mm
E
9. Solve: 3(x+4) ≤36
x> 8
x≤8
x≤12
X>12

Answer:

86

Step-by-step explanation:

43 x 2=86

Answer:

54,710

Step-by-step explanation:

multiply the average by 5 to get the amout that they should all have togetehr (271,000) and the add the 4 people's money together (216,290) and then subtract them

The annual income of the fifth salesperson is $54710 if the average annual income for five salespeople last year was $54,200.

It is defined as the single number that represents the mean value for the given set of data or the closed value for each entry given in the set of data.

It is given that:

The average annual income for five salespeople last year was $54,200. Four of the salespeople earned these annual amounts: $58,125; $53,190; $48,975 and $56,000.

Let x be the annual income of the fifth salesperson:

$54,200 = ($58,125+$53,190+$48,975+$56,000+x)/5

271000 = 216 290 + x

x = $54710

Thus, the annual income of the fifth salesperson is $54710 if the average annual income for five salespeople last year was $54,200.

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No, the siblings do not have enough quilting squares to make a 2.7-meter line. The total length of their 42 quilting squares is approximately 2.7 meters, which is equal to the desired length.

To determine if they have enough squares, we need to convert the measurements to a consistent unit.

Rounded to the nearest tenth, the total length of the quilting squares is approximately 2.7 meters.

Since the total length of the quilting squares (2.7 meters) is equal to the desired 2.7 meter line, the siblings have just enough squares to make the line.

Therefore, they have enough quilting squares to make a 2.7 meter line, rounded to the nearest tenth.

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The correct choice is B. The solution is the empty set.

To solve the equation cotθ + 3cscθ = 5 over the interval [0°, 360°), we can rewrite the equation using trigonometric identities.

Recall that cotθ = 1/tanθ and cscθ = 1/sinθ. Substitute these values into the equation:

1/tanθ + 3(1/sinθ) = 5

To simplify the equation further, we can find a common denominator for the terms on the left side:

(sinθ + 3cosθ)/sinθ = 5

Next, we can multiply both sides of the equation by sinθ to eliminate the denominator:

sinθ(sinθ + 3cosθ)/sinθ = 5sinθ

simplifies to:

sinθ + 3cosθ = 5sinθ

Now we have an equation involving sinθ and cosθ. We can use trigonometric identities to simplify it further.

From the Pythagorean identity, sin²θ + cos²θ = 1, we can rewrite sinθ as √(1 - cos²θ):

√(1 - cos²θ) + 3cosθ = 5sinθ

Square both sides of the equation to eliminate the square root:

1 - cos²θ + 6cosθ + 9cos²θ = 25sin²θ

Simplify the equation:

10cos²θ + 6cosθ - 25sin²θ - 1 = 0

At this point, we can use a trigonometric identity to express sin²θ in terms of cos²θ:

1 - cos²θ = sin²θ

Substitute sin²θ with 1 - cos²θ in the equation:

10cos²θ + 6cosθ - 25(1 - cos²θ) - 1 = 0

10cos²θ + 6cosθ - 25 + 25cos²θ - 1 = 0

Combine like terms:

35cos²θ + 6cosθ - 26 = 0

Now we have a quadratic equation in terms of cosθ. We can solve this equation using factoring, quadratic formula, or other methods.

However, when solving for cosθ, we can see that this equation does not yield any real solutions within the interval [0°, 360°). Therefore, the solution to the equation cotθ + 3cscθ = 5 over the interval [0°, 360°) is the empty set.

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184,219,440 ways.

What is contestant?

A participant in a contest or competition is known as a contestant. A contestant is someone who challenges election results.

There are 570 contestants, and any one of them can win the first prize.

One of the remaining 569 people can receive the second prize.

Third may be assigned to any of the remaining 568.

We can accomplish this in 570*569*568 ways

= 184,219,440 ways.

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The variance of the sample means that is found in the sample distribution that we have here is 0.3333

This is the measure of dispersion that is used to show the spread of the data that is contained in a data set

The formula that we are to use here is given as

b² - a² / b - a

we have to put the values in this question

(14 - 2)² / 14 - 2

= 144 / 12

= 12

From here we would have to solve for the variance.

The variance = 12 / 35

= 0.3333

Hence the variance that we have in the question is equal to 0.3333

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Answer:

-1/4

Step-by-step explanation:

Step 1: Simplify both sides of the equation.

16f=−4

Step 2: Divide both sides by 16.

