write the following phrase as a variable
expression. Use x to represent "a number"
negative six subtracted from three times.
number
a

Answer:

x = 19

Step-by-step explanation:

So cos and sin are closely related, but they are not equal. In order for these two to be equal to each other, the angles (in the parenthesis by the cos and by the sin) have to be complementary. That is, they have to add up to 90°

Use this idea to set up an equation.

x + 16 + 3x - 2 = 90

Combine like terms.

4x + 14 = 90

Subtract 14.

4x = 76

Divide by 4.

x = 19

x = 19

If you are kooking for the angles:

x + 16

= 19 + 16

= 35

and

3x - 2

= 3(19) - 2

= 57 - 2

= 55

Check: 35 + 55=90

Also,

cos35 = sin55

The probability that it is raining if the flight has been delayed is 0.07, or 7%.

We can use the following formula to calculate the probability that it is raining if the flight has been delayed:

P(Rain|Delayed) = P(Rain and Delayed) / P(Delayed)

We are given that P(Rain) = 0.07 and P(Delayed) = 0.18. We can also use the fact that P(Rain and Delayed) = P(Rain) * P(Delayed):

= 0.07 * 0.18

= 0.0126.

Substituting these values into the formula, we get:

P(Rain|Delayed) = 0.0126 / 0.18 = 0.07

Therefore, the probability that it is raining if the flight has been delayed is 0.07, or 7%.

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The x-intercepts are (4,0)(5,0) of the following graph.

In the context of a graph, an x-intercept is a point where a curve or line crosses the x-axis. It is the point at which the value of y is zero. In other words, the x-intercept is the value of x when the function or equation crosses the x-axis.

To find the x-intercepts of a function, you can set y equal to zero and solve for x. The resulting values of x will be the x-intercepts.

In the context of a graph, a y-intercept is a point where a curve or line crosses the y-axis. It is the point at which the value of x is zero. In other words, the y-intercept is the value of y when the function or equation crosses the y-axis.

To find the y-intercept of a function, you can set x equal to zero and solve for y. The resulting value of y will be the y-intercept.

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The area and perimeter of the parallelogram are: 56 square units and 30 units respectively

In Euclidean geometry, a parallelogram is a simple (non-self-intersecting) quadrilateral with two pairs of parallel sides. The opposite or facing sides of a parallelogram are of equal length and the opposite angles of a parallelogram are of equal measure

The parameters that will help us do the math are

base = 7

height = 8

Area = 8*7 = 56 square units

perimeter 2b + 2h

perimeter = 2*7 + 2*8

= 14 +16

P = 30 units

Therefore, the perimeter of the parallelogram and area are 30 units and 56 square units

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Answer:

x+100

Step-by-step explanation:

x^2-10,000/x-100

x^2-10000 is a difference in squares and can be factored.

x^2-10000 = (x+100)(×-100).

(x+100)(x-100)/(x-100)

(x-100) cancel each other.

x+100 remains.

Answer: Cost of  a giant cookies = $1.39

Cost of a cake= $6.95

Cost of a pie= $4.95

Step-by-step explanation:

Let price of a giant cookie = x

Then,

price of a cake = 5x

Price of a pie = 5x-2

Cost of  30 cakes, 40 pies, and 200 giant cookies = 30 (5x)+40(5x-2)+200x

= 150x+200x-80+200x   [By distributive property a(b+c)=ab+ac]

= 550x-80

Given cost = $684.50

\(\Rightarrow\ 550x-80=684.50\\\\\Rightarrow\ 550x= 684.50+80\)

\(\Rightarrow\ 550x=764.50\\\\\Rightarrow\ x=\dfrac{764.50}{550}\\\\\Rightarrow\ x=1.39\)

Cost of  a giant cookies = $1.39

Cost of a cake = 5 x $1.39  = $6.95

Cost of a pie = $6.95 -  $2 = $4.95

Answer:

D.

