 30

Hence,

The req. number is 30.

Given that :

To Find :

Solution :

Let's assume the number as x

According to the question :

\(\qquad \sf \: { \dashrightarrow \dfrac{2}{3}x - 13 = 7 }\)

Adding 13 to both sides we get :

\(\qquad \sf \: { \dashrightarrow \dfrac{2}{3}x - 13 + 13 = 7 + 13 }\)

\(\qquad \sf \: { \dashrightarrow \dfrac{2}{3}x = 20 }\)

Now, Multiplying both sides by \( \dfrac{3}{2} \) we get :

\(\qquad \sf \: { \dashrightarrow \dfrac{2}{3}x \times \dfrac{3}{2} = 20 \times \dfrac{3}{2} }\)

\(\qquad \sf \: { \dashrightarrow \dfrac{ \cancel2}{ \cancel3}x \times \dfrac{{ \cancel3}}{ \cancel{2}} = \cancel{20} \times \dfrac{3}{ \cancel{2}} }\)

\(\qquad \sf \: { \dashrightarrow x = 10 \times {3} }\)

\(\qquad \bf \: { \dashrightarrow x = 30 }\)

Therefore, The number is 30.

Answer:

Step-by-step explanation:

To find the equation for the nth term in the sequence, we need to determine the pattern or rule that generates the sequence.

From the given information, we can see that the sequence is not arithmetic because the differences between consecutive terms are not constant. Instead, the sequence appears to be quadratic because the second difference between consecutive terms is constant.

Using the given values of a₁, a₃, and a₅, we can find the first few differences:

a₃ - a₁ = 4 - (-6) = 10

a₅ - a₃ = 14 - 4 = 10

So, the first difference is 10, which indicates a linear term in the equation for an. We can now use the given value of a₁ and the first difference to find the constant term in the quadratic equation. Let d be the common difference, then we have:

a₂ = a₁ + d = -6 + 10 = 4

a₄ = a₃ + d = 4 + 10 = 14

a₆ = a₅ + d = 14 + 10 = 24 - 1

a₇ = a₆ + d = 24 - 1 + 10 = 33

Now, we can find the second difference between consecutive terms:

a₄ - 2a₃ + a₂ = 14 - 2(4) + (-6) = 0

a₆ - 2a₅ + a₄ = 19 - 2(14) + 4 = -5

a₇ - 2a₆ + a₅ = 33 - 2(19) + 14 = 9

Since the second difference is constant (-5), this confirms that the sequence has a quadratic term in its equation. Let's assume the equation for the nth term is:

an = an² + bn + c

Substituting the values we know, we get three equations:

a₁ = a₁² + b₁ + c --> -6 = c

a₃ = a₃² + b₃ + c --> 4 = 9a + b + c

a₅ = a₅² + b₅ + c --> 14 = 25a + 5b + c

Solving this system of equations, we get:

a = 1/2, b = 19/2, and c = -6

Therefore, the equation for the nth term in the sequence is:

an = (1/2)n² + (19/2)n - 6.

Force is a vector quantity, and a force can be resolved into its components to get the effect of the force.

The responses are;

Reasons:

a) The force with which the person is pulling the railroad car, F = 310 N

The vector force on the rope \(\vec {v}_{rope}\) = 310 × cos(25°)·i + 310 × sin(25°)·j

Which gives;

The component of the vector acting along the railroad, towards the right is the i component

Therefore, the force the person exerts toward the right while trying to move the car is approximately

b) The direction of the rope of the second person, θ = 18°

The force required to get the railroad car moving = 620 N

The force the second person has to exert to the right is therefore;

F × cos(18°) = 620 - 310 × cos(25°)

Therefore;

\(\displaystyle F = \mathbf{\frac{620 - 310 \times cos(25^{\circ})}{ cos(18^{\circ})}} \approx 356.49\)

The force the second person must exert in the given direction, is therefore;

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The depth of the aquarium is approximately 4 feet when rounded to the nearest whole number (since 3.64 is closer to 4 than it is to 3 when rounded to the nearest whole number).

To calculate the depth of the aquarium, we need to use the formula for volume of a rectangular prism,

which is V = lwh where V is the volume, l is the length, w is the width, and h is the height (or depth, in this case).

