A mover in a moving truck is using a rope to pull a 424 lb box up a ramp that has an incline of 22°. What is the force needed to hold the box in a stationary position to prevent the box from sliding down the ramp?

Answer:

$2000

Step-by-step explanation:

Simple Interest = $70

Rate = 3.5%

Time = 1

Principal = ?

Simple Interest = (Principal × Rate × Time)/100

Principal = (Simple Interest × 100)/(Rate × Time)

Principal = (70 × 100)/(3.5 × 1)

Principal = 7000/3.5

Principal = 14000/7

Principal = 2000

Answer:

mean = 5+9+9+6+6+11+8+4/7 = 8.29

median = 6

mode = 6

range = 11 - 4 = 7

Answer:

Step-by-step explanation:

5 , 9 , 6 , 6 , 11 , 8 , 4

Mean = sum of all data ÷ number of data

         [tex]= \frac{5+9+6+6+11+8+4}{7}\\\\= \frac{49}{7}\\\\= 7[/tex]

Median: To find median, arrange in ascending order and medianis the middle term

4 , 5 , 6 , 6 , 8 , 9 , 11

Middle term = 4th term

Median = 6

Mode: a number that appears most often is mode

6 appears 2 times

Mode = 6

Range:

Range = maximum value - minimum value

          = 11 - 4

          = 7

Answer:

if x is 16 then 3/4(16) - 12

when you simplify 4 by 16

3(4)-12

12-12=0

Answer:

Hi! The answer to your question is B) He can walk 12 miles in 1 minute.

To find Unit rate divide the biggest number by the smallest; Example: [tex]120/10[/tex]

Step-by-step explanation:

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Answer:

The A matches the table x+3

The sewing kits bought by Ms, Clark is 17 in number.

The equation model is defined as the model of the given situation in the form of an equation using variables and constants.

Here,

As given in the question, Ms. Clark spent $89.85 on sewing kits that cost $5 each plus $4.85 tax on the total bill.

Let the number of sewing kits be x,
According to the question,
5x + 4.85 = 89.85
5x = 89.85 - 4.85
5x = 85
x = 17

Thus, the sewing kits bought by Ms, Clark is 17 in number.

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Answer:

Rotation about 180*

Translation about 7 units to the right and 8 down

Step-by-step explanation:

Answer:  h < 6

Step-by-step explanation:

3h - 5 < 13

3h < 18

h < 6

Answer:

h<6

Step-by-step explanation:

Answer:

80 minutes.

Step-by-step explanation:

do I need to explain? I hate explaining :(

Answer:

3

Step-by-step explanation:

3x2 +x −14 = 0 12 −4(3)(−14) = 1+168 =169 = 132

The roots of 3x² + x = 14 are real, irrational and unequal

A quadratic equation is a second-order polynomial equation in a single variable x, ax² + bx +c=0 with a ≠ 0 .

Given equation is :

3x² + x = 14

3x² + x - 14=0

we have, a=3, b=1 c=-14

D= b²-4ac

  = 1²-4*3*(-14)

  = 1+168

  = 169

As, D>0

Hence, the roots are real.

Now,

x= -b±√b²-4ac/2a

 = -1±√169/2*3

 =-1±13/6

x= -1-13/6  and x= -1+13/6

x= -7/3  and x= 12/6=2

Hence, the roots are real, irrational and unequal.

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Answer:

Step-by-step explanation:

The Residual for an observed value of (2, 402) is -4.

The regression analysis and the least squares regression line was found to be ŷ = 400 3x.

The observed value is (2, 402).To find the residual for an observed value of (2, 402),

we need to use the formula for residual

Residual = Observed value - Predicted value

where Observed value = (2, 402) , Predicted value = ŷ = 400 + 3x , Putting x = 2 in the above equation

we get,

ŷ = 400 + 3(2) = 406

Now, Residual = Observed value - Predicted value= 402 - 406= -4

Therefore, the residual for an observed value of (2, 402) is -4.

