The compound inequality which represents the recommendation of economists for a GDP growth rate to be between 7.1 and 7.9 percent (inclusive) is given by '7.1 ≤ g ≤ 7.9'. This mathematical expression indicates that the acceptable rates are all the values including and between 7.1 & 7.9.
Explanation:In the context of mathematics, specifically the subject of inequalities, the student's question is asking to represent the given GDP rates as a compound inequality. A compound inequality is a statement with two inequalities joined by the word 'and' or 'or'.
Here, economists recommend the GDP growth rate to be between 7.1 and 7.9 percent (inclusive). So, the GDP growth rate (let's denote it as 'g') is more than or equal to 7.1 percent and, at the same time, less than or equal to 7.9 percent. So, the compound inequality which represents this situation is 7.1 ≤ g ≤ 7.9. So the correct option from the provided ones is the first one: '7.1 ≤ g ≤ 7.9'.
This inequality tells us that the growth rates 'g' are all the values including and between 7.1 & 7.9. This is crucial information for economists when monitoring the health and progress of a nation's economy. The percentage rate of GDP growth is a measure of economic success and can impact many aspects like standard of living, employment rates, and business growth.
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Bronson builds a rectangular deck for his friend. the width of the deck is 29 feet. the perimeter of the deck must be at least 134 feet.
a. write an inequality that represents all possible values for the length of the deck.
b. find all possible values for the length of the deck.
Can somebody tell me if this is factorable? I've been trying this with a friend and we can't come up with any numbers. x^2 + 9x - 4
The perimeter of an isosceles triangle is 7.5m, and the length of a leg is 2m. Find the length of the base.
As per linear equation, the length of the base is 3.5m.
What is a linear equation?A linear equation is an equation that has the highest power of the variable as 1.
Given, the perimeter of an isosceles triangle is 7.5m.
The length of a leg is 2m.
Therefore, the length of the other leg is 2m.
Let, the length of the base is 'x'.
Therefore, [tex](2 + 2 + x) = 7.5[/tex]
⇒ [tex]4 + x = 7.5[/tex]
⇒ [tex]x = 7.5-4[/tex]
⇒ [tex]x = 3.5[/tex]
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A password is 4 characters long and must consist of 3 letters and 1 of 10 special characters. If letters can be repeated and the special character is at the end of the password, how many possibilities are there?
1st digit = 1 of 26 letters
2nd digit = 1 of 26 letters
3rd digit = 1 of 26 letters
4th digit = 1 of 10 special characters
26 x 26 x 26 x 10 = 175,760 possibilities
A gardener charges an initial fee of $37.50 plus a rate of $44.90 per hour. Write a function that shows the total fees for H hours of work
Two pounds is equivalent to approximately how many kilograms
how would solve 2s + s = 36
Maya made $252 for 12 hours of work. at the same rate, how many hours would she have to work to make $168 ?
Answer:
8
Step-by-step explanation:
252/12 = 21
168/ 21 = 8
Vector's map has the scale missing. He knows that the distance for the lake to the youth center is 8 miles. On the map, they are two inches apart. What is the scale for Vector's map
Answer:
The scale factor is 1/4.Step-by-step explanation:
Givens
The actual distance from the lake to the youth center is 8 miles.On the map, the distance is 2 inches.According to the problem, each 2 inches are equivalent to 8 miles of actual distance.
The scale factor can be found by dividing
[tex]s=\frac{2}{8}=\frac{1}{4}[/tex]
Therefore, the scale factor of Vector's map is 1/4, because the actual distance is 4 times bigger.
which factorization is equivalent to 6x squared + 7x - 10?
What is the transformation of C(9, 3) when dilated by a scale factor of 3, using the origin as the center of dilation?
The transformation of C(9, 3) when dilated by a scale factor of 3, using the origin as the center of dilation is:
C'(27,9)
Step-by-step explanation:Dilation transformation--
A dilation transformation is a transformation which changes the size of the original figure but the shape remain unchanged.
i.e. if any figure is dilated by a scale factor k with the center of dilation as origin.
Then the change pr transformation in each of the vertices of the figure is given by:
(x,y) → (kx,ky)
We are given a point C which is located at C(9,3)
Hence, here k=3
Hence, we get:
C(9,3) → C'(9×3,3×3)
i.e. C(9,3) → C'(27,9)
A sea turtle swims at a speed of 27 kilometers per hour. A girl swims 14 decimeters per second. 1 m = 10 dm 1000 m = 1 km How much faster does the sea turtle swim than the girl in meters per minute?
Final answer:
Calculate how much faster a sea turtle swims than a girl in meters per minute by converting their speeds to a common unit and finding the difference.
