Answer:
x ≤ - 5/3
Step-by-step explanation:
Let the number be x
The sum of a number times 9 and 30 is at most 15 translates algebraically to
9x + 30 ≤ 15
Subtracting 30 both sides:
9x ≤ -15
Dividing by 9 both sides:
x ≤ - 15/9
or
x ≤ - 5/3
what is a shape with 7 sides?
The shape with 7 sides is called a heptagon.
There a several shapes which has more number of sides than the usual shapes like square, circle or triangle.
As the number of the sides in the shape increases the propertied of the shape also changes. If the shape has 7 sides it is called a heptagon and if it has 6 sides than it is called a hexagon, it it has a 5 sides it is called a pentagon.
If all the 7 sides of the pentagon are equal in magnitude then the heptagon is said to be a regular heptagon but is not equal then they are called heptagon with different features.
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Please help me for 30 points!!.
Answer: Correct option is B
Step-by-step explanation: 3/6 + 2/6 = 5/6
It is assumed that approximately​ 15% of adults in the u.s. are​ left-handed. consider the probability that among 100 adults selected in the​ u.s., there are at least 30 who are​ left-handed. given that the adults surveyed were selected without​ replacement, can the probability be found by using the binomial probability formula with x counting the number who are​ left-handed? why or why​ not?
a. Yes, because the 100 adults represent less than 5% of the U.S. adult population, the trials can be treated as independent.
b. No, because the 30 adults represent more than 5% of the sample size, the trials are dependent.
c. No, because the 100 adults were selected without replacement, the selections are dependent.
d. No, because the probability of being right-handed is greater, x must count the number of right-handed adults.
No, the probability be found by using the binomial probability formula with x counting the number who are left-handed. The correct option is (c) No, because the 100 adults were selected without replacement, the selections are dependent.
The binomial distribution assumes that the trials are independent, meaning that the outcome of one trial does not affect the outcome of any other trial. However, in this case, the 100 adults were selected without replacement, which means that the outcome of one selection affects the probability of the next selection. Therefore, the trials are dependent, and the binomial probability formula cannot be used.
Instead, we can use the hypergeometric distribution to calculate the probability of at least 30 left-handed adults in a sample of 100 adults selected without replacement from the U.S. population. The hypergeometric distribution takes into account the fact that the selections are dependent and is appropriate for this type of problem.
Therefore, the correct option is (c) No, because the 100 adults were selected without replacement, the selections are dependent.
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a. Find the perimeter of a triangle whose side
lengths are 5 cm, 8√3 cm, and √27 cm. Give
the answer as a radical expression in simplest
form.
Answer:
[tex]5+11\sqrt{3}[/tex]
---------------
Perimeter is the sum of side lengths:
[tex]P=5+8\sqrt{3}+\sqrt{27} =5+8\sqrt{3}+\sqrt{3^2*3} =5+8\sqrt{3}+3\sqrt{3}=5+11\sqrt{3}[/tex]how to convert 1gb to mb?
Answer:
To convert GB to MB multiply the value of a GB by 1000 to get mb.
1gb x 1000 equals 1000 mb
Which of the contexts below could not be modeled by an exponential function?
• A car depreciates at a rate of 3.7% per year.
• A sunflower was growing at a rate of 2.75 inches per week.
• A certain population of 25 aggressive zombies quadruples every week.
Money invested in a savings account grows at an annual rate of 2.2%.
Answer:
The context that could not be modeled by an exponential function is "A car depreciates at a rate of 3.7% per year." Exponential functions are typically used to model situations involving growth or decay that occur at a constant rate over time. In this case, the rate of depreciation of the car is decreasing over time, so it cannot be modeled by an exponential function. A linear function or a more complex model may be more appropriate.
What is the conversion of 52c to f?
52 °C is equal to 125.6 °F.
The Celsius( symbol °C) is an SI( International System of Units) deduced unit of temperature.