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Answer:

The answer is postulate

In the given situation, "angle 4 is the angle of elevation from the radar tower to the person" is the description of angle 4.In trigonometry, an angle of elevation or inclination is the angle between the horizontal and the line of sight of an observer looking upwards. An angle of depression is the angle between the horizontal and the line of sight of an observer looking downwards.

In the given situation, angle 4 refers to the angle formed between the horizontal and the line of sight from the radar tower to the person. As the angle is formed while looking upwards from the radar tower to the person, it is called the angle of elevation. Hence, the correct description of angle 4 in this situation is "angle 4 is the angle of elevation from the radar tower to the person."

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The area of the banner is 562.5 square units.

To calculate the area of the banner, we can divide it into two triangles and then find the sum of their areas.

First, let's calculate the base and height of each triangle:

Triangle 1: Vertices (-15,10), (0,-5), and (30,-5)

The base of Triangle 1 is the distance between (-15,10) and (30,-5), which is 30 - (-15) = 45 units.

The height of Triangle 1 is the distance between (-15,10) and (0,-5), which is 10 - (-5) = 15 units.

Triangle 2: Vertices (0,-5), (30,-5), and (15,10)

The base of Triangle 2 is the distance between (0,-5) and (15,10), which is 15 units.

The height of Triangle 2 is the distance between (0,-5) and (30,-5), which is 30 - 0 = 30 units.

Now, let's calculate the area of each triangle using the formula for the area of a triangle: Area = (base * height) / 2.

Area of Triangle 1 = (45 units * 15 units) / 2 = 337.5 square units

Area of Triangle 2 = (15 units * 30 units) / 2 = 225 square units

Finally, to find the total area of the banner, we sum the areas of the two triangles:

Total Area = Area of Triangle 1 + Area of Triangle 2

Total Area = 337.5 square units + 225 square units

Total Area = 562.5 square units

Therefore, the area of the banner is 562.5 square units.

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The radius of the circle is 144 units.

To find the radius of the circle, we can use the formula that relates the circumference of a circle to its radius and the central angle intercepted by an arc.

The formula is:

Arc length = 2πr * (θ/360)

Where:

Arc length is the length of the intercepted arc

r is the radius of the circle

θ is the central angle in degrees

In this case, we are given that the arc length is 48π and the central angle is 120°. Let's substitute these values into the formula and solve for r:

48π = 2πr * (120/360)

Simplifying the equation:

48 = 2r * (120/360)

48 = r * (1/3)

r = 48 * 3

r = 144

Therefore, the radius of the circle is 144 units.

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Answer:

I belive the answer is A

Step-by-step explanation:

So any answer with 22t would make sense, so you have A and C. In C though, it is subtracting 22, but since 6195 is the total it would have to include the 22 so it is A.

Answer:

0.25

Step-by-step explanation:

4/16 --> 1/4 and 1/4 = 0.25

Answer:

12 units

Step-by-step explanation:

1st, I found the distance for the two parallel sides on the hexagon. I counted the lines to be 2 units each, which makes 4 units. And since all sides of a hexagon are equal. All the sides make 12 units, or centimeters. Therefore, the perimeter is 12 units

If the continuous distribution is given then The age of people who have retired represents Normal distribution.

a) The age of people who have retired would likely follow a normal distribution, as it tends to have a symmetric bell-shaped curve.

b) The number of red Smarties in boxes of Smarties would have a discrete distribution, as it can only take on certain whole numbers and cannot be fractionally or continuously measured.

c) The shoe sizes of Stouffvillians may exhibit a bimodal distribution, as there might be two distinct peaks indicating two groups with different average shoe sizes.

d) The wait time between calls to Pizza Pizza could potentially follow an exponential distribution, as it is often used to model the time between events in a Poisson process, such as the arrival of phone calls. The distribution would have a long tail, representing longer wait times occurring less frequently.