Given that the aquarium holds 11.35 cubic feet of water, the volume of the aquarium can be represented by V = 11.35 cubic feet.We are also given that the length of the aquarium is 2.6 feet and the width is 1.1 feet.

Substituting these values into the formula for volume,

we get:11.35 = 2.6 × 1.1 × h

Simplifying this expression:

11.35 = 2.86h

Dividing both sides by 2.6 × 1.1,

we get:h ≈ 3.64 feet (rounded to two decimal places)

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Answer:

Step-by-step explanation:

We know that:

Solution:

Now, let's re-organize the second equation into slope intercept form.

Hence, the two equations in slope intercept form are:

Answer:

78.59$

Step-by-step explanation:

Therefore, the mean weight is 57.97 kg. Therefore, the median weight is 57.5 kg. Therefore, there is no mode in this data set. Therefore, the standard deviation of the weights is 9.1654 kg. Therefore, the variance of the weights is 84.0169 kg². Therefore, the coefficient of variation of the weights is 15.80%.

Statistics is a branch of mathematics that deals with the collection, analysis, interpretation, presentation, and organization of data. It involves designing experiments and surveys to collect data, summarizing and describing data using numerical and graphical methods, and drawing conclusions or making predictions based on the data.

Here,

a) Mean:

The formula for the mean (also called the average) is:

mean = (sum of all the values) / (number of values)

So, we add up all the weights and divide by 30:

mean = (57+52+60+53+45+75+60+55+58+53+52+86+45+80+65+46+85+70+65+82+46+50+40+50+56+43+62+47+56+75) / 30

mean = 57.97 (rounded to two decimal places)

b) Median:

To find the median, we need to first arrange the weights in order from smallest to largest:

40, 43, 45, 45, 46, 46, 47, 50, 50, 52, 52, 53, 53, 55, 56, 56, 57, 58, 60, 60, 62, 65, 65, 70, 75, 75, 80, 82, 85, 86

There are 30 values, so the median is the middle value. Since there are an even number of values, we take the average of the two middle values:

median = (57 + 58) / 2

median = 57.5

c) Mode:

The mode is the value that occurs most frequently in the data. In this case, we can see that there is no value that occurs more than once.

d) Range:

The range is the difference between the largest and smallest values in the data set. The smallest value is 40, and the largest value is 86, so:

range = largest value - smallest value

range = 86 - 40

range = 46

e) Standard deviation: The formula for the standard deviation is:

standard deviation:

= √((sum of (each value minus the mean)²) / (number of values - 1))

We already calculated the mean in part (a), so we can use it here. First, we need to calculate the sum of (each value minus the mean) squared:

(57-57.97)² + (52-57.97)² + ... + (75-57.97)²

= 2426.3100

Then, we plug in the values into the formula:

standard deviation = √(2426.3100 / (30-1))

standard deviation = √(84.0169)

standard deviation = 9.1654 (rounded to four decimal places)

f) Variance:

The variance is the square of the standard deviation:

variance = standard deviation²

variance = 9.1654²

variance = 84.0169

g) Coefficient of variation:

The coefficient of variation is a measure of relative variability, defined as the standard deviation divided by the mean, expressed as a percentage:

coefficient of variation = (standard deviation / mean) x 100%

coefficient of variation = (9.1654 / 57.97) x 100%

coefficient of variation = 15.80% (rounded to two decimal places)

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After answering the given query, we can state that The expression for the difference between a number s and -6 is: s - (-6) or s + 6

In numbers, you can multiply, split, add, or take away. The following is how a phrase is made together: Numeric number, expression, and arithmetic operator The elements of a mathematical expression are integers, factors, and functions.   It is feasible to use contrasting words and terms. Any mathematical declaration containing variables, integers, and a mathematical action between them is known as an expression, also known as an algebraic expression. As an example, the expression 4m + 5 is composed of the expressions 4m and 5, as well as the variable m from the provided equation, which are all separated by the mathematical symbol +.

The expression for the difference between a number s and -6 is:

s - (-6)

or

s + 6

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The satay in of a line is written as y = slope(x) + y intercept.

