A cart weighing 40 lb is placed on a ramp inclined at 15° to the horizontal. The cart is held in place by a rope inclined at 60° to the horizontal, as shown in the figure. Find the force that the rope must exert on the cart to keep it from rolling down the ramp.

To determine the base of a parallelogram, we can use the formula for the area of a parallelogram, which is A = b*h, where A is the area, b is the base, and h is the height.

We are given the height (h) and the area (A), so we can rearrange the formula to solve for the base (b):
b = A/h

Substituting the given values for A and h:
b = 15/6

Simplifying:
b = 2.5

Therefore, the base of the parallelogram is 2.5 feet.

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Answer:

Step-by-step explanation: g

Following are the measures of the angles given :∠ ABC = 180, ∠ BCD = 180, ∠ CDA = 270, ∠ DAB = 270.

What is parallel lines ?

Parallel lines are two or more lines that are always the same distance apart and never intersect, no matter how far they are extended.

Since AB is parallel to DC and AD is parallel to BC, we know that angles A and C are corresponding angles and angles B and D are also corresponding angles. Corresponding angles are congruent when two parallel lines are intersected by a transversal.

So, we have:

∠ A = ∠ C

∠ B = ∠ D

Given:

∠ D = 3x - 75

∠ B = x + 35

We can solve for x using the fact that the sum of the angles in a quadrilateral is 360 degrees:

∠ A + ∠ B + ∠ C + ∠ D = 360

Substituting the values we know, we get:

∠ A + (x + 35) + ∠ C + (3x - 75) = 360

Simplifying, we get:

4x - 40 = 360

4x = 400

x = 100

Now we can substitute x = 100 into the expressions for ∠ B and ∠ D to find their values:

∠ B = x + 35 = 100 + 35 = 135

∠ D = 3x - 75 = 3(100) - 75 = 225

Since angles A and C are corresponding angles, we know that:

∠ A = ∠ C = 180 - ∠ B = 180 - 135 = 45

Therefore, we have:

∠ ABC = ∠ A + ∠ B = 45 + 135 = 180

∠ BCD = ∠ B + ∠ C = 135 + 45 = 180

∠ CDA = ∠ C + ∠ D = 45 + 225 = 270

∠ DAB = ∠ D + ∠ A = 225 + 45 = 270\

So, we can see that angles ABC and BCD are straight angles (180 degrees) and angles CDA and DAB are reflex angles (more than 180 degrees).

Therefore, Following are the measures of the angles given :∠ ABC = 180, ∠ BCD = 180, ∠ CDA = 270, ∠ DAB = 270.

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Answer: Factors

Step-by-step explanation:

The sum of the two polynomials is 12x^(5) - 5x^(3) - 5x^(2).

To find the sum of the two polynomials, we need to add the coefficients of the like terms. Like terms are terms that have the same variable and exponent.

Step 1: Identify the like terms in the two polynomials.
- The like terms are 8x^(5) and 4x^(5), -5x^(3) and 0 (since there is no x^(3) term in the second polynomial), x^(2) and -6x^(2).

Step 2: Add the coefficients of the like terms.
- 8x^(5) + 4x^(5) = 12x^(5)
- -5x^(3) + 0 = -5x^(3)
- x^(2) + -6x^(2) = -5x^(2)

Step 3: Combine the terms to get the sum of the two polynomials.
- 12x^(5) + -5x^(3) + -5x^(2)

Step 4: Simplify the expression if possible.
- There are no like terms that can be combined, so the expression is already simplified.

The sum of the two polynomials is 12x^(5) - 5x^(3) - 5x^(2).

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The supplementary angles are ∠GDF and ∠EDG, ∠CED and ∠BEC. The correct options are C and D.

Angles that add up to 180 degrees are referred to as supplementary angles. For instance, angle 130° and angle 50° are complementary angles since the sum of these two angles is 180°. The sum of complementary angles is 90 degrees.

The sum of the two angles ∠GDF and ∠EDG is equal to 180°. So these angles are supplementary to each other.

The sum of the two angles ∠CED and ∠BEC is equal to 180°. So these angles are supplementary to each other.

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The probability that a person from the survey who has a tablet also has a laptop is 0.058, or approximately 5.8%.

What is probability?