Answer:

first option;

x-int: -5, 1

y-int: -1

Step-by-step explanation:

x-int: describes where the function touches the x-axis (left to right). This function touches the points (0,-5) and (0,1).

y-int: describes where the function touches the y-axis (up and down). This function touches the point (0,-1).

67 people can maximize the profit.

Let's aasume that x represent the number of people.

so, the number of people on the tour = x + 50

The cost function would be:

C = 6000 + 32x

and the revenue:

R = (200 - 2x)(50 + x)

R = 10000 - 100x + 200x - 2x^2

R = 10000 + 100x - 2x²

So, the profit would be:

P = R - C

P = 10000 + 100x - 2x² - 6000 - 32x

P = 4000 + 68x - 2x²

Now we take the derivative of profit function:

P' = 68 - 4x

Consider P'(x) = 0

68 - 4x = 0

4x = 68

x = 17

So, the number of people on tour: 50+17 = 67

This means that 67 people can maximize the profit.

and the profit would be:

P = 4000 + (68 × 17) - (2 × 17²)

P = $4578

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Answer:

$11.19

Step-by-step explanation:

15.98•0.70=11.19

Answer:

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Step-by-step explanation: 3pooopppppp391ti194i19iq09r4it0941it09134t901i4t943it09431ti934it9134t91i3t90349it9130ti1093it109ti190ti0910i9ti90i9103ti9i91349ti9139i04t09i34ti9130ti109ti0914ti1903ti9304ti094t130ti1043it10i0i41i(3+4=7)d

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Answer:

(0, 6)

Step-by-step explanation:

Given function:

\(y=\log_4(2x+64)+3\)

The y-intercept of a function is the point at which the curve crosses the y-axis, so when x = 0.

Therefore, to find the y-intercept, substitute x = 0 into the function:

\(\implies y=\log_4(2(0)+64)+3\)

\(\implies y=\log_4(64)+3\)

Rewrite 64 as 4³:

\(\implies y=\log_4(4)^3+3\)

\(\textsf{Apply the log power law}: \quad \log_ax^n=n\log_ax\)

\(\implies y=3\log_4(4)+3\)

\(\textsf{Apply log law}: \quad \log_aa=1\)

\(\implies y=3(1)+3\)

\(\implies y=3+3\)

\(\implies y=6\)

Therefore, the y-intercept of the given function is (0, 6).

Answer:

If the scale factor is 1/800, it means that 1 cm on the scale drawing represents 800 cm or 8 meters in real life.

So, to find the actual distance between the house and the barn, we need to convert the distance on the scale drawing (4.8 cm) to meters and then multiply by the scale factor:

Actual distance = (Distance on scale drawing in cm) x (Conversion factor)

where the conversion factor is:

Conversion factor = (1 cm) / (100 cm/m) = 0.01 m/cm

Plugging in the values, we get:

Actual distance = (4.8 cm) x (0.01 m/cm) x (8 meters/1 cm) = 0.384 meters

Therefore, the actual distance between the house and the barn is 0.384 meters.

Step-by-step explanation:

least value is q

greatest value is n-q

close to zero is q-n

We will have obtuse-angled triangle if it has an obtuse angle which measures more than 90 degrees but less than 180 degrees

What are interior angles?

An Interior Angle is an angle inside a shape.

An obtuse-angled triangle is a triangle in which one of the interior angles measures more than 90 degrees.

In an obtuse triangle, if one angle measures more than 90°, then the sum of the remaining two angles is less than 90°.

Here, the triangle ABC is an obtuse triangle, as ∠A measures more than 90 degrees. Since, ∠A is 120 degrees, the sum of ∠B and ∠C will be less than 90° degrees.  

In the above triangle, ∠A + ∠B + ∠C = 180° (because of the Angle Sum Property)

Since ∠A = 120°, therefore, ∠B + ∠C= 60°.  

Hence, if one angle of the triangle is obtuse, then the other two angles with always be acute.

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Area shaded represents the area bounded by both the graphs of the functions y = sin(πx) and y = x³ - 4x.

An area bounded by two curves is the area under the smaller curve subtracted from the area under the larger curve. This will get you the difference, or the area between the two curves.

Given is the region {r} bounded by the graphs of y = sin(πx) and y = x³ - 4x.

Refer to the graph attached. The shaded region is the area bounded by both the graphs of the functions y = sin(πx) and y = x³ - 4x.

Therefore, area shaded represents the area bounded by both the graphs of the functions y = sin(πx) and y = x³ - 4x.

