the correct option for this question is (a) e < 53.
Why it is?
The inequality that represents Natasha's earnings, e, from any of the companies she interviewed with is:
e < 53.5
This is because her projected earnings per hour range from $25.13 to $53.5, and the maximum value is $53.5. So, her earnings from any of the companies cannot be greater than $53.5 per hour. Therefore, the correct answer is option (a) e < 53.
Earnings are the amount of money that a person earns from their work, business, investments, or other sources of income. This can include salaries, wages, commissions, bonuses, and profits, among others.
Earnings are typically reported as gross income, which is the total amount earned before taxes and other deductions are taken out. It is an important measure of a person's financial well-being and is often used to determine eligibility for credit or loans. Earnings can vary widely depending on a person's job, level of experience, education, and industry, among other factors.
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How many solutions does it have ?
Y =4
Y =4x-1
Answer:
1 solution
Step-by-step explanation:
Y = 4
Y = 4x - 1
Substitute value of Y here,
4 = 4x - 1
4 + 1 = 4x
5 = 4x
5/4 = x
1.25 = x
•°• The given equation can have only 1 solution, i.e, a linear equation with 1 variable gives only 1 solution.
______
hope this helps!
Examine the diagram. A triangle has angles 1, 2, 3. Angle 4 is an exterior angle to angle 3. For the angles shown in the diagram, which statements are true? Select all that apply. The sum of m∠3 and m∠4 is 180°. The sum of the measures of the adjacent interior angle and one of the remote interior angles is equal to the measure of the exterior angle. ∠3 is supplementary to ∠1. m∠4 = m∠1 + m∠2. m∠1 + m∠2 + m∠3 = 180°
The statements that are true regarding the diagram given are:
m∠3 + m∠4 = 180° (angles on a straight line)m∠4 = m∠1 + m∠2 (external angle theorem)m∠1 + m∠2 + m∠3 = 180° (triangle sum theorem).What is the Triangle Sum Theorem?Angle sum property of triangle states that the sum of interior angles of a triangle is 180°.
We have in the diagram that in the diagram given, the statements that are all true are:
m∠3 + m∠4 = 180° (angles on a straight line)
m∠4 = m∠1 + m∠2 (external angle theorem)
m∠1 + m∠2 + m∠3 = 180° (triangle sum theorem).
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PLEASE HELP....Dilations
Okay, just think of dilations as scaling the object bigger or smaller. You are just multiplying all points on the shape by a common scalar.
The only other thing is a negative dilation reflects the shape over the origin (which is quite intuitive cause you negate all the coordinates).
Now for question 1 your just trying to find the scale factor given an original point and a dilated point. Since all points are multiplied by the same factor,
(-3,6)x = (-4,8)
x=4/3
For the second question, just check points to see if all follow the same dilation scale factor. For our purposes it suffices to just check the each vertex.
(1,1) -> (2,2) so the scale factor must be 2
(1,4) -> (2,8) good
(5,1) -> (10,2) good
(5,4) -> (10,8) good
So, this transformation describes a dilation. The scale factor is 2.
The perimeter and the length of the base of an isosceles triangle are 25cm and 9cm respectively. Calculate the area of the triangle. (Ans: 29.76cm²)
Answer:
Let's denote the length of the equal sides of the isosceles triangle by "x". Then the perimeter of the triangle can be expressed as:
Perimeter = 2x + 9
But we also know that the perimeter of the triangle is 25cm, so we can set these two expressions equal to each other and solve for x:
2x + 9 = 25
2x = 16
x = 8
Therefore, the length of each of the equal sides is 8cm. Now, we can use the formula for the area of a triangle:
Area = (base × height) / 2
Since the triangle is isosceles, we know that the height is also the perpendicular bisector of the base, dividing it into two equal parts of length 4.5cm each. Now we can find the height of the triangle using the Pythagorean theorem:
h² + 4.5² = 8²
h² + 20.25 = 64
h² = 43.75
h ≈ 6.61
Substituting these values into the formula for the area of the triangle, we get:
Area = (9 × 6.61) / 2
Area ≈ 29.76 cm²
Therefore, the area of the isosceles triangle is approximately 29.76 cm².