Probability is a way to gauge how likely something is to happen. Many things are difficult to forecast with absolute confidence. Using it, we can only make predictions about the likelihood of an event happening, or how likely it is. Probability can range from 0 to 1, with 0 denoting an impossibility and 1 denoting a certainty.

We are given that 62% of respondents have a tablet and 30% have a laptop.

Let T represent the event of having a tablet and L represent the event of having a laptop.

Then, we know -

P(T) = 0.62

P(L) = 0.30

We are also given that 12% of respondents who have a laptop also have a tablet.

In other words, the probability of having a tablet given that a person has a laptop is -

P(T|L) = 0.12

We can use this conditional probability to find the probability that a person who has a tablet also has a laptop, denoted by P(L|T).

By Bayes' theorem, we have -

P(L|T) = P(T|L) × P(L) / P(T)

Substituting the values we know, we get -

P(L|T) = 0.12 × 0.30 / 0.62

Simplifying this expression, we get -

P(L|T) = 0.058

Therefore, the probability value is 0.058, or 5.8%.

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A company establishes a sinking fund to pay a debt of $150,000 due in 4 years. The required payment at the beginning of each six-month period is $6,235.54.

The sinking fund payment will earn interest at a rate of 9% per year, compounded semi-annually. This means the effective interest rate per six-month period is [tex](1 + 0.09/2)^2 - 1 = 0.045 = 4.5%[/tex]

Using the formula for the future value of an annuity, [tex]FV = R[((1+r)^n - 1)/r][/tex], where r is the interest rate per period and n is the number of periods, we can calculate the required payment R as:

[tex]150,000 = R[((1+0.045)^8 - 1)/0.045][/tex]

R = 6,235.54

Therefore, the company needs to make payments of $6,235.54 at the beginning of each six-month period to accumulate enough money in the sinking fund to pay off the $150,000 debt in 4 years.

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Answer: cos B-sin²A = cos²A-sin-B

Step-by-step explanation:

Answer: cos B-sin²A = cos²A-sin-B

Explanation:

Using the double angle identity, we can express the left side of the equation as:

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

Now, using the Pythagorean identity, we can rewrite the right side of the equation as:

cos²A-sin-B = cos A.cos B - sin A.sin B

Hence, we can conclude that cos(A + B).cos(A-B) = cos B-sin²A = cos²A-sin-B

Answer: Read the step by step explanation for the answer.

Step-by-step explanation:

We can prove this trigonometric identity using the product-to-sum and Pythagorean identities as follows:

Starting with the left-hand side (LHS):

cos(A + B).cos(A - B)

Using the product-to-sum identity:

= [cos A cos B - sin A sin B][cos A cos B + sin A sin B]

= cos²A cos²B - sin²A sin²B

Using the Pythagorean identity:

= cos²A(1 - sin²B) - sin²A(1 - cos²B)

= cos²A - cos²A sin²B - sin²A + sin²A cos²B

= cos²A - sin²A + sin²A cos²B - cos²A sin²B

Using the Pythagorean identity:

= cos²A - sin²A + sin²A(1 - sin²B) - cos²A sin²B

= cos²A - sin²A + sin²A - sin²A sin²B - cos²A sin²B

= cos²A - sin²A + sin²A cos²B - sin²B cos²A

= cos²A - sin²A + cos²A sin²B - sin²B cos²A

Using the Pythagorean identity:

= cos²A - sin²A + cos²A - sin²B

= 2cos²A - sin²A - sin²B

= cos²A + cos²A - sin²A - sin²B

= cos²A + sin²A cos²B - sin²B

= RHS

Therefore, we have shown that (b) cos(A + B).cos(A-B) = cos B-sin²A = cos²A-sin-B.

Answer:

III

Step-by-step explanation:

The option that would most likely contribute toward lowering the premium a policyholder pays for life insurance is III - maintaining good health.

Choosing whole instead of term insurance, decreasing the death benefit, and taking up smoking would increase the premium a policyholder pays for life insurance. Whole life insurance typically has higher premiums than term life insurance, decreasing the death benefit reduces the amount of coverage provided by the policy, and taking up smoking increases the risk of premature death and therefore increases the likelihood that the policy will need to pay out.

On the other hand, maintaining good health reduces the risk of premature death and lowers the likelihood that the policy will need to pay out. Therefore, insurance companies typically offer lower premiums to policyholders who maintain good health.