Step-by-step explanation:

at + ab = c

subtract ab from both sides

at= c - ab

divide a from both sides

t = c - ab/a

1. The price elasticity of demand for pen is 0.5

2. The cross price elasticity of demand for the commodity is 0.667

3. The cross price elasticity of demand is 0.8

The degree to which demand reacts to a change in an economic component is known as elasticity of demand. The most prevalent economic component considered when calculating elasticity is price. Income level and the accessibility of substitutes are further considerations. Elasticity gauges how demand changes in response to shifting economic conditions.

Given:

1. The demand for pen decreased from 100 to 70.

So, the percentage change in quantity

= (100 -70) / 100 = 0.3 = 30%

percentage change in the price

= (5 - 2) / 5

= 3/5

= 60 %

So, Cross price elasticity = 30% / 60% = 0.5

2. The quantity demanded of a commodity decreased from 50kg to 30kg.

So, the percentage change in quantity

= (50- 30)/50

= 40%

and, percentage change in price

= (8- 5)/5

= 60%

Then, cross price elasticity

= 40% / 60%

= 0.6667

Now, If the price of the commodity rather decreased from Gh¢5.00 to Gh¢2.50

So, the percentage change in price

= (5 - 2.5)/5

= 50%

Then, cross price elasticity

= 40% / 50%

= 0.8

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Answer:

1. 2 units from the origin on the x axis

2. 3 units from the origin on the y axis

Hello !

Answer:

\( \boxed{h = 6}\)

Step-by-step explanation:

He has grown :

We also know that in total, he has grown 11 vegetables.

We will have to solve an equation !

\(h + 2h + 5 = 11\)

\( \iff3h + 5 = 11\)

We want to isolate h.

\(3h + 5 - 5= 11 - 5 \\ \iff3h = 6 \\ \iff \frac{3h}{3} = \frac{6}{3} = 2\)

The value of h is 2.

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The coordinates of each points are:

A = (-0.5, -5)

B = (0.8, -1.8)

C = (-2.6, -2.2)

D = (-1.5, -8.9)

E = (2.5, -6.5)

F = (-1.5, 3.1)

G = (-2.4, 4.1)

H = (1.5, 3)

I = (2.7, 1.5)

J = (-1.5, 0)

K = (-6.5, 0)

We have,

The coordinates of each point are in an ordered form.

i.e

(x, y)

x is the x-axis value.

y is the y-axis value.

Thus,

A = (-0.5, -5)

B = (0.8, -1.8)

C = (-2.6, -2.2)

D = (-1.5, -8.9)

E = (2.5, -6.5)

F = (-1.5, 3.1)

G = (-2.4, 4.1)

H = (1.5, 3)

I = (2.7, 1.5)

J = (-1.5, 0)

K = (-6.5, 0)

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Answer:

3/5

Step-by-step explanation:

Sine is opposite/hypotenuse

The opposite side of <A is 3 and the hypotenuse is 5

The price per cup when a 2-quart carton of yogurt costs $5.36 is $0.67.

A word problem in mathematics simply refers to a question that is written as a sentence or in some cases more than one sentence which requires an individual to use his or her mathematics knowledge to solve the real.life scenario given.

In this case, a 2-quart carton of yogurt costs $5.36. It should be noted that 1 quart = 4 cups.

Therefore, 2 quarts will be:

= 2 × 4.

= 8 cups

Therefore, the price per cup will be:

= $5.36 / 8

= $0.67

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Answer: 60.93 < μ < 69.07

Step-by-step explanation: The true mean of a set of data is between an interval of values with a percentage of precision, e.g., a 99% confidence interval means we are 99% confident the true mean is between the lower and upper limits.