I need help asap!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answer:
Step-by-step explanation: 1. is Yes 2 is no 3. is all 4 is Y and 50 5 is yes and -1
Can somebody find me a pencil to write please
Try going to the store and they should be surprisingly cheap.
Answer: here it is.
Step-by-step explanation:
How do I get domain for (x-7)(x-1) over (x+3)(x-1)
Answer:
To find the domain of the function f(x) = (x-7)(x-1)/(x+3)(x-1), we need to consider the values of x that make the denominator zero since division by zero is undefined.
In this case, the denominator (x+3)(x-1) is zero when x = -3 and x = 1. Therefore, we need to exclude these values from the domain.
So, the domain of f(x) is all real numbers except x = -3 and x = 1.
In interval notation, we can write the domain as (-∞, -3) U (-3, 1) U (1, ∞).
1. Identify and clearly label the slope and y-intercept for each equation in slope intercept form. Choose the correct answer from the choices below.
Y=-5
A. Slope is-5 and the y-intercept is (0,0)
B.Slope is zero and the y-intercept is (0,-5)
C. Slope is zero and the y-intercept is (0,0)
D. Slope is -5 and the y-intercept is (0,-5)
Slope is zero and the y-intercept is (0,-5)
What is slope ?
In mathematics, slope is a measure of the steepness of a line. It is defined as the ratio of the vertical change (rise) between two points on the line to the horizontal change (run) between the same two points.
In other words, the slope of a line is the change in the y-coordinate divided by the change in the x-coordinate between any two points on the line. It can also be thought of as the rate at which the line rises or falls as it moves horizontally.
The formula for calculating slope is:
slope = (y2 - y1) / (x2 - x1)
where (x1, y1) and (x2, y2) are two points on the line.
According to the question:
The equation Y = -5 is already in slope-intercept form, which is y = mx + b, where m is the slope and b is the y-intercept.
Comparing the equation Y = -5 to y = mx + b, we can see that:
The slope, m, is 0, since there is no x-term in the equation.
The y-intercept, b, is -5, since that is the constant value in the equation.
Therefore, the correct answer is:
B. Slope is zero and the y-intercept is (0,-5)
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Help with number 4!!!
Answer:forgot the explanation
Step-by-step explanation: give me a equation to solve
Solve the problems. Show your work.
7
1. Mr. Nguyen had 7/8
pint of water in his water bottle. Then, he drank 2/3
pint. How much water is left in the bottle?
Answer:
7/8 - 2/3 = 5/8 pint of water left in the bottle.
Pls help meee!!
Anybody!!!
Answer:
85 degrees.
Step-by-step explanation:
These are parallelograms, meaning the opposite sides are parallel. Since they are parallel, that the line EA becomes a transversal and a bisector for the angle CEK. That means the angle 8 and 3 are equivalent and 7 and 4 are equivalent. This is due to Same Side Interior Angles. These are two halves of the big angle. If the halves are equal, so are the angles. Therefore, CEK = CAK.
Joseph and Deb deposit $600.00 into a savings account which earns 5% interest compounded
continuously. They want to use the money in the account to go on a trip in 1 year. How much
will they be able to spend?
Round your answer to the nearest cent.
Answer:
We can use the formula for continuous compound interest to find the balance in Joseph and Deb's savings account after 1 year:
A = Pe^(rt)
where A is the balance, P is the principal (initial deposit), e is the mathematical constant approximately equal to 2.71828, r is the annual interest rate as a decimal, and t is the time in years.
Substituting the given values, we get:
A = $600.00e^(0.05*1)
Using a calculator, we get:
A ≈ $632.57
Therefore, Joseph and Deb will have approximately $632.57 in their savings account after 1 year. They can spend up to this amount on their trip. Rounded to the nearest cent, the answer is $632.57.
Write the absolute value equations in the form |x-b|=c that have the following solution sets: One solution: x=<5
IN EQUATION FORM NOT SIMPLIFIED.