Answer:

answer is B

Step-by-step explanation:

II, III

Step-by-step explanation:

I think it might be A

I am not sure

The quadrilateral MNOP if MN=OP and MP=NO, then it must be square (option d).

First of all, since the opposite sides are equal in length (MN=OP and MP=NO), we know that MNOP is a parallelogram. A parallelogram is a quadrilateral with opposite sides parallel and equal in length.

If we were given additional information about the angles of the quadrilateral, we could determine whether MNOP is a rectangle or a rhombus.

Lastly, it is worth noting that MNOP cannot be a square, because a square is a special type of quadrilateral with all four sides equal in length and all four angles equal to 90 degrees.

In summary, based on the information given in the question, we can conclude that MNOP is a parallelogram, but we cannot determine whether it is a rectangle or a rhombus without additional information. We can also rule out the possibility that it is a square.

Hence the option (d) is correct.

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Complete Question:

Choose ALL answers that describe the quadrilateral MNOP if MN=OP and MP=NO?

a) Parallelogram

b) Rectangle

c) Rhombus

d) Square

e) Trapezoid

y = 2.50 / (1 + 15.80^−x)

You can use technology to approximate the given data with a logistic regression curve y = N/(1 + Ab^−x).

To do this, you'll need to calculate the parameters A, N, and b. To calculate A and N, you can use the values of y at the extremes of x. At x = 0, y = 3.0 and at x = 150, y = 9.9. So, A = (9.9 - 3.0) / (1 - 0.003^150) and N = 9.9 - A*0.003^150. Then, b can be calculated using the average of the logarithm of all x values. The final logistic regression curve will be:

y = 2.50 / (1 + 15.80^−x)

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The average percentage of time spent studying is 8.64%.

To find the average percentage of time spent studying, we need to first add up the total hours and total percentage of all the students. Then, we can divide the total percentage by the total hours to find the average percentage of time spent studying.

Total hours = 18 + 10 + 2 + 6 + 8 = 44 hours
Total percentage = 100% + 80% + 50% + 70% + 80% = 380%

Average percentage = Total percentage / Total hours = 380% / 44 hours = 8.64%
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Complete question

Find the average percentage of time spent on studying. data. Nina: 18 hours, 100%; Johannes: 10 hours, 80%; Al-Rahim: 2 hours, 50%; Caroline: 6 hours, 70%; Saul: 8 hours, 80%

Answer: 515,783

Step-by-step explanation:  f(x)= a(1+r)^x      450,000(1+0.023)^6

Triangle ABC and ADC are similar if BE is parallel to CD.

What does a triangle similarity mean?

Two triangles are comparable if the measurements of their corresponding sides are proportionate. The same is true if the lengths of two sides in one triangle are proportional to the lengths of the corresponding sides in another triangle and the included angles are congruent.

What is the triangle Theorem's similarity?

According to the fundamental theorem of similarity, a line segment can divide two triangle sides into proportionate segments if and only if it is parallel to the third side of the triangle.

We are given that BE is parallel to CD.

As per the theorem of similarity, the two triangles are similar when the a line segment of the triangle is parallel to that of another triangle.

So, from this we get that the Triangle ABC and ADC are similar.

Hence, Triangle ABC and ADC are similar.

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The inequality is 3x + 2y ≥ 93 and the grade received is A for the test

Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.

In an inequality, the two expressions are not necessarily equal which is indicated by the symbols: >, <, ≤ or ≥.

Given data ,

Let the inequality equation be represented as A

Now , the value of A is

Let the number of multiply questions be x

Let the number of matching questions be y

Substituting the values in the equation , we get

3x + 2y ≥ 93

when x = 20 and y = 18

On simplifying the equation , we get

3 ( 20 ) + 2 ( 18 ) ≥ 93

60 + 36 ≥ 93

96 ≥ 93

Therefore , the student receives an A grade for the test

Hence , the inequality is true

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Option D, {5+(-1/3)+(-10)}+(2/3+7), would be easier to simplify if we use the commutative property.

What is the commutative property, and how can it be used to simplify expressions?

The commutative property is a property of addition and multiplication that allows us to change the order of the numbers being added or multiplied without changing the result.

