What is the conversion of 150cm in feet ?

The answer is: A. tan P= 3/4, tan Q=5/4

Trigonometric ratios are mathematical functions that relate the angles of a right triangle to the ratio of the lengths of its sides. There are three primary trigonometric ratios, known as sine, cosine, and tangent, and their reciprocal functions, known as cosecant, secant, and cotangent.

The primary trigonometric ratios are defined as follows:

Sine (sin): The sine of an angle is the ratio of the length of the opposite side to the length of the hypotenuse of a right triangle.

sin θ = opposite/hypotenuse

Cosine (cos): The cosine of an angle is the ratio of the length of the adjacent side to the length of the hypotenuse of a right triangle.

cos θ = adjacent/hypotenuse

Tangent (tan): The tangent of an angle is the ratio of the length of the opposite side to the length of the adjacent side of a right triangle.

tan θ = opposite/adjacent

The reciprocal trigonometric ratios are defined as follows:

Cosecant (csc): The cosecant of an angle is the reciprocal of the sine of the angle.

csc θ = 1/sin θ

Secant (sec): The secant of an angle is the reciprocal of the cosine of the angle.

sec θ = 1/cos θ

Cotangent (cot): The cotangent of an angle is the reciprocal of the tangent of the angle.

cot θ = 1/tan θ

Trigonometric ratios are widely used in mathematics, science, and engineering to solve problems involving right triangles, as well as to model and analyze periodic phenomena such as sound waves, light waves, and electromagnetic waves.

Since angle R is a right angle, we can use the tangent ratio for angles P and Q as follows:

tan P = RP / RQ = 12 / 16 = 3 / 4

tan Q = PQ / RQ = 20 / 16 = 5 / 4

Therefore, the answer is: A. tan P= 3/4, tan Q=5/4

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The sum to infinity of the sequence is 96/13

Every term in a geometric sequence is obtained by multiplying the term before it by the same number. [tex]\mathrm{a_n= a_1 r^{n -1 }}[/tex] is the general term for it. The common ratio is denoted by the number r. Any term in the sequence can be used to find it by dividing it by the term before it.

Given the nth term of a geometric sequence expressed as:

Tn = Σ12(-5/8)ⁿ

The sum to infinity of the sequence is expressed as;

S∞ = a/1-r

where

a is the first term = 12

r is the common ratio = -5/8

Substitute

S∞ =  12/1-(-5/8)

S∞ = 12/1+5/8

S∞ = 12/(13/8)

S∞ =12 *8/13

S∞ = 96/13

Hence, the sum to infinity of the sequence is 96/13

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Answer:

x² + y² = z²

Step-by-step explanation:

The side of the bottom square is y.

The side of the left square is x.

The side of the right square is z.

These sides are also the legs and hypotenuse of the right triangle.

We use the Pythagorean Theorem.

x² + y² = z²

This type of scientific experiment is commonly used in microbiology and is called a bacterial culture or bacterial colony.

The scientist likely used a sterile nutrient-rich medium in a petri dish to create an environment in which the bacteria could grow and reproduce. By observing the growth and behavior of the bacteria in the colony, the scientist can study various aspects of bacterial biology, such as metabolism, genetics, and response to environmental conditions. Bacterial cultures can also be used in medical and industrial settings to produce antibiotics, vaccines, and other products.

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The GDP deflator reflects only the prices of all goods and services produced domestically, whereas the CPI (Consumer Price Index) reflects the prices of a fixed basket of goods and services purchased by consumers.

The GDP deflator is a measure of the average level of prices of all new, domestically produced, final goods and services in an economy. It measures the ratio of the value of goods and services produced in a given year at current prices to their value at base year prices. In contrast, the CPI measures the average change over time in the prices paid by urban consumers for a fixed basket of goods and services, including food, housing, transportation, and other goods and services. The GDP deflator is often used to adjust nominal GDP (Gross Domestic Product) to real GDP, which is a measure of economic output that takes into account the effects of inflation. The CPI, on the other hand, is used to adjust income and spending data for changes in the cost of living. In summary, while both the CPI and GDP deflator are measures of inflation, they reflect different aspects of the economy. The CPI reflects the prices paid by consumers for a fixed basket of goods and services, while the GDP deflator reflects the prices of all goods and services produced domestically.