The Fahrenheit( symbol °F) is a unit of temperature that was extensively used previous to metrication.
How to Convert Celsius to Fahrenheit
F = [tex]\frac{9}{5}[/tex]C + 32
C = [tex]\frac{5}{9}[/tex](F - 32)
To convert 52 degrees Celsius to Fahrenheit,
We can use the following formula:
°F = (°C x 1.8) + 32
where °F is the temperature in Fahrenheit,
°C is the temperature in Celsius.
Substituting 52 for °C, we get:
°F = (52 x 1.8) + 32
Simplifying the expression:
°F = 93.6 + 32
°F = 125.6
Therefore, 52 degrees Celsius is equal to 125.6 degrees Fahrenheit.
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Solve for x. Round to the nearest tenth of a degree, if necessary.
2.1
D
4
to
E
Answer:
[tex]31.7^\circ[/tex]
Step-by-step explanation:
We use the property that the sin of the angle of a right triangle is the ratio of the side opposite that angle divided by the hypotenus
Therefore
[tex]\begin{aligned}\sin x & = \dfrac{2.1}{4}\\& = 0.525\\\end{aligned}\\\begin{aligned}x &= sin^{-1}(0.525)\\& = 31.7^\circ \end{aligned}[/tex]
Which measurement represents the height of the parallelogram
In Connexus.com
Unit 2: measurement
Lesson 1: Area and perimeter of parallelograms
The measurement that represents the height of the parallelogram is A. 3 m.
Where is the height of a parallelogram ?The height of a parallelogram is the perpendicular distance between its two parallel bases. It is the distance between the two parallel bases measured at a 90-degree angle.
To find the height of a parallelogram, draw a perpendicular line from one base to the other. The length of this line is the height of the parallelogram.
On the given image, the line that shows the perpendicular distance between its two parallel bases is 3 m so this is the height.
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unit 7 polygons and quadrilaterals homework 3 rectangles
If you are trying to find the missing measures of a rectangle, you should know that all rectangles have four sides, and each side has a length.
In other words, if you have a rectangle, two of the angles must be 90 degrees, and the other two angles must also be 90 degrees. To find the missing measures of a rectangle, you need to use the properties of rectangles.
First, find the length of each side. The length of all sides of a rectangle should be the same. Then, calculate the area of the rectangle. You can do this by multiplying the length of one side with the length of the other side.
Finally, you can use the Pythagorean Theorem to find the missing measures.
The Pythagorean Theorem states that the square of the length of the hypotenuse of a right triangle is equal to the sum of the squares of the other two sides.
Using this theorem, you can find the length of the hypotenuse of the rectangle.
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Complete Question:
if each quadrilateral is given, then define the steps to find the missing measures a rectangle.
find the missing side x 4 13
The length of missing side of the given right triangle by using pythagoras theorem is x = 12.369 .
Pythagoras Theorem :The hypotenuse side of a right-angled triangle's square is equal to the sum of the squares of the other two sides, according to Pythagoras' Theorem. The Perpendicular, Base, and Hypotenuse of this triangle are its three sides. Because to its position opposite the 90° angle, the hypotenuse in this case is the longest side. A right triangle's positive integer sides (let's say sides a, b, and c) are squared to obtain a Pythagorean triple equation.
Formula for Pythagoras' Theorem :Consider about the triangle given above:
the perpendicular to "a,"
B stands for base,
The letter "c" stands in for the hypotenuse.
The definition provides the following as the Pythagoras Theorem formula:
[tex]Hypotenuse^2 = Base^2 + Perpendicular^2\\\\c^2 = a^2 + b^2[/tex]
The right triangle's sides are as follows:
Perpendicular ( p ) = x
Base ( b ) = 4
Hypotenuse ( h ) = 13
Finding the length of missing side
Using Pythagoras theorem
[tex]p^2 +b^2=h^2[/tex]
plug the values
[tex]x^2+4^2=(13)^2[/tex]
Evaluate the power
[tex]x^2+16=169\\\\x^2=169-16\\\\x^2=153\\\\x=\sqrt{153}\\\\x= 12.369[/tex]
The length of missing side x = 12.369
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The complete question is ,
Find the missing side of the given right triangle whose sides are given as base = 4 units , hypotenuse = 13 units .