That is, [tex]a + b = b + a[/tex] and [tex]a \times b = b \times a[/tex].

To simplify expressions, we can use the commutative property to rearrange the order of the terms in a way that makes the arithmetic easier to perform.

Find the expression:

We are given the expression -1/3-10+7+2/3+5, and we want to know which option would be easier to simplify using the commutative property.

Option D, {5+(-1/3)+(-10)}+(2/3+7), would be easier to simplify using the commutative property because we can group the terms that have like terms together. Specifically, we can group the negative terms together and the positive terms together:

{5+(-1/3)+(-10)}+(2/3+7) = {(5)+[(-1/3)+(-10)]}+{(2/3)+7}

Now we can simplify each group separately. For the first group, we can add the terms inside the brackets using the commutative property:

{-1/3+(-10)} = -10 - 1/3 = -31/3

For the second group, we can add the terms directly:

{2/3+7} = 2/3 + 21/3 = 23/3

Substituting these results back into the original expression, we get:

-1/3-10+7+2/3+5 = -31/3 + 23/3 + 5

Now we can add the terms directly to get:

-31/3 + 23/3 + 5 = -8/3 + 5 = 7/3

Therefore, the expression simplifies to 7/3.

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Answer:  2+n

Step-by-step explanation:

Tn=T1 + (n-1) d

3+(n-1)1

3+n-1

3-1+n

2+n

Answer:

The price of per ounce of strawberries is $ 0.25.

Step-by-step explanation:

Pounds to ounce conversion:

As we know that,

 One pound = 16 Ounce

Since, Jill bought a pound of strawberries for $4

It means that,

Price of 16 Ounces of strawberries = $ 4

So taht,  Price of one ounce of strawberries

Hence, the price of per ounce of strawberries is $ 0.25.

Answer:

0.25

Step-by-step explanation:

16 ounces = 1 pound

4.00 / 16 = 0.25

Standard form of the number 3.5 × 10⁷ is 35000000.

In the United States and countries using US conventions, the standard form is the usual way of writing numbers in decimal notation.

The standard form of a number is a way of writing the number in a form that follows certain rules. Any number that can be written as a decimal number.

Given number

3.5 × 10⁷

In standard form, digits are written left or right of decimal

number can be written as

= 35000000

Hence, 35000000 is standard form of the number 3.5 × 10⁷.

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The height of the cylinder is approximately 2.45 inches.

Volume is the measure of the space occupied by a three-dimensional object. It is typically expressed in cubic units.

The volume of a cylinder is given by the formula V = πr²h, where V is the volume, r is the radius, and h is the height.

Substituting the given values, we get:

1 and 1/16 = π(1/4)²h

Simplifying and solving for h, we get:

h = (1 and 1/16) / (π(1/4)²)

h = (17/16) / (π/16)

h = 17/π

Approximating using π = 22/7, we get:

h ≈ 17 / (22/7)

h ≈ 2.45 inches (rounded to two decimal places)

Therefore, the height of the cylinder is approximately 2.45 inches

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The solutions of the equation on the interval [0,2π) are x= 5π/6, 11π/6, 2π/3, and 5π/3.

To solve the trigonometric equation sin 2x=−√3/2 on the interval [0,2π), we need to find the values of x that satisfy the equation. We can do this by using the inverse sine function and the periodicity of the sine function.

First, let's find the general solution of the equation:
sin 2x=−√3/2
2x= sin⁻¹(−√3/2) + 2πn or 2x= π - sin⁻¹(−√3/2) + 2πn, where n is an integer
2x= -π/3 + 2πn or 2x= 4π/3 + 2πn
x= -π/6 + πn or x= 2π/3 + πn

Now, we need to find the values of x that are in the interval [0,2π). We can do this by plugging in different values of n until we find all the solutions in the interval.

For x= -π/6 + πn:
When n=0, x= -π/6 (not in the interval)
When n=1, x= 5π/6 (in the interval)
When n=2, x= 11π/6 (in the interval)
When n=3, x= 17π/6 (not in the interval)

For x= 2π/3 + πn:
When n=0, x= 2π/3 (in the interval)
When n=1, x= 5π/3 (in the interval)
When n=2, x= 8π/3 (not in the interval)

Therefore, the solutions of the equation on the interval [0,2π) are x= 5π/6, 11π/6, 2π/3, and 5π/3. These are the exact form answers. If we want to round them to two decimal places, we get x= 2.62, 5.24, 1.05, and 3.14.