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Complete Question

the CPI for this year is calculated by dividing the using by the using and multiplying by 100. however, the GDP deflator reflects only the prices of all goods and services            . Fill in the blanks.

An equation in slope-intercept form to represent this linear function is y = 65x + 40.

The line with m as the slope, m and c as the y-intercept is the graph of the linear equation y = mx + c. The values of m and c are real integers in the slope-intercept form of the linear equation.

The slope, m, is a measure of how steep a line is. Sometimes, the gradient of a line is referred to as its slope. A line's y-intercept, ab, denotes the y-coordinate of the location where the line's graph crosses the y-axis.

Let the fee per month = x.

Given that, A membership at Rocky Heights Climbing Gym costs $65 per month plus a $40 initial fee.

y = 65x + 40.

Hence, an equation in slope-intercept form to represent this linear function is y = 65x + 40.

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Answer:

I don't really understand geo especially proof so I guess u have to ask ur teachers

The value of 1 dollar is 0.94 Euro

The United States dollar (symbol: $; code: USD; also abbreviated US dollar or US dollar to distinguish it from other dollar-denominated currencies; called dollar, US dollar, American dollar or colloquially alone) is the  currency of the United States dollar. United States and several other countries. The Coinage Act of 1792 established the American dollar along with the Spanish silver dollar, divided it into 100 cents, and authorized the minting of dollar and cent coins. US banknotes are issued as Federal Reserve notes, often called greenbacks because they are predominantly green.

US monetary policy  is managed by the Federal Reserve System, which serves as the nation's central bank.

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Square feet (ft²) to square meters (m²) conversion can be done by multiplying the number of square feet by 0.09290304.

This conversion factor is based on the fact that one square meter is equal to 10.7639 square feet. So, to convert a given area in square feet to square meters, you simply need to multiply that number by 0.09290304. Conversely, to convert from square meters to square feet, you would multiply the number of square meters by 10.7639. This conversion is commonly used in construction and real estate, as well as in international trade and commerce.

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The proportion of sampled smokers that like risky things is 0.555.

The propotion of smokers that like risky things will be obtained by dividing the total number of smokers that like risky things by the total number of boys that were sampled.

To obtain this, we will have

Total number of smokers that like risky things= 45

Total number of smokers that don't like risky things = 36

Total number of smokers = 81

So, 45/81

= 0.555

Since we are asked to keep the result in decimal form, we will divide the figure to obtain 0.555.

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The usual sign for greater than and less than is "<", the pointed side is always towards the smaller quantity.

When we compare two quantities in mathematics we us the sign"<".

Now, let us say that there are two quantities a and b, and a is greater than b. So, we can write the relation as, a > b. So, we see that b is less than as a and a is greater than b.

Now, to remember this, the pointed side of the sign will be always towards the quantity that is smaller.

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the new coordinates of the room are Q(2.3125, 4.125), R(7.3125, 4.125), S(7.3125, 6.125), and T(2.3125, 6.125). the dimensions of the new room on the blueprint are 5.78125 inches by 2 inches and in feet 0.48 feet by 0.17 feet.

To find the new coordinates of the room, we can first calculate the dimensions of the original room and then increase them by 25%. The length of the room is the distance between points R and S, which is:

√(7-2)² + (4-4)² = 5 units

The width of the room is the distance between points Q and T, which is:

√(2-2)² + (6-4)² = 2 units

To increase the dimensions of the room by 25%, we can multiply the length and width by 1.25.

The new length is: 5 × 1.25 = 6.25 units

The new width is: 2 × 1.25 = 2.5 units

To find the new coordinates of the room, we can add half of the increase in each dimension to the original coordinates.

The new coordinates of Q are: (2 + 0.625/2, 4 + 0.25/2) = (2.3125, 4.125)

The new coordinates of R are: (7 + 0.625/2, 4 + 0.25/2) = (7.3125, 4.125)

The new coordinates of S are: (7 + 0.625/2, 6 + 0.25/2) = (7.3125, 6.125)

The new coordinates of T are: (2 + 0.625/2, 6 + 0.25/2) = (2.3125, 6.125)

Therefore, the new coordinates of the room are Q(2.3125, 4.125), R(7.3125, 4.125), S(7.3125, 6.125), and T(2.3125, 6.125).