The dimensions of an above-ground, rectangular pool are 25 feet long, 18 feet wide, and 6 feet deep. How much water can fit in the pool?
Answer:
2700ft³ or 76455.49 litre
Step-by-step explanation:
Given
Length = 25 feet
Width = 18 feet
Height = 6 feet
Formula for Volume of cuboid = Length×Width×Height
So,
Volume of the pool = 25×18×6 = 2700ft³ or 76455.49 liters aprox.
The dimensions of a cone are shown in the diagram.
Which measurement is closest to the volume of the sugar cone in cubic inches?
the volume of the sugar cone is closest to 14.14 cubic inches.
How to determine?
The volume of a cone can be calculated using the formula V = (1/3)πr²2h, where r is the radius of the base, h is the height of the cone, and π is approximately 3.14.
In this case, the diameter of the cone is 3 inches, which means the radius, r, is half of that or 1.5 inches. The height of the cone is given as 6 inches.
Plugging these values into the formula, we get:
V = (1/3)π(1.5²2)(6)
V ≈ 14.14 cubic inches
Therefore, the volume of the sugar cone is closest to 14.14 cubic inches.
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State whether each of the following statement is true or false. Justify your answer.
(i) {2,3,4,5} and {3,6} are disjoint sets.
(ii) {a,e,i,o,u} and {a,b,c,d} are disjoint sets
(iii) {2,6,10,14} and {3,7,11,15} are disjoint sets
(iv) {2,6,10} and {3,7,11} are disjoint sets
The answer is (i) The statement is False, (ii) The statement is false, (iii) The statement is true, (iv) The statement is true.
(i) Let A = {2, 3, 4, 5} and B = {3, 6}
Now A∩B
= {2, 3, 4, 5} ∩ {3, 6} = {3}
Hence, A and B are not disjoint. So the statement is false.
(ii) Let A = {a, e, i, o, u} and B = {a, b, c, d}
Now A∩B
= {a, e, i, o, u} ∩ {a, b, c, d}= {a}
Hence, A and B are not disjoint. So the statement is false.
(iii) Let A = {2, 6, 10, 14} and B = {3, 7, 11, 15}
Now, A∩B
= {2, 6, 10, 14} ∩ {3, 7, 11, 15} = Φ
Hence, A and B are disjoint sets. So the statement is true.
(iv) Let A = {2, 6, 10} and B = {3, 7, 11}
Now A∩B
= {2, 6, 10} ∩ {3, 7, 11} = Φ
Hence, A and B are disjoint sets. So the statement is true.
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what is solution set calculator online
A solution set calculator online is a tool used to find the set of values that satisfy an equation or system of equations.
It is useful in a variety of mathematical fields such as algebra, calculus, and linear algebra. The calculator takes in the equation(s) and returns the solution set, which is the set of values that satisfy the equation(s). These calculators can be used for both linear and nonlinear equations, and can help in finding the solutions to problems that are difficult or time-consuming to solve by hand.
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Consider the following function. g ( x ) = x 3 − 6 A) Find its average rate of change over the interval [ − 2 , 2 ] . B) Compare this rate with the instantaneous rates of change at the endpoints of the interval.
A- The average rate of change of g(x) over the interval [-2, 2] is 4, B- the instantaneous rates of change at the endpoints are different from the average rate of change over the interval.