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-13 is the  value of b in linear equation.

What in mathematics is a linear equation?

A linear equation is a first-order (linear) term plus a constant in the algebraic form y=mx+b, where m is the slope and b is the y-intercept. Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables.

                              Equations with variables of power 1 are referred to as linear equations. One example with only one variable is where ax+b = 0, where a and b are real values and x is the variable.

y = 6x + 4

 y = mx + c

is a straight line  of gradient of c.

  m = 6

y = 6x + c

the line passes through points(x,y) where x = 3 and y = 5

      5 = 6 * 3 + c

        c = 5 - 18

         c = -13

         y = 6x - 13

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Answer:0.1

Step-by-step explanation:

0.1

The simplified expression without parentheses is [tex]-8a^5b^7 + 18a^3b^5[/tex].

To rewrite the expression without parentheses and simplify it as much as possible, we need to distribute the term (-2a^(3)b) to each term inside the parentheses. This is done by multiplying the term outside the parentheses with each term inside the parentheses.

So, we have:
[tex](4a^2b^6-9b^4)(-2a^3b) = (4a^2b^6)(-2a^3b) - (9b^4)(-2a^3b)[/tex]

Next, we simplify the terms by combining like terms and using the rules of exponents:

[tex]= -8a^5b^7 + 18a^3b^5[/tex]

So, the simplified expression without parentheses is [tex]-8a^5b^7 + 18a^3b^5[/tex].

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Answer:

964 1/4m

Step-by-step explanation:

length x width x height

Answer:

964.25 is the volume

Step-by-step explanation:

To find the volume of a rectangular prism your going to do length times width times height.

Your length is 7 1/4m

Your height is 14m

Your width is 9 1/2m

So we are going to do 7 1/4 * 9 1/2 * 14

Which will give you 964.25

a) The number of turning points of the function is 3.
b) The end behavior of the function is that as x approaches positive infinity.
c) The potential real zeros of the function are the factors of the constant term, 8. These are ±1, ±2, ±4, and ±8.
d) Using Descartes' Rule of Signs, there are 3 sign changes in the polynomial, so there can be 3 or 1 positive real zeros.
e) Using synthetic division and the potential real zeros, we can find that the rational zeros are -2 and 4.
f) The graph of the function is shown below with the turning points and zeros labeled.

The number of turning points of the function is 3. because the degree of the polynomial is 4 and the number of turning points is one less than the degree.

f(x) approaches positive infinity and as x approaches negative infinity, f(x) approaches negative infinity. This is because the leading coefficient is positive and the degree is even.

There are 2 sign changes in the polynomial with the x values replaced with -x, so there can be 2 or 0 negative real zeros.

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The factored form of the polynomial is p(z) = (2z - 5)(z^(2) + 2z + 37).

To write the polynomial p(z) in factored form as a product of linear and quadratic expressions using integer coefficients only, we need to find the other zeros of the polynomial.

Since one of the zeros is a complex number, z = -1 + 6i, the other complex zero will be its conjugate, z = -1 - 6i. This is because complex zeros of polynomials with real coefficients always come in conjugate pairs.

Now, we can write the quadratic expression that has these two complex zeros as

(z - (-1 + 6i))(z - (-1 - 6i)) = (z + 1 - 6i)(z + 1 + 6i) = (z + 1)^(2) - (6i)^(2) = z^(2) + 2z + 1 - 36i^(2) = z^(2) + 2z + 37.

Since the polynomial p(z) is of degree 3, there must be one more zero, which we can find by dividing p(z) by the quadratic expression we just found:

p(z)/(z^(2) + 2z + 37) = 2z^(3)/(z^(2) + 2z + 37) - z^(2)/(z^(2) + 2z + 37) + 64z/(z^(2) + 2z + 37) - 185/(z^(2) + 2z + 37) = 2z - 5

So the other zero is z = 5/2.

Now,
p(z) = 2(z - 5/2)(z^(2) + 2z + 37) = (2z - 5)(z^(2) + 2z + 37)

So the factored form of the polynomial is p(z) = (2z - 5)(z^(2) + 2z + 37).

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