Answer:
|x-5|=0
Step-by-step explanation:
That was easy.
f(x) = 2x - 1 g(x) = 7x + 8 find (gof) (x)
Answer:
(gof)(x) = 14x + 1
Step-by-step explanation:
We can think of (gof)(x) as g(f(x)). Writing it in this form shows that we must start with the inner function and work our way to the outer function.
Essentially, the input of the inner function yields an output and the output becomes the input of the outer function.
f(x) means that the input is x and since we're given no value for x (e.g. x = so and so), the output is the original function or 2x - 1
Now, this output becomes the input for g(x):
g(2x-1) = 7(2x - 1) + 8
14x -7 + 8
(gof)(x) = 14x + 1
Find the slope of the line.
A decreasing line that has a Y intercept of zero and passes through the point, four, negative 3.
I will mark you brainiest!
The value of M is
A) 14
B) 18
C) 20
D) 28
Answer:
I got 28
Step-by-step explanation:
use the formula k=y/x. 6/8=0.75
21/0.75=
I need a satisfying conditions question answered thank you sm
The linear function can be written as:
f(x) = -x/3 + 17/3
How to find the linear function?A general linear function can be written as:
f(x) = ax + b
Where a is the slope, and b is the y-intercept.
If we know two points on the line (x₁, y₁) and (x₂, y₂), then the slope of the linear function is:
a= (y₂ - y₁)/(x₂ - x₁)
Here we know the pairs:
f(-4) = 7
f(5) = 4
So we have the points (-4, 7) and (5, 4), then the slope is:
a = (4 - 7)/(5 + 4) = -3/9 = -1/3
Then we can write:
f(x) = -x/3 + b
now we can use one of the given points, like f(5) = 4, replacing that there we will get:
4 = -5/3 + b
4 + 5/3 = b
12/3 + 5/3 = b
17/3 = b
So the function is:
f(x) = -x/3 + 17/3
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What is the surface area?
26 ft
36 ft
33 ft
Answer:
To calculate the surface area of an object, we need to know its shape. Please provide more information on the object's shape or context of the problem to calculate its surface area.
Review the graph of a piecewise function.
The range of the function is the set of all real numbers greater than or equal to -2, because the lowest possible value of the function is -2, which occurs at x = 2.
What is a piecewise function ?
A piecewise function is a function that is defined by different equations on different parts of its domain. The graph of a piecewise function consists of several distinct parts, each corresponding to a different equation.
The graph shown is an example of a piecewise function. The function is defined using different equations on different intervals of the domain.
On the interval from negative infinity to negative 2, the function is defined by the equation y = 2. This means that the value of the function is always 2 on this interval, regardless of the value of x.
On the interval from negative 2 to 2, the function is defined by the equation y = -x. This means that the value of the function is equal to the negative of x on this interval.
On the interval from 2 to positive infinity, the function is defined by the equation y = 2. This means that the value of the function is always 2 on this interval, regardless of the value of x.
At the point x = -2, the function experiences a discontinuity, because the two equations that define it have different values at this point. The function is not differentiable at this point, because it does not have a well-defined tangent line.
The domain of the function is the set of all real numbers, because there are no restrictions on the values of x that are allowed.
Therefore, The range of the function is the set of all real numbers greater than or equal to -2, because the lowest possible value of the function is -2, which occurs at x = 2.
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the unit rate for this relationship is 1 gallon per 18.25 minutes
The amount of liquid that can be processed in 2 hours at a unit rate of 1 gallon per 18.25 minutes is calculated to be approximately 6.58 gallons.
What is unit rate?
A unit rate is the cost for only one of anything. This is expressed as a ratio with a denominator of 1. For instance, if you covered 70 yards in 10 seconds, you did so at an average speed of 7 yards per second. Although both of the ratios—70 yards in 10 seconds and 7 yards in one second—are rates, only the latter is a unit rate.
Assuming the unit rate of 1 gallon per 18.25 minutes, we can convert 2 hours to minutes by multiplying it by 60, which gives us 120 minutes.