To find the dimensions of the new room in inches on the blueprint, we can use the Pythagorean theorem: The new length is:

√(7.3125-2.3125)² + (4.125-4.125)² = 5.78125 units

The new width is: √(7.3125-7.3125)² + (6.125-4.125)² = 2 units

Therefore, the dimensions of the new room on the blueprint are 5.78125 inches by 2 inches.

To find the dimensions of the new room in feet in the new house, we can convert the dimensions to feet by dividing by 12:

The new length is: 5.78125 inches / 12 inches/ft = 0.48 ft

The new width is: 2 inches / 12 inches/ft = 0.17 ft

Therefore, the dimensions of the new room in the new house are 0.48 feet by 0.17 feet.

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Complete Question

A rectangular room has coordinates Q (2, 4), R(7, 4), 5 (7, 6), and T(2, 6) on the blueprint. The homeowner wants the dimensions of this room to be 25% larger. What are the coordinates of the new room? What are the dimensions of the new room, in inches, on the blueprint? What will the dimensions of the new room be, in feet, in the new house?

[tex]\frac{1}{10}[/tex] of electricity is made up of other resources and it can be found by addition and subtraction of fractions.

Examine the fractions' denominators. Find the LCM of the denominators and rationalise them to make the denominators of the fractions the same. Add the fraction numerators while keeping the denominator constant. To get the final sum, simplify the fraction.

To subtract fractions, first calculate the denominator's LCM. Step 2: Multiply the numerator and denominator by the same number to get the LCM value. Step 3: When the denominator and numerator are equal, subtract the numerator. Step 4: If necessary, simplify the resulting fraction.

[tex]\frac{5}{10} + \frac{2}{10} + \frac{2}{10} + x = 1.\\\frac{9}{10} + x = 1.\\\frac{10x+ 9}{10} = 1\\10x + 9= 10\\x= \frac{1}{10}[/tex]

hence, 1/10 of the electricity is made up of other resources.

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Answer: 2 15/22

Step-by-step explanation: To solve this, let's first turn the mixed numbers into improper fractions. When we do so, we get 13/2 and 42/11. Now, we make a common denominator. We can turn both denominators into 22. When we do so, we get 143/22 and 84/22. Now, we subtract. When we subtract the two fractions, we get 2 15/22.

Answer:

(0,3)

Step-by-step explanation:

Line a could also be referred to as line EC.

In mathematics, a line can be named in a variety of ways depending on the context. One common way to name a line given a starting point and an ending point is to use the names of the two points.

For example, if the starting point is labeled A and the ending point is labeled B, we can refer to the line as "line AB" or "line BA" (the order doesn't matter, as the line extends in both directions).

In this case therefore, line a can be referred to as line EC which are the letters at the starting and ending points.

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The value of weight of 64 kg when converted to pounds is   141.09568 pounds.

kilogram is the standard unit of mass in the International System of Units (SI), while pounds are a common unit of mass used in the United States and other countries.

To Know how to convert between different units of measurement is essential for accurate calculations and comparisons. convert 64kg to pounds, you can use the formula: 1 kilogram is equal to 2.20462 pounds.

Therefore, to convert 64kg to pounds, you would multiply 64 by 2.20462.

64 x 2.20462 =  141.09568 pounds

So, weight of 64kg is equivalent to  141.09568 pounds.

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Answer:

true

Step-by-step explanation:

log2(5x+3)=log2(4x-3)

log2(5x+3)/log2(4x-3)

division turns to minus

log2(5x+3-4x-3)

log2(x)

a. To find the angle QCP, we can start by finding the coordinates of the points P, Q, and C. Since P and Q are midpoints of the edges FG and GH, respectively, we can find their coordinates as follows:

P = (0, y, z) where y = (3+4)/2 = 3.5 and z = (0+4)/2 = 2

Q = (x, y, 0) where x = (3+4)/2 = 3.5 and y and z are the same as before.

Since C is the center of the cube, we can find its coordinates as:

C = (2, 2, 2)

Now we can use the dot product formula to find the angle QCP:

cos(QCP) = (PC · QC) / (|PC| · |QC|)

where PC and QC are the vectors from P to C and from Q to C, respectively.

PC = C - P = (2, 2 - 3.5, 2 - 2) = (2, -1.5, 0)

QC = C - Q = (2 - 3.5, 2 - 3.5, 0) = (-1.5, -1.5, 0)

|PC| = sqrt(2² + (-1.5)² + 0²) = sqrt(5.25)

|QC| = sqrt((-1.5)² + (-1.5)² + 0²) = sqrt(4.5)

PC · QC = 2(-1.5) + (-1.5)(-1.5) + 0 = -3 + 2.25 = -0.75

cos(QCP) = (-0.75) / (sqrt(5.25) * sqrt(4.5)) = -0.166666...