To find the interval, use

x±\(z\frac{s}{\sqrt{n}}\)

z is z-score related to the % of confidence level

In this case, a 99% confidence interval is 2.576

x is sample mean

Calculating:

\(x=\frac{63+69+62+66}{4}\)

x = 65

65±\(2.576\frac{3.16}{\sqrt{4}}\)

65±4.07

Confidence Interval: 60.93 < μ < 69.07

Meaning that we are 99% sure the population means is between 60.93 and 69.07.

Answer:

A sample size of 1031 is required.

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of \(\pi\), and a confidence level of \(1-\alpha\), we have the following confidence interval of proportions.

\(\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}\)

In which

z is the zscore that has a pvalue of \(1 - \frac{\alpha}{2}\).

The margin of error is of:

\(M = z\sqrt{\frac{\pi(1-\pi)}{n}}\)

37% of freshmen do not visit their counselors regularly.

This means that \(\pi = 0.37\)

98% confidence level

So \(\alpha = 0.02\), z is the value of Z that has a pvalue of \(1 - \frac{0.02}{2} = 0.99\), so \(Z = 2.327\).

You would like to be 98% confident that your estimate is within 3.5% of the true population proportion. How large of a sample size is required?

A sample size of n is required.

n is found when M = 0.035. So

\(M = z\sqrt{\frac{\pi(1-\pi)}{n}}\)

\(0.035 = 2.327\sqrt{\frac{0.37*0.63}{n}}\)

\(0.035\sqrt{n} = 2.327\sqrt{0.37*0.63}\)

\(\sqrt{n} = \frac{2.327\sqrt{0.37*0.63}}{0.035}\)

\((\sqrt{n})^2 = (\frac{2.327\sqrt{0.37*0.63}}{0.035})^2\)

\(n = 1030.4\)

Rounding up:

A sample size of 1031 is required.

Using a calculator, the trigonometric ratio of sin 98 is approximately 0.9848.

One of the trigonometric ratio we have in mathematics is the sine ratio. We can use calculator to find the sine of an angle without making use of tables. To do this on your calculator, enter the sine function followed by the degree of the angle you want to find its sine. You will get your answer.

Using a calculator, we can find the sine of 98 degrees as follows:

sin 98° ≈ 0.9848

Rounding this to four decimal places, we get:

sin 98° ≈ 0.9848

Therefore, sin 98° is approximately equal to 0.9848.

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(c) The argument is valid, and we can conclude that Penelope missed class because she got a detention.

(e) The argument is valid, and we can conclude that Penelope did not miss class because she got an A and did not get a detention.

(c) To prove this argument's validity, we need to define the predicates and express the hypotheses and conclusion using them:

Let "M(x)" be the predicate "x missed class", and "D(x)" be the predicate "x got a detention".

Hypotheses: M(Penelope), D(Penelope)

Conclusion: M(Penelope)

Using modus ponens, which states that if P implies Q and P is true, then Q must be true, we can conclude that M(Penelope) is true:

From M(Penelope) and "Every student who missed class got a detention", we have D(Penelope)

From D(Penelope), we have M(Penelope)

So, the argument is valid, and we can conclude that Penelope missed class because she got a detention.

(e) To prove this argument's validity, we need to define the predicates and express the hypotheses and conclusion using them:

Let "M(x)" be the predicate "x missed class", "D(x)" be the predicate "x got a detention", and "A(x)" be the predicate "x got an A".

Hypotheses: A(Penelope), ~D(Penelope)

Conclusion: ~M(Penelope)

Using modus tollens, which states that if P implies Q and Q is false, then P must be false,

we can conclude that M(Penelope) is false:

From A(Penelope) and "Every student who missed class or got a detention did not get an A",

we have ~M(Penelope) & ~D(Penelope)

From ~D(Penelope), we have ~M(Penelope)

So, the argument is valid, and we can conclude that Penelope did not miss class because she got an A and did not get a detention.

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The option that is extraneous solution of

√-3x-2=x+2 is A. -6.

From the information given, taking square both sides

-3x - 2 = (x + 3)²

On applying identity   = a² + b² + 2ab

Then ,

-3x -2 =  x² + 2² + 2 * 2 *x

-3x -2 =  x² + 4 + 4x.