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Answer:

square root -91/3

Step-by-step explanation:

just took the test

The right option is missing. The correct answer is tan(0) = -(√91)/3.

The trigonometric expression tan(0) has a value of -(√91)/3 when cos(0) = -3/10.

The values of all trigonometric functions dependent on the value of the ratio of sides of a right-angled triangle are known as trigonometric ratios. The trigonometric ratios of a right-angled triangle's sides about any of its acute angles are known as that angle's trigonometric ratios.

The three sides of the right-angled triangle are:

Hypotenuse (the longest side)

Perpendicular (opposite side to the angle)

Base (Adjacent side to the angle)

The six trigonometric ratios are sine (sin), cosine (cos), tangent (tan), cotangent (cot), cosecant (cosec), and secant (sec).

The trigonometry ratios for a specific angle ‘θ’ is given below:

Trigonometric Ratios:

Sin θ =  Perpendicular/Hypotenuse

Cos θ = Base/Hypotenuse

Tan θ = Perpendicular/Base or Sin θ/Cos θ

Cot θ = Base/Perpendicular or 1/tan θ

Sec θ = Hypotenuse/Base or 1/cos θ

Cosec θ = Hypotenuse/Perpendicular or 1/sin θ

According to the Pythagoras theorem, we can say that in a right-angled triangle:

Hypotenuese² = Base² + Perpendicular²

We are given cos(0) = -3/10, 0 being an obtuse angle (90° < 0 < 180°, since 0 is an angle in quadrant II)

We need to remember that in quadrant II, sine is always positive, cosine is negative, and tangent is also negative.

We are asked to find the value of tan(0).

We know cos(0) = Base/Hypotenuse.

So we let the hypotenuse be 10k, and let the base be 3k. Let the perpendicular be p.

By Pythagoras' Theorem,

Hypotenuese² = Base² + Perpendicular²

or, (10k)² = (3k)² + p²

or, 100k² = p² + 9k²

or, p² = 100k² - 9k² = 91k² = (k√91)²

or, p = k√91

Now, we can find the value of tan(0):

tan(0) = Perpendicular/Base = -(k√91)/3k = -(√91)/3

(Negative value taken as tan is negative in quadrant II)

∴ The trigonometric expression tan(0) has a value of -(√91)/3 when cos(0) = -3/10.

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The length of a United States dollar bill is approximately 15.6 centimeters or 6.14 inches.

This measurement applies to the most commonly used denomination, the one-dollar bill, which features notable figures such as George Washington on the front and the Great Seal of the United States on the back.

To determine the length of a dollar bill, you can use a ruler or a measuring tape. Start by placing the ruler or tape at one end of the bill and measure all the way to the other end. Ensure that the measuring tool is aligned properly and straight along the length of the bill to obtain an accurate measurement.

The length of a dollar bill is standardized by the United States Bureau of Engraving and Printing to ensure uniformity in currency dimensions. This standardization is crucial for machine readability and compatibility with various automated systems, such as vending machines, bill counters, and cash registers.

It's important to note that while the length of a dollar bill is relatively consistent, there may be slight variations due to factors like wear and tear, manufacturing tolerances, or regional printing variations. However, these differences are generally minimal and do not significantly impact the bill's overall length.

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Answer:

1. The perimeter of a parallelogram is the sum of the lengths of all four sides. If two consecutive sides of a parallelogram measure 4 m and 9 m, respectively, then the other two sides must also measure 4 m and 9 m, respectively (since opposite sides of a parallelogram are equal in length). Therefore, the perimeter of the parallelogram is:

Perimeter = 4 m + 9 m + 4 m + 9 m = 26 m

So the perimeter of the parallelogram is 26 meters.

2. In a square, both diagonals are equal in length. If one diagonal measures (2x + 4) in and the other diagonal measures 16 in, then we can write:

2x + 4 = 16

Solving for x, we get:

x = 6

So the value of x is 6 inches.

3. In a trapezoid, the length of the median is equal to the average of the lengths of the two parallel sides. If QR is parallel to TS and mQR = 12 cm, then mTS must also be equal to 12 cm. Let x be the length of the base of the trapezoid.

Then, we have:

mUV = (mQR + mTS)/2

Substituting the given values, we get:

24 cm = (12 cm + 12 cm + x)/2

Simplifying, we get:

24 cm = (24 cm + x)/2

Multiplying both sides by 2, we get:

48 cm = 24 cm + x

Subtracting 24 cm from both sides, we get:

x = 24 cm

So the length of the base of the trapezoid is 24 cm, and the length of the median UV is 24 cm.