Therefore, the angle QCP is cos⁻¹(-0.166666...) ≈ 100.53° (rounded to two decimal places).

b. To find the total surface area of the solid remaining after pyramid PGQC is removed, we need to find the area of the four triangular faces and the square base of the pyramid and subtract them from the total surface area of the cube.

The square base of the pyramid has side length PQ = sqrt((3.5 - 3)² + (3.5 - 4)² + 2²) = sqrt(2.5) and area PQ² = 2.5 cm².

Each of the triangular faces has base PQ and height equal to the distance from P or Q to the plane containing the opposite vertex and the center of the cube. This distance is equal to the length of the perpendicular from the vertex to the opposite face, which is half the length of the diagonal of the cube.

The diagonal of the cube is sqrt(3² + 4² + 4²) = sqrt(41), so the height of each triangular face is sqrt(41)/2.

Therefore, the area of each triangular face is (1/2)PQ(sqrt(41)/2) = (sqrt(41)/4) cm².

The total surface area of the cube is 6s², where s is the length of a side of the cube. Since the volume of the cube is 1728 cm³, we have s³ = 1728, or s = 12 cm.

Therefore, the total surface area of the cube is 6(12²) = 864 cm².

The total surface area of the solid remaining after the pyramid is removed is:

864 - 4(sqrt

a. The tree diagram representing the above situation is illustrated below.

b. The percentage of employees hold management positions is 10%

c. The probability that she/he has a graduate degree is 85%.

In this case, the businessman can choose any 3 suits and 4 ties, so the number of combinations is equal to the number of ways of choosing 3 suits multiplied by the number of ways of choosing 4 ties.

This is equal to 6 x 8 = 48.

The records of the company also provide us with some useful information about the probability of holding a management position.

We can see that 20% of the employees have only a high school diploma and 10% of those employees hold management positions.

This means that the probability of holding a management position given that a person has a high school diploma is 10%.

Similarly, of those having bachelor degrees, 60% hold management positions, meaning the probability of holding a management position given that a person has a bachelor degree is 60%.

Lastly, 85% of the employees who have graduate degrees hold management positions, so the probability of holding a management position given that a person has a graduate degree is 85%.

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Answer:

75 degrees

Step-by-step explanation:

since this figure has four sides we can figure out the measure of the interior angles by using the formula, (n-2)*180, where 'n' = number of sides

(4-2)180 = 2(180) = 360

also, we know that since AB is parallel to DC that the figure is a rhombus where adjacent angles are supplementary

therefore, we can find 'x' by writing this equation:

12x - 3 + 9x - 6 = 180

simplify:

21x - 9 = 180

21x = 189

x = 9

also, we know that opposite angles in a rhombus are equal so if we substitute '9' for 'x' in angle C we will know the measure of angle A:

m<A = 9(9)-6

m<A = 81-6

m<A = 75 degrees

Answer:

The percent decrease of the sale price of the sofa from the regular price is 17%.

Step-by-step explanation:

Sure! Here are the steps to find the percent decrease:

The percent decrease of the sale price from the regular price is 17%.

Answer:

17% is the percen

Answer:

[tex]y = \frac{Pa}{b} - za[/tex]

Step-by-step explanation:

See picture below :)

The conditional of the given statement is;

Option B: Conditional: If an angle is a right angle, then it is not an obtuse angle. True.

Option C: Conditional: If an angle is obtuse, then it is not a right angle. True.

A conditional statement is represented in the form of “if…then”. Let p and q are the two statements, then statements p and q can be written as per different conditions, such as;

p implies q

p is sufficient for q

q is necessary for p

p ⇒ q

By definition, obtuse angles are angles that are greater than 90 degrees.

Right angles are defined as angles that are equal to 90 degrees.

Thus, If an angle is a right angle, then it is not an obtuse angle.

Similarly, If an angle is obtuse, then it is not a right angle.

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As they want to compare who takes the longest time to ride their bike to school, such data will be considered as numerical because it involves quantitative measurements (time taken to ride a bike) and can be represented by numbers.