On adding both sides by 3x

-2 =  x² + 4 + 4x + 3x

-2 =  x² + 4 + 7x

On adding both sides by 2

0 =  x² + 4 + 7x + 2

On switching sides

x² +7x + 6 = 0

On Factoring

x² +6x + x + 6 = 0

x ( x+ 6 ) +1 (x +6 ) = 0

On grouping

( x +1) ( x +6) = 0

x = -1, -6.

An extraneous solution is a root of a transformed equation that is not a root of the original equation. Therefore, -6 is the extraneous solution.

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Complete question

Which of the following is an extraneous solution of sqrt(-3x-2)=x+2 a.-6 b.-1 c.1 d.6

The statement that describes the distribution based on the given information is:

A) The distribution is approximately Normal, with a mean of 128 messages and a standard deviation of 98 messages.

The graph shows a normal distribution, as indicated by the shape of the curve. The highest point of the curve (the peak) is at 128, which represents the mean of the distribution.

The standard deviation measures the spread of the data, and based on the information given, it is 98. Therefore, option A accurately describes the distribution.

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Answer:

Step-by-step explanation:

You haven't provided functions to choose from!

The geometrical series is a series of numbers. The nth term of the series is [8× 0.5⁽ⁿ⁻¹⁾].

The geometrical series is a series of numbers where the ratio of any two consecutive numbers is constant.

In a geometric series, r is the ratio between any two consecutive terms, therefore, the ratio of these terms can be written as,

r = (4/8) = (1/2)

Also, a₁ is the first term of the series, therefore, the first term of the series will be 8.

Thus, the nth term of this series will be equal to,

\(n^{th} = a_1 \times r^{(n-1)}\\\\n^{th} = 8 \times (\dfrac{1}{2})^{(n-1)}\)

Hence, the nth term of the series is [8× 0.5⁽ⁿ⁻¹⁾].

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Answer:

B

Step-by-step explanation:

RANGE  are the Y values

Answer:

b

Step-by-step explanation:

The required point is W.

What is the co-plaer and non co-planer?

Co-planar refers to a set of objects that lie in the same plane or lie on the same flat surface. They have the same elevation and do not intersect each other.

Non-coplanar refers to a set of objects that are not in the same plane or do not lie on the same flat surface. They have different elevations and may intersect each other.

W is a point that is not co-planar with R, S, and T.

Consider the provided plane.

We need to find the point that is not co-planar with R, S, and T.

Co-planar: Two object or points are said to be co-planer if they lie in the same plane.

Non co-planar: Two object or points are said to be non co-planer if they don't lie in same plane.

Now consider the provided plane, the point W is not lie in the plane V.

While point R, S and T lie in the plane V.

Hence, the required point is W.

W is a point that is not co-planar with R, S, and T.

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FromHello, Volent strawberry is here to help!

Answer: 15.0 yd2

I hope this helps!

Bye have a nice day!

From: Miko

Answer:

1. Multiply the two legs of the triangle

  3 x 10 = 30

2. Divide that number by 2

  30 / 2 = 15

The area of the triangle is 15 yd2

x-x

Answer:

35

Step-by-step explanation:

You can easily graph this in desmos for a visual understanding.

The slope of a line is received by (y2-y1)/(x2-x1). Assuming that Days is X and the cost is Y, we get (160-90)/(4-2), and it makes 70/2, which equates out to 35. Because the prices become more and more expensive, the slope is positive 35.

The time it will take the tank to be empty is;

t = 1.26 minutes

The image of the initial tank is missing and so i have attached it.