Explanation:
To find out how much faster the sea turtle swims than the girl in meters per minute, we need to convert their speeds to a common unit. Let's first convert the girl's speed to kilometers per hour:
Girl's speed = 14 decimeters per second = 1.4 meters per second = 5.04 kilometers per hour
Now, we compare the speeds:
Sea turtle speed = 27 kilometers per hour
Girl's speed = 5.04 kilometers per hour
Sea turtle swims 21.96 kilometers per hour faster than the girl. To find how much faster this is in meters per minute:
21.96 km/h * 1000 m/km / 60 min/h = 366 meters per minute
what number should the fraction 7/8 be multiplied by in order to equal 1
The solution is 8/7
The number which should by multiplied with 7/8 to get 1 is 8/7 or the reciprocal of the number
What is an Equation?
Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the number be represented as = N
The value of n is given by
The number ( 7 / 8 ) x N = 1
On simplifying the equation , we get
( 7/8 ) x N = 1
Multiply by 8 on both sides of the equation , we get
7N = 8
Divide by 7 on both sides of the equation , we get
N = 8/7
Therefore , the number N is 8/7
Hence , the number is 8/7 or reciprocal of 7/8
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A bell tolls every 10 minutes. Another bell tolls every 15 minutes. Both bells toll at 6:00 PM. They will toll together again at??
Triangle ABC is shown below.
What is the length of line segment AC?
7
9
14
18
Answer:
Option C. AC = 14 units
Step-by-step explanation:
In the given triangle ABC shown in the figure ∠ABC = ∠ACB
Since angles are equal so opposite sides of equal angles will be equal.
Now mAB = mAC
By putting values in terms of x
2x = 3x - 7
x = 7
Now mAC = 3x - 7
By putting value of x = 7
mAC = 3×7 - 7 = 21 - 7 = 14
Therefore length of line segment AC is 14 units.
In how many different ways can a panel of 12 jurors and 2 alternates be chosen from a group of 17 prospective jurors?
Final answer:
To find the different ways of choosing a panel of 12 jurors and 2 alternates from 17 prospective jurors, calculate the combinations separately (C(17, 12) for jurors and C(5, 2) for alternates) and multiply them, yielding a total of 61,880 different ways.
Explanation:
The question asks in how many different ways a panel of 12 jurors and 2 alternates can be chosen from a group of 17 prospective jurors. To solve this, we use the concept of combinations in mathematics. Since the order in which we select the jurors and alternates does not matter, we are dealing with combinations, not permutations.
First, we choose the 12 jurors from the 17, which is the combination of 17 taken 12 at a time. This can be calculated using the formula for combinations:
C(n, k) = n! / (k! * (n - k)!),
where 'n' is the total number of items, 'k' is the number of items to choose from, and '!' denotes factorial.
For the 12 jurors, we compute C(17, 12) which equals 17! / (12! * (17 - 12)!) = 17! / (12! * 5!) = 6188.
Next, we need to choose 2 alternates from the remaining 5 jurors. The calculation is C(5, 2) which equals 5! / (2! * (5 - 2)!) = 5! / (2! * 3!) = 10.
Since choosing jurors and alternates are independent events, we multiply the two combinations to get the total number of different ways to choose the panel:
6188 (ways to choose jurors) * 10 (ways to choose alternates) = 61,880 different ways.
Write 247.903 in expanded form
Answer:
The answer is
247.903=200.000+47.000+7.000+0.900+0.003
Step-by-step explanation:
In order to determine the expanded form, we have to know about the rule. The expanded form is a way of writing numbers to see the math value of individual digits. When numbers are separated into individual place values and decimal places they can also form a mathematical expression.
For example:
6.432 in expanded notation form is 6.000 + 0.400 + 0.030 + 0.002
In this case:
247.903=200.000+47.000+7.000+0.900+0.003
HELP WITH THESE MATH PROBLEMS
which of the following is a solution of x^2+6x=-22
A 6foot tree casts a 3.25 ft shadow. How tall is a tree that casts a 10 ft shadow?
The height of the tree is 18.46 feet.
What is Proportion?In general, the term "proportion" refers to a part, share, or amount that is compared to a total.
A mathematical comparison of two numbers is called a proportion. According to proportion, two sets of provided numbers are said to be directly proportional to one another if they increase or decrease in the same ratio. "::" or "=" are symbols used to indicate proportions.
Given:
A 6 foot tree casts a 3.25 ft shadow.
let the height of the tree who cast shadow 10 ft.
So, Using Proportion
6 / 3.25 = x / 10
60 = 3.25 x
x= 60/ 3.25
x= 18.46 feet
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Final answer:
To determine the height of a tree that casts a 10 ft shadow, using the ratio from a 6 ft tree that casts a 3.25 ft shadow, we find the tree is approximately 18.46 feet tall through the concept of similar triangles.
Explanation:
The question asks how tall a tree is that casts a 10 ft shadow, given that a 6 ft tree casts a 3.25 ft shadow. This problem can be solved using the concept of similar triangles, where the ratio of the heights of the trees is equal to the ratio of the lengths of their shadows.
To find the height of the tree that casts a 10 ft shadow, we set up the proportion as follows:
Height of first tree / Shadow of first tree = Height of unknown tree / Shadow of unknown tree
Substituting the given values:
6 ft / 3.25 ft = Height of unknown tree / 10 ft
By cross-multiplying and solving for the height of the unknown tree, we get:
(6 ft × 10 ft) / 3.25 ft = 18.46 ft
Therefore, a tree that casts a 10 ft shadow is approximately 18.46 feet tall.