Numerical data, also known as quantitative data, is information that is typically presented in the form of numbers and does not include any language or descriptive information. It's always measurable and can be added up.

We can perform mathematical and arithmetic operations on this type of data, and it can be expressed in decimal or fraction form. It can be useful in presenting information such as height, weight, distance and age, for example.

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To find the values of the standard normal random variable z for the given probabilities, we can use a standard normal distribution table or calculator. A. P(z≤z0)=0.6997, z0=0.52. B. P(−z0≤z≤z0)=0.8026, z0=1.29. C. P(−z0≤z≤0)=0.4702, z0=-0.63. D. P(−1<z<z0)=0.159, z0=0.49

A. P(z≤z0)=0.6997

To find the value of z0 such that P(z≤z0) = 0.6997, we can use a standard normal distribution table or calculator. Looking up the value, we get z0 ≈ 0.52.

B. P(−z0≤z≤z0)=0.8026

To find the value of z0 such that P(−z0≤z≤z0) = 0.8026, we can use the symmetry property of the standard normal distribution. Since the probability is split equally on both sides of the mean, we can find the z-score that corresponds to a probability of (1-0.8026)/2 = 0.0987 on the left tail. Looking up this value, we get z ≈ -1.29. Therefore, z0 ≈ 1.29.

C. P(−z0≤z≤0)=0.4702

To find the value of z0 such that P(−z0≤z≤0) = 0.4702, we can use the symmetry property again. Since the probability is split equally on both sides of the mean, we can find the z-score that corresponds to a probability of (1-0.4702)/2 = 0.2649 on the right tail. Looking up this value, we get z ≈ 0.63. Therefore, z0 ≈ -0.63.

D. P(−1<z<z0)=0.159

To find the value of z0 such that P(−1<z<z0) = 0.159, we can subtract the probability of the left tail (P(z<-1)) from the total probability (0.159 + P(z<-1) = 1). Looking up the value of P(z<-1) in a standard normal distribution table, we get 0.1587. Therefore, the probability of the right tail (P(z<z0)) is 1 - 0.159 - 0.1587 = 0.6823. Looking up the z-score that corresponds to this probability, we get z0 ≈ 0.49.

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The division of [tex]14x^3-21x^2-7x $ by $-7x[/tex] is -2x-2.

What is polynomial division?

Polynomial division is a method used to divide two polynomials, which are algebraic expressions consisting of one or more terms, using long division.

To perform polynomial division of [tex]14x^3- 21x^2 - 7x[/tex] by −7x, we can follow these steps:

Write the dividend [tex](14x^3 - 21x^2 - 7x)[/tex] in descending order of powers of x, filling in any missing terms with a coefficient of 0:

[tex]14x^3 - 21x^2 - 7x + 0[/tex]

Write the divisor (-7x) to the left of a long division bracket and divide the first term of the dividend by the first term of the divisor. Place the result above the long division bracket.

-2x

Multiply the divisor by the quotient and write the result below the dividend. Subtract this product from the dividend and bring down the next term.

[tex]14x^3 - 21x^2 - 7x + 0\\\\-(-7x)(-2x)\\\\14x^2[/tex]

Repeat steps 2 and 3 with the new dividend (14x^2) and the same divisor (-7x).

[tex]-2x - 2\\\\14x^2 + 0x\\\\-(-7x)(-2x + 2)\\\\-14x[/tex]

Repeat steps 2 and 3 with the new dividend (-14x) and the same divisor (-7x).

2

[tex]14x^2 + 0x + 0[/tex]

[tex]-(-7x)(-2x + 2 - 2/7)[/tex]

0

The final result of the polynomial division is the quotient -2x - 2 with no remainder.

Therefore, the division of [tex]14x^3-21x^2-7x $ by $-7x[/tex] is:

[tex]14x^3-21x^2-7x \div -7x = -2x - 2.[/tex]

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Answer:

x = -2 | y = -6
x = 1 | y = 6
x = 2 | y = 10

Step-by-step explanation:

The equations are x - 5 = 7, x - 7 = 5 and x - 4 = 8

The solution to the equation is given as

x = 12

The subtraction property of equality states that if we subtract the same number from both sides of an equation, the equation remains true.

Using the above as a guide, we have the following:

Each of these equations is equivalent to x = 12, since we have simply subtracted the same value from both sides of the equation.

Hence, the solution to each of these equations is x = 12.

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