A) To find the average rate of change of the function g(x) over the interval [-2, 2], we need to compute the difference quotient:
average rate of change = [g(2) - g(-2)] / [2 - (-2)]
First, we find the values of the function at the endpoints of the interval:
g(-2) = [tex]-2^{3}[/tex] - 6 = -14
g(2) = [tex]2^{3}[/tex] - 6 = 2
Substituting these values into the
average rate of change = (2 - (-14)) / (2 - (-2)) = 16 / 4 = 4
Therefore, the average rate of change of g(x) over the interval [-2, 2] is 4.
B) To compare this rate with the instantaneous rates of change at the endpoints of the interval, we need to find the derivatives of the function at x=-2 and x=2 using the power rule of differentiation:
g'(x) = 3[tex]x^{2}[/tex]
g'(-2) = 3[tex]-2^{2}[/tex] = 12
g'(2) = 12
The instantaneous rate of change at x=-2 is 12, and the instantaneous rate of change at x=2 is also 12. These values are equal to the average rate of change over the interval [-2, 2], which is 4.
This means that the function g(x) is not a linear function over the interval [-2, 2], and the instantaneous rates of change at the endpoints are different from the average rate of change over the interval.
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step to calculate determine equilibrium concentration ?
The steps to calculate the equilibrium concentration have been explained below.
Equilibrium concentration is a state in a chemical reaction, at which the rate of forward reaction becomes the same as the rate of backward reaction.
Calculating equilibrium concentration requires several steps depending on the type of equilibrium you are dealing with which are,
1)Write the balanced chemical equation for the reaction.
2)Write the equilibrium expression that describes the relationship between the concentrations of the reactants and products at equilibrium.
3)Determine the initial concentrations of the reactants and/or products
4)Determine the direction of the reaction by comparing the initial concentrations of the reactants and products with the equilibrium constant (Keq).
5)Calculate the change in concentration between the equilibrium concentration and the initial concentration.
6)Calculate the equilibrium concentration by adding the change in concentration to the initial concentration.
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Jessica makes $48,960.00 per year. She has a clothing budget of 5 % of her monthly budget. What was the average amount of money that Jessica's budget allowed for clothing the first six months of 2001?
Answer: Jessica's average clothing budget for the first six months of 2001 was $102.
Explanation: To calculate the average amount of money that Jessica's budget allowed for clothing in the first six months of 2001, we first need to find her monthly budget.
We can do this by dividing her annual salary by 12 (the number of months in a year):
$48,960 / 12 = $4,080 per month
Next, we need to find her clothing budget for one month. We're told that her clothing budget is 5% of her monthly budget, so we can calculate this as follows:
5% of $4,080 = (5/100) x $4,080 = $204
Therefore, Jessica's clothing budget for one month is $204.To find her average clothing budget for the first six months of 2001, we simply need to multiply her monthly clothing budget by the number of months (i.e., 6):
$204 x 6 = $1,224
Finally, we divide this total by the number of months to find the average: $1,224 / 6 = $102
how to convert 44 kg to lbs
44 kg is approximately equal to 97.0034 pounds ( rounded to four decimal places )
The conversion factor to convert kg to lbs is 2.20462
1 kg = 2.20462 pounds
The conversion is the process of changing the unit of one quantity to another units
The conversion factor is defined as the number that is used to change one unit to another units by multiplying or dividing
The mass in lbs = The mass in kg × conversion factor
Substitute the values in the equation
1 kg = 2.20462 pounds
44 kg = 44 × 2.20462
Multiply the numbers
= 97.0034 pounds ( rounded to four decimal places )
Therefore, 44 kg is 97.0034 pounds
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What is 729 cube rooted?
The value of 729 cube root is 9.
The cube root function is important in various mathematical applications, including calculus, geometry, and physics.
The cube root of 729 is the number that when multiplied by itself three times, results in 729. This number is often represented as the symbol ³√729.
In other words, if we cube the cube root of 729, we get back the original number 729. The cube root of 729 is 9, since 9 x 9 x 9 = 729.
In mathematical terms, the cube root of 729 can be expressed as: ³√729 = 9.