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12+85% is $22.20

80%x12=9.6

5%x12=0.6

9.6+0.6=10.2

12+10.2=22.20

 Answer: $22.20  

Answer:

A would be the answer

Step-by-step and

Answer:

$8.75

Step-by-step explanation:

Cost price= $9.75

Selling price= $1.00

profit= C.P-.SP

= 9.75-1.00

= $8.75

mode is 4 and the median is also 4

mode is the number that appears the most which is 4 and median is the number that is in the middle when you line up all the numbers in order  (0,2,2,3,3,4,4,4,4,5,5,5,6,6,10)

If We consider the string w = [tex]CA^pG^pT^pC[/tex], then L ∉ RLs by pumping lemma.

To prove that L ∉ RLs using the RL pumping theorem, we assume L is a regular language and apply the pumping lemma for RLs. Let p be the pumping length of L.

We consider the string w = [tex]CA^pG^pT^pC[/tex], where |w| ≥ p. According to the pumping lemma, we can decompose w into uvxyz such that |vxy| ≤ p, |vy| > 0, and for all k ≥ 0, the string [tex]u(v^k)x(y^k)z[/tex] is also in L.

However, by examining the structure of L, we see that the number of A's and G's is dependent on each other and must match the number of T's.

Since pumping up or down would alter this balance, there is no way to satisfy the condition for all k, leading to a contradiction. Therefore, L cannot be a regular language, and we conclude that L ∉ RLs.

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a. Matrix A is invertible when |A| = -m ≠ 0 then statement true.

b. The system AX = B has no solution when m = 0 and n ≠ 0 has a real number then statement true.

c. The system AX = B has an infinite number of solutions when m = n = 0 then statement true.

d. Columns of the augmented matrix (AB) are linearly independent when m ≠ 0 and n= 0 then statement true.

e. The system AX = 0 has a unique solution when m ≠ 0 then statement true.

f. At least one eigenvalue of the matrix A is zero when m = 0 then statement true.

g. Columns of the matrix A form a basis in R³ when m ≠ 0 then statement true.

Given that,

The augmented matrix of a system of linear equations AX = B was reduced to upper-triangular form so that

[A|B] = [tex]\left[\begin{array}{ccc}2&1&0 \ | \ 2\\0&-1&3 \ | \ 1 \\0&0&m \ | \ n\end{array}\right][/tex]

Where m and n are real numbers.

We know that,

a. We have to prove matrix A is invertible.

For A to be invertible.

|A| ≠ 0

|A| is the determinant of the matrix A.

|A| = 2(-m) -1(0) + 0(0) = -m

Here, m is the real number.

So, |A| = -m ≠ 0

Therefore, Matrix A is invertible when |A| = -m ≠ 0 then statement true.

b. We have to prove the system AX = B has no solution.

When Rank[A|B] > Rank[A]

m = 0 and n ≠ 0 has a real number

Therefore, The system AX = B has no solution when m = 0 and n ≠ 0 has a real number then statement true.

c. We have to prove the system AX = B has an infinite number of solutions.

When m = n = 0, and Rank[A] < 3

Therefore, The system AX = B has an infinite number of solutions when m = n = 0 then statement true.

d. We have to prove columns of the augmented matrix (AB) are linearly independent.

When m ≠ 0 and m∈R and n= 0

Therefore, Columns of the augmented matrix (AB) are linearly independent when m ≠ 0 and n= 0 then statement true.

e. We have to prove the system AX = 0 has a unique solution.

When [tex]\left[\begin{array}{ccc}2&1&0 \\0&-1&3 \\0&0&m \end{array}\right]\left[\begin{array}{ccc}x\\y\\z\end{array}\right] =\left[\begin{array}{ccc}0\\0\\0\end{array}\right][/tex]

The equation are 2x + y = 0, -y + 3z = 0 and mz = 0

m ≠ 0 should be any real number except zero.

Therefore, The system AX = 0 has a unique solution when m ≠ 0 then statement true.

f. We have to prove at least one eigenvalue of the matrix A is zero.

When λ = 2, 1, m

m = 0 then eigen value is zero

Therefore, At least one eigenvalue of the matrix A is zero when m = 0 then statement true.

g. We have to prove columns of the matrix A form a basis in R³.

When m ≠ 0

Therefore, Columns of the matrix A form a basis in R³ when m ≠ 0 then statement true.

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