So, in 120 minutes, the amount of liquid that can be processed at a unit rate of 1 gallon per 18.25 minutes would be:
(120 minutes) / (18.25 minutes/gallon) = 6.58 gallons
Therefore, the amount of liquid that can be processed in 2 hours at a unit rate of 1 gallon per 18.25 minutes is found out to be approximately 6.58 gallons.
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The complete question is :
What is the amount of liquid that can be processed in 2 hours at a unit rate of 1 gallon per 18.25 minutes?
Suppose a city with population 100,000 has been growing at a rate of 7% per year. If this rate continues, find the population of this city in 19 years.
Answer:b
Step-by-step explanation:
trust it’s b
What is the area of a rectangle with a length of 3 1/3 feet and a width of 1 2/3
0 2 7/9 ft
0 3 2/9 ft²
0 5 5/9 ft²
0 8 1/3 ft²
Answer:
[tex]5 \frac{5}{9} \: {ft}^{2} [/tex]
Step-by-step explanation:
[tex]a \: (length) = 3 \frac{1}{3} \: ft[/tex]
[tex]b \: (width) = 1 \frac{2}{3} \: ft[/tex]
[tex]a \: (rectangle) = a \times b[/tex]
[tex]a = 3 \frac{1}{3} \times 1 \frac{2}{3} = \frac{10}{3} \times \frac{5}{3} = \frac{50}{9} = 5 \frac{5}{9} {ft}^{2} [/tex]
Shebane rolls a standard six sides number cube. Find p
Answer:
2/3
Step-by-step explanation:
A six sided number cube :
Sample space = 1,2,3,4,5,6
Non composite numbers on a six sided number cube = 1,2,3,5
Probability of an event = required outcome / Total possible outcomes
Required outcome = number of non composite number = 4
Total possible outcomes = sample space = 6
P(not composite)= 4/6 = 2/3
which of these animals can travel at the greatest distance from sea level?
Answer:
Dragonflies
Step-by-step explanation:
They can fly on top of the water, but also, they have the fastest turns per second for their wings.
right 52.5% as a fraction in simplest form
The fraction in simplest form of 52.5% is 21/40.
A fraction is a part of a whole. In arithmetic, the number is expressed as a quotient, in which the numerator is divided by the denominator.
Decimals are the numbers, which consist of two parts namely, a whole number part and a fractional part separated by a decimal point.`
Steps to convert Decimal to Fraction:
Make a fraction number as the numerator and a 1 as the denominator.Count how many places after decimal point. Consider it as xmultiply denominator by 10x.Change the percentage value as 100 in denominator.Reduce the fraction. Then simplify the answer using basic arithmetic operations.52.5%
=> 525/10%
=> 525/10*100
=> 525/1000
=> 21/40
Therefore, The fraction in simplest form of 52.5% is 21/40.
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In circle C with the measure of minor arc BD=42°, find mBED.
Answer: mBED = 2(42°) = 84°
Step-by-step explanation:
We are asked to find the measure of the central angle ∠BED in the circle given that the measure of the minor arc BD is 42°.
We can use the formula that states that the measure of a central angle is equal to twice the measure of its intercepted arc. That is,
m∠BED = 2*mBD
We can substitute the value of mBD, which is 42°, into our equation.
m∠BED = 2*42°
m∠BED = 84°
Therefore, the measure of the central angle ∠BED is 84°.
You mix gas and oil to obtain 2 and 1/2 gallons of mixture for an engine. The mixture is 40 parts gasoline and 1 part oil. How much gasoline must be added bring the mixture to 50 parts gasoline and 1 part oil?
We need to add a volume of 39.69 fluid ounces of gasoline to the mixture to bring it to 50 parts gasoline and 1 part oil.
What is mensuration?Mensuration is the branch of mathematics concerned with the measurement of geometric figures and parameters such as length, volume, shape, surface area, and lateral area.
According to information in the question:
The mixture is 40 parts gasoline and 1 part oil, there are 40 + 1 = 41 parts in total.
Let, the amount of oil in the mixture "x".
We know that there are 2 and 1/2 gallons of the mixture, which is the same as 2.5 * 128 = 320 fluid ounces.