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Find the area of the square ABCD. A D BE IC 14 m- [?] m[ ]
Answer:
196 m²
Step-by-step explanation:
area = side × side
area = 14 m × 14 m
area = 196 m²
FOOTBALL A college running back ran for 1732 total yards in the regular season. The table shows his cumulative total number of yards gained after select games
The college running back ran for a total of 1732 yards in the regular season.
We can use the table provided to find out how many yards he gained after select games.
127 + 252 + 372 + 495 + 612 + 732 + 853 + 974 + 1089 + 1212 + 1335 + 1458 + 1581 + 1704 = 1732
From the table, we can see that the running back gained 127 yards in the first game, 252 yards in the second game, 372 yards in the third game, and so on. By adding up the yards gained in each game, we can find the total number of yards gained in the regular season.
Therefore, the college running back ran for a total of 1732 yards in the regular season.
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An angle measures 63.4° less than the measure of its supplementary angle. What is the measure of each angle?
The measure of the angles required are,
Angle A = 58.3deg
Angle B = 121.7deg
What are Supplementary Angles?If two angles sum up to 180 degrees, they are referred to as supplementary angles. When paired, supplementary angles result in a straight angle (180 degrees). In other words, if angle 1 plus angle 2 equals 180 degrees, angle 1 and angle 2 are supplementary. In this case, Angles 1 and 2 are referred to as "supplements" of one another.
Supplementary angles, by definition, add to to a sum of 180deg.
So what we know is:
Angle B + Angle A = 180deg
Angle B - 63.4deg = Angle A
By substitution:
Angle B + (Angle B - 63.4deg) = 180deg
Using the commutative property of addition, we can re-write the equation as:
(Angle B + Angle B) - 63.4deg = 180deg
We can add 63.4deg to both sides of the equation:
(Angle B + Angle B) - 63.4deg + 63.4deg = 180deg + 63.4deg
By simplifying, that gives us:
2(Angle B) = 243.4deg
Dividing both sides of the equation by 2, we can determine the measure of Angle B:
Angle B = 243.4deg/2 = 121.7deg
Now we have the measure of one of the angles, which we can plug back into our first equation:
Angle B + Angle A = 180deg
121.7deg + Angle A = 180deg
Subtracting 121.7deg from both sides, we get:
Angle A = 180deg - 121.7deg = 58.3deg
There’s your answer:
Angle A = 58.3deg
Angle B = 121.7deg
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What is the conversion of 77 f to c?
The conversion of 77 f to c is equal to 25°C.
To convert temperatures in degrees Fahrenheit to Celsius, deduct 32 and multiply by .5556 ( or 5/9).
Temperatures, across the world, are measured either in Fahrenheit( the US temperature scale) or Celsius( the metric scale), two of the most popular and extensively used scales.
Temperature Conversion- Degrees Fahrenheit into Degrees Celsius.
To convert a temperature from Fahrenheit (°F) to Celsius (°C), we can use the formula:
°C = (°F - 32) x 5/9
By applying this formula, we can convert 77 °F to Celsius as follows
°C = (77 - 32) x 5/9
°C = 45 x 5/9
°C = 25
Therefore, 77°F is equal to 25°C.
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what is 1 c sugar in grams?
The 1 c sugar is 200 grams.
Gram (originally grams; [1] SI unit symbol g) is a mass unit in the International System of Units (SI), equal to one thousandth of a kilogram.
Originally defined from 1795 as "the absolute mass of a volume of pure water equal to one hundredth of a cubic meter [1 cm3] and at the melting point of ice", [2] the defining temperature (~ 0 °C) ) was later changed to
°C, which is the maximum density of water to temperature.
At the end of the 19th century, however, an attempt was made to make the basic unit the kilogram and a unit derived from the gram. In 1960, the new International System of Units defined the gram as one thousandth of a kilogram (ie, a gram is 1 × 10–3 kg). As of 2019, the International Bureau of Weights and Measures defines the kilogram as a fixed numerical value of Planck's constant (h) of 6.62607015×10−3
kg⋅m2⋅s−1.[3][
] ]
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What is bell curve percentages
The Bell Curve is a symmetrical curve that represents the probability distribution of a random variable.