Let's call the area of the hole be A_h

Thus, volumetric rate;  = A_h(√2gh)

dV/dt = -cA_h(√2gh)

Now, volume of tank is;

V = ¹/₃πr²h

V' = dv/dt =  (¹/₃πr²h)dh/dt

Thus; -cA_h(√2gh) = (¹/₃πr²h)dh/dt

t = (2(√H - √h))/(3c√2g × (r'/r)²)

where;

r' is radius of circular hole = 4 inches = 0.333 ft

h = 0 since the tank has a hole

c = 0.6

g = 32 ft/s²

H = 8 ft

Thus; r/H = tan 30°

r = 8 tan 30°

r = 4.6188 ft

Thus;

t = (2(√8 - √0))/(3 × 0.6(√2 × 32) × (0.333/4.6188)²)

t = 75.5757 seconds

Converting to minutes gives; t = 1.26 minutes

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Answer:

100 miles

Step-by-step explanation:

Let m be the number of miles.

\(100 + .30m = 50 + .80m\)

\(100 = 50 + .50m\)

\(.50m = 50\)

\(m = 100\)

Answer:

100

Step-by-step explanation:

You can put into a graph such as desmos and see where the lines intersect. the x value of the intersection is the answer you want.

(a) The average cost in 2011 is  

(b) A graph of the function g for the period 2006 to 2015 is shown below.

(c) Assuming that the graph remains accurate, its shape suggest that the average cost increases at a slower rate as time goes on.

Based on the information provided, we can logically deduce that the average annual cost (in dollars) for health insurance in this country can be approximately represented by the following function:

g(x) = -1736.7 + 1661.6Inx

where:

x = 6 corresponds to the year 2006.

For the year 2011, the average cost (in dollars) is given by;

x = (2011 - 2006) + 6

x = 5 + 6

x = 11 years.

Next, we would substitute 11 for x in the function:

g(11) = -1736.7 + 1661.6In(11)

g(11) = $2247.64

Part b.

In order to plot the graph of this function, we would make use of an online graphing tool. Additionally, the years would be plotted on the x-axis while the average annual cost would be plotted on the x-axis of the cartesian coordinate as shown below.

Part c.

Assuming the graph remains accurate, the shape of the graph suggest that the average cost of health insurance increases at a slower rate as time goes on.

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Complete Question:

The average annual cost (in dollars) for health insurance in a country can be approximated by the function g(x) = -1736.7 + 1661.6Inx, where x = 6 corresponds to the year 2006.

(a) Estimate the average cost in 2011.

(b) Graph the function g for the period 2006 to 2015

(c) Assuming that the graph remains accurate, what does the shape of the graph suggest regarding the average cost of health insurance?

Answer:

ima say C

Step-by-step explanation:

its really the only one that makes sense in the situation.

Answer:

x= I just want free points

The labeling of bases and height in a trapezium is not fixed and can vary based on the context or problem. It doesn't matter where they are on the trapezium, as long as they are clearly defined and consistent within the given situation.

In a trapezium (or trapezoid), the labeling of the bases and height is not fixed or standardized. It can vary depending on the context or the specific problem being considered. However, there are a few general guidelines to keep in mind when labeling a trapezium.

Bases: The trapezium has two parallel sides, often referred to as the "top base" and the "bottom base." The bases are usually labeled based on their relative lengths or position in the trapezium. The longer parallel side is commonly referred to as the "top base," while the shorter parallel side is referred to as the "bottom base." However, this is not a strict rule and can vary depending on the problem or preference.

Height: The height of a trapezium is the perpendicular distance between the bases. It is generally labeled as a vertical line segment connecting the bases. The placement of the height is not fixed, and it can be drawn from any point on the top base to any point on the bottom base, as long as it forms a perpendicular line. The height is usually labeled with the symbol "h" or sometimes "x" or "y" depending on the context.

It's important to note that the labeling of the bases and height is primarily for communication and clarity. As long as the labeling is consistent and clearly defined within the given problem or context, it does not have to conform to any specific arrangement or be in a rectangular shape. The key is to ensure that the labels are clearly understood and can be used to calculate the desired quantities or solve the problem at hand.

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