(If this isn't right, I'm sorry!)

4. In an isosceles trapezoid, the diagonals are equal in length. If one diagonal measures 42 cm and one leg measures 23 cm, then we can use the Pythagorean theorem to find the length of the other leg:

d^2 = l^2 + (b/2)^2

where d is the length of the diagonal, l is the length of each leg, and b is the length of the base. Substituting the given values, we get:

42^2 = 23^2 + (b/2)^2

Simplifying, we get:

b^2/4 = 42^2 - 23^2

b^2/4 = 1253

Multiplying both sides by 4, we get:

b^2 = 5012

Taking the square root of both sides, we get:

b = sqrt(5012) ≈ 70.77

So the length of the other diagonal is also 42 cm.

5. The area of a kite is equal to half the product of the lengths of its diagonals. If mHP = 10 cm and mOE = 18 cm, then we can write:

Area = (mHP x mOE)/2

Substituting the given values, we get:

Area = (10 cm x 18 cm)/2 = 90 cm^2

So the area of the kite is 90 square centimeters.

I hope this helps! I'm sorry if this was wrong. If you need more help, ask me! :]

Answer:

15

Step-by-step explanation:

the first triangle inequality theorem, the lengths of any two sides of a triangle must add up to more than the length of the third side.

7 + 9 = 16

16 must be more than the third side

15 is the largest whole number less than 16

Answer:

62.5%

Step-by-step explanation:

the product of the two numbers=xy

the product of the altered numbers=(0.75x)(0.5y) OR 0.375xy

finally you subtract this from one to get your decrease: 1-0.375=0.625

then simply convert that to a percent, leaving you with 62.5%. hope this helps!

Answer:

a is the awnsers don't ask why

Answer:

The student is correct.

Step-by-step explanation:

Given that 5x² = 20:

It is true that the value of x = 2 because 2² = 4, and when you multiply 4 with 5, you'll get a product of 20:

5x² = 20

5(2)² = 20

5(4) = 20

20 = 20

Therefore, the student is correct that x = 2.

The equation which represents the curve will be f(x) = 2•(1/4)ˣ. Then the correct option is C.

Let a is the base and x is the power of the exponent function and b is the y-intercept. The exponent is given as

f(x) = aˣ + b

The graph is given below.

The curve is passing through (0, 2), then the equation of the curve which satisfies the curve will be f(x) = 2•(1/4)ˣ.

Then the correct option is C.

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Answer:

$3.0375

Step-by-step explanation:

Original price of dinner = $2.25

If cost percentage of 35%, then the additional cost paid will be;

35% * 2.25

= 0.35 * 2.25

= $0.7875

Target price = Original price + additional cost

Target price = $2.25 + $0.7875

Target price = $3.0375

The postfix expression of "7+5-3*2(6*7)/4" is "7 5 + 3 2 * 6 7 * 2 * - 4 /". Evaluating the postfix expression gives the result of the expression. The prefix expression for the given infix expression is "/ - + 7 5 * 3 * 2 ( * 6 7 ) 4".

To convert the infix expression "7+5-3*2(6*7)/4" into postfix expression, we follow the rules of operator precedence and associativity. The postfix expression is obtained by placing operators after their operands.

The postfix expression for the given infix expression is:

"7 5 + 3 2 * 6 7 * 2 * - 4 /"

To evaluate the postfix expression, we use a stack data structure. We scan the postfix expression from left to right and perform the corresponding operations.

Starting with an empty stack, we encounter the operands "7" and "5". We push them onto the stack. Then we encounter the operator "+", so we pop the last two operands from the stack (5 and 7), perform the addition operation (7 + 5 = 12), and push the result back onto the stack.

We continue this process for the remaining operators and operands in the postfix expression. Finally, after evaluating the entire expression, the result left on the stack is the final answer.

To convert the infix expression into prefix expression, we follow similar rules but scan the expression from right to left. The prefix expression is obtained by placing operators before their operands.

The prefix expression for the given infix expression is:

"/ - + 7 5 * 3 * 2 ( * 6 7 ) 4"

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Answer:

Step-by-step explanation:

Answer:

1020 cm²

Step-by-step explanation:

The area of a trapezoid is given by:

Area=(big base+small base)/2 ×h

So,

Area=(TR+PA)/2 ×h

Area=(54+31)/2 ×24

Area=85/2 ×24

Area=42.5×24

Area=1020 cm² or Area=0.102 m²

Answer:

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