The Bell Curve, also known as the normal distribution or Gaussian distribution, is a statistical concept used to describe the distribution of a set of data. The Bell Curve is a symmetrical curve that represents the probability distribution of a random variable.
The Bell Curve is often used to describe the distribution of scores on a test or exam. In this context, the Bell Curve is used to represent the distribution of scores across a population. The mean score (average score) is represented by the highest point on the curve, and the standard deviation is represented by the width of the curve.
In terms of percentages, the Bell Curve can be divided into different standard deviations, with each standard deviation representing a certain percentage of the population. The percentages of the population within each standard deviation are as follows:
68.27% of the population falls within one standard deviation of the mean.
95.45% of the population falls within two standard deviations of the mean.
99.73% of the population falls within three standard deviations of the mean.
These percentages are useful for understanding how scores or data are distributed across a population and can be used to set cutoff scores or define performance categories.
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A big ship drops its anchor. E represents the anchor's elevation relative to the water's surface (in meters) as a function of time t (in seconds).
E=−2.4t+75
How far does the anchor drop every 5 seconds?
Answer:12
Distance for the anchor drop every 5 seconds is,
⇒ E = 63 meters
What is mean by Multiplication?Multiplication means to add number to itself a particular number of times. Multiply will be viewed as a process of repeated addition.
Given that;
A big ship drops its anchor.
Here, E represents the anchor's elevation relative to the water's surface (in meters) as a function of time t (in seconds).
E = - 2.4t + 75
Now, Distance for the anchor drop every 5 seconds is,
Put t = 5;
E = - 2.4t + 75
E = - 2.4 × 5 + 75
E = - 12 + 75
E = 63 meters
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What is the slope of a line perpendicular to a line with a slope of five
Answer: It is undefined
Step-by-step explanation:
Hope this helps-just had a test on this!
Find the orthogonal trajectories for the family of curves. (enter your solution in the form f(x, y) = c or y = f(x, c) where c is a needed constant. ) y = ce5x
Refer to the attached image.
At Silver Gym, membership is $45 per month, and personal training sessions are $25 each. At Fit Factor, membership is $75 per month, and personal training sessions are $15 each. In one month, how many personal training sessions would Sarah have to buy to make the total cost at the two gyms equal?
Answer:
3
Step-by-step explanation:
Set the equations. Let the variable x denote the amount of months that are needed.
Silver Gym:
In Silver Gym, the membership is a flat fee (constant) of $45, and training sessions are $25 for each session (25x, x denoting the amount of sessions).
Therefore, total cost is:
Total Cost (c) = Training session x Training cost per session + Flat Fee
or
c = 25x + 45
Fit Factor:
In Fit Factor, the membership is a flat fee (constant) of $75, and training sessions are $15 for each session (15x, x denoting the amount of sessions).
Therefore, the total cost is:
Total Cost (c) = Training session x Training cost per session + Flat Fee
or
c = 15x + 75
~
You are trying to solve for the amount of training sessions that have to be bought in which both prices will be the same. Note that both equations are equal to c. Based on the transitive property of equality, if a = b and b = c, then a = c. Therefore:
c = 25x + 45
c = 15x + 75
15x + 75 = c = 25x + 45
15x + 75 = 25x + 45
Isolate the variable, x. Note the equal sign, what you do to one side, you do to the other. Subtract 25x and 75 from both sides of the equation:
15x (-25x) + 75 (-75) = 25x (-25x) + 45 (-75)
15x - 25x = 45 - 75
-10x = -30
Next, divide -10 from both sides of the equation:
(-10x)/-10 = (-30)/-10
x = -30/-10 = 3
3 personal training sessions is your answer.
~
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