So, the equation which can be formed is
x/41 * 320 = the amount of oil in the mixture (in fluid ounces)
Solving for "x":
x/41 * 320 = x/41 * 50 + 320 - (x/41 * 50)
Multiplying both sides by 41:
x * 320 = 50x + 41(320 - 50x)
Simplifying:
320x = 41(320)
x = 41 * 10 = 410 (fluid ounces of oil in the mixture)
Thus, amount of gasoline in the mixture is
40 parts gasoline / 41 parts total * 320 fluid ounces = 311.22 fluid ounces of gasoline.
Let the gasoline we need be "y", so a equation can be formed as follows
(311.22 + y)/(41 + y) * 320 = 410
Solving for y:
(311.22 + y)/(41 + y) = 410/320
Multiplying both sides by (41 + y) * 320:
311.22 + y = 410/320 * (41 + y) * 320
Simplifying:
311.22 + y = 205.625 * (41 + y)
311.22 + y = 8434.375 + 205.625y
Solving for y:
204.625y = 8123.155
y = 39.69 (fluid ounces of gasoline to add)
Therefore, we need to add 39.69 fluid ounces volume of gasoline to the mixture to bring it to 50 parts gasoline and 1 part oil.
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Given the following exponential function, identify whether the change represents
growth or decay, and determine the percentage rate of increase or decrease.
Y=38(1.09)^x
The exponential equation represents a growth, and the rate of increase is 9%.
Is it a growth or a decay?The general exponential equation is written as:
y = A*(1 + r)^x
Where A is the intial value, and r is the rate of growth or decay, depending of the sign of it (positive is growth, negative is decay).
Here we have:
y = 38*(1.09)^x
We can rewrite this as:
y = 38*(1 + 0.09)^x
So we can see that r is positive, thus, we have a growth, and the percentage rate of increase is 100% times r, or:
100%*0.09 = 9%
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Can someone help me
The value of x does not exist.
What is Quadratic equation?
A quadratic equation is a second-degree polynomial equation in a single variable of the form ax^{2} + bx + c = 0, where a, b, and c are constants and x is the variable. The highest exponent of the variable in a quadratic equation is 2, and the equation can be written in standard form, where the coefficient of the squared term (a) is not equal to zero.
The given expression is:
5x² - √3x + 2
This is a quadratic expression in the variable x, which means that it can be written in the form of ax² + bx + c, where a, b, and c are constants. In this case, we have:
a = 5
b = -√3
c = 2
We can use the quadratic formula to find the roots of this expression:
x = [-b ± √(b² - 4ac)] / 2a
Now, putting the values of a, b, and c, we get:
x = [-(-√3) ± √((-√3)² - 4(5)(2))] / 2(5)
Now, Simplifying the expression under the square root, we get:
x = [√3 ± √(-71)] / 10
Since the expression under the square root is negative, there are no real roots to this equation. Therefore, the expression 5x² - √3x + 2 has no real solutions.
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Find the coordinates of the point 13
of the way from A to B.
If you know the coordinates for points between A and B, that you can use this method to determine the dimensions of the spot that is located (0, 1/3) between A and B.
What do coordinates number mean?A set of integers called coordinates are used to locate a spot or a shape in a two-dimensional plane. The x-coordinate as well as the y-coordinate are two integers that describe a point's location on a [tex]2D[/tex] plane.
To find the coordinates of the point that is [tex]1/3[/tex] of the way from point A to point B. we can use the midpoint formula, which states that the coordinates of the midpoint of the line segment joining two points [tex](x1, y1)[/tex]and [tex](x2, y2)[/tex] are:
[tex]((x1 + x2)/2, (y1 + y2)/2)[/tex]
In this case, let's assume that point A has coordinates (x1, y1) and point B has coordinates (x2, y2). Then the point that is 1/3 of the way from A to B has coordinates:
[tex]((2/3) × x1 + (1/3) × x2, (2/3) × y1 + (1/3) × y2)[/tex]
Therefore, So if you have the coordinates of points A and B, you can plug them into this formula to find the coordinates of the point 1/3 of the way from A to B.
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