In the given equation the y-intercept is -1

The graph of the function is:

From this, we can conclude that the polynomial has three turning points

Function graph that has y- intercept of 3 is g(x) = 3\((\frac{1}{4}) ^{x}\).

y- intercept will be 3 when we will put value of x = 0 and y will be 3 that graph will have y intercept 3

A) h(x) = 5\((2)^{x}\)

when x = 0

Any number with zero power is always 1

h(x) = 5

B) h(x) = 5\((0.5)^{x}\) + 0.5

when x = 0

h(x) = 5 + 0.5

h(x) = 5.5

C) g(x) = 3\((\frac{1}{4}) ^{x}\)

when x = 0

g(x) = 3

Here we get y intercept as 3.

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Remember to make use of the grid paper to maintain accuracy and proportionality across all four views.

Certainly! Below is a verbal description of how you can draw the four different views of the object on square grid paper:

Left View: Start by drawing the left side of the object as you would see it from a leftward perspective.

Capture its shape, height, and any visible features. Use the grid lines to maintain proportion and accuracy.

Back View: Move to the back of the object and draw what you see from that viewpoint.

Focus on its rear-facing details, contours, and any distinguishing characteristics. Utilize the grid paper to ensure proper alignment.

Front View: Now, face the object directly and draw its front view. Pay attention to its overall shape, dimensions, and any frontal features or patterns.

Utilize the grid lines to maintain symmetry and precision.

Right View: Finally, position yourself on the right side of the object and draw its appearance from that angle.

Portray the right-facing side, capturing its unique attributes and maintaining consistency with the previous views.

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Answer:

  a) 3/4

  b) 3/4

  c) 3/4

  d) all are 3/4

Step-by-step explanation:

The slope of a line is defined as the change in y divided by the change in x. This is often referred to as "rise over run":

  slope = Δy/Δx = "rise"/"run"

The triangles are drawn against the line so that you can use them to identify values of "rise" (vertical change) and "run" (horizontal change) between two points on the line.

__

The slope of the segment AC is found by dividing the "rise" (BC = 3) by the "run"(AB = 4)

  slope of AC = BC/AB = 3/4

__

The slope of FH is similarly computed. Here, it is made a little more difficult, because you must estimate the value of GH.

 slope of FH = GH/FG = 1.5/2 = 0.75 = 3/4

__

The slope of CE is ...

  slope of CE = DE/CD = 6/8 = 3/4

__

The slopes in a), b), c) are all 3/4.

You can reasonably draw the conclusion that the slope of a line is the same everywhere. A line has constant slope.

Answer:

  207/1000

Step-by-step explanation:

The symbol % is effectively equivalent to /100.

  20.7% = 20.7/100 = 207/1000

207 has no factors that are 2 or 5, so this fraction cannot be reduced.

Hello !

(9 + x)/2 = (7 + 3 + x)/3

3(9 + x) =2(7 + 3 + x)

27 + 3x = 14 + 6 + 2x

27 + 3x = 20 + 2x

27 - 20 = 2x - 3x

7 = -x

x = -7

you can check it works for the 2 averages

Answer:C

Step-by-step explanation:

A.Is correct since 40 plus 8.032 is 48.031 (Check Your selves)

B.Is correct since 48 ones = 48 and 31 thousandths =0.31

C.Is Wrong since 48(Well is correct )plus 0.31 not 0.031,not 31 thousandths.

D.Correct since 40 plus 8=48 and 0.03+0.0001 is 0.031.

Hope this helped!

If you are reading this hope you have a wonderful day and may your dreams come true!

Tell me if its wrong

lfu29

It's C. 48+0.31. because it's not the same

114 is 95% of 120

100% of 120 is 120, therefore 95 percent of 120 equals 114. To learn how to solve 114 is 95 percent of what number, see the step-by-step instructions below.

114 is 95 Percent of What Number?

Formula = Number x 100

Percent = 114 x 100

95 = 120

The following shows the steps to derive this formula and find out 95% of the number is 114.

Step 1: If 95% of a number is 114, then what is 100% of that number? Set up the equation.

114

95% = Y

100%

Step 2: Solve for Y

Using cross multiplication of two fractions, we get

95Y = 114 x 100

95Y = 11400

Y = 11400

100 = 120