Write the inverse function for the function,f(x)=1/2x+4then, find the value of ƒ-^1(4) type your answers in the box
The inverse function of the above function is f(x) = 2x - 8 and therefore the function at 4 would be equal to 0.
You can find the inverse of any function by switching the f(x) and x terms. Once you have done that, solve for the new f(x). Finally, what you'll have remaining is the inverse function. The work is done for you below:
f(x) = 1/2x + 4 ----> Switch the x and f(x)
x = 1/2f(x) + 4 ---> subtract 4 from both sides
x - 4 = 1/2f(x) ----> multiply both sides by 2
f(x) = 2x - 8
This would be your inverse function. Now to find f-1(4) you would put 4 in for x in your new inverse function.
f(x) = 2x - 8
f(4) = 2(4) - 8
f(4) = 8 - 8
f(4) = 0
In the last year a total of 2783 earthquakes occurred in the country. Of these, 85.8% were minor tremors w/ magnitudes of 3.9 or less on the richer scale. How many minor earthquakes occurred in the country last year? Round to nearest whole number.
here you go the brainless
Chris's uncle has a model car. the model is 6 inches long and 3 inches wide. the actual car is 75 inches long. what is the car's actual width, if we assume the model's proportions are accurate? if necessary, round to the nearest tenth of an inch.
I believe the right answer would be 37.5
Evaluate each expression below.
Click on "Undefined" as needed.
0/9=
3÷0 =
The value of 0 divided by 9 is 0, while the value of 3 divided by 0 is undefined because division by zero does not result in a finite number in mathematics.
Explanation:The expressions presented here involve division, a basic operation in mathematics. Let's evaluate each one respectively.
0/9 = 0: This is because zero divided by any number equals zero. 3 ÷ 0 = Undefined: Division by zero is undefined in mathematics because there is no number that you can multiply by 0 to get a non-zero number. Learn more about Division in Mathematics here:
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A physicist working in a large laboratory has found that light particles traveling in a particle accelerator increase velocity in a manner that can be described by the linear function −4x + 3y = 21, where x is time and y is velocity in kilometers per hour. Use this function to determine when a certain particle will reach 40km/hr.
The particle will reach 40km/hr when X=_____
Final answer:
To determine when the particle will reach a velocity of 40km/hr, substitute the value of y into the linear function and solve for x. The particle will reach 40km/hr when x = 24.75.
Explanation:
To determine when a certain particle will reach a velocity of 40km/hr, we need to find the value of x in the given linear function −4x + 3y = 21. Since y represents velocity, we can substitute 40 for y and solve for x.
By substituting 40 for y, we get −4x + 3(40) = 21. Simplifying the equation, we have −4x + 120 = 21. Rearranging the equation, we get −4x = 21 - 120 = -99.
Dividing both sides of the equation by -4, we find that x = 99 / 4 = 24.75.
Therefore, the particle will reach 40km/hr when x = 24.75.
To determine when the particle will reach 40 km/hr, substitute the value into the equation and solve for x. The particle will reach 40 km/hr when x = 24.75.
Explanation:The linear function −4x + 3y = 21 describes the relationship between time (x) and velocity (y) of light particles in a particle accelerator. To determine when a certain particle will reach 40 km/hr, we can substitute the value of y as 40 into the equation and solve for x.
−4x + 3(40) = 21
Simplifying the equation, we get -4x + 120 = 21
Combining like terms, -4x = 21 - 120 = -99
Dividing both sides by -4, we find that x = -99/(-4) = 24.75
Therefore, the particle will reach 40 km/hr when x = 24.75.
Simplify the expression. –10z – 28z
18
18z
–38z
38z
How do I write and graph an inequality in two variables and use them to solve a real-world problem?
which statement is true about this argument ?
premises:
If a quadrilateral is a square, then the quadrilateral is a rectangle.
If a quadrilateral is a rectangle then the quadrilateral is a parallelogram.
conclusion:
If a quadrilateral is a square, then the quadrilateral is a parallelogram.
A. the argument is not valid because the premises are not true.
B.the argument is valid by the law of syllogism
C. the argument is valid by the law of detachment
D. the argument is not valid because the conclusion does not follow from the premises.
The statement that is true about this argument is B. The argument is valid by the law of syllogism.
The law of syllogism means that an argument can be based on deductive reasoning. In such a case, there are premises and a conclusion.
A quadrilateral is a shape that has four sides. Therefore, based on the premises given, a quadrilateral is a square, then the quadrilateral is a parallelogram.
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Suppose you want to build a fish tank in the shape of a right rectangular box with square base and no top which will hold 6 cubic feet of water. the glass for the sides costs $1 per square foot, and the metal for the bottom costs $1.50 per square foot. what dimensions for the tank will minimize the cost?