Let's start by finding the amount that Alex earns per hour before overtime. We know that he works 40 hours, so if we let his hourly pay be x, then his total pay before overtime can be expressed as 40x.
Since Alex gets 50% more than his usual pay for overtime, his overtime pay per hour would be 1.5x, or his usual pay plus 50% of his usual pay. This means that for the 6 hours of overtime he worked, he would earn a total of 6 * 1.5x = 9x.
Now we can write an expression for Alex's total pay, including overtime:
Total pay = 40x + 9x
Simplifying this expression, we get:
Total pay = 49x
So Alex's total pay, including overtime, is 49 times his hourly pay.
mitos com a 15 A landscape designer is designing a garden in the shape of a right triangle. Which of the following could NOT be the lengths of the sides of the triangle? A 16 m, 30 m, 34 m B 10 yd, 14 yd, 17 yd 10 yd, 10.5 yd, 14.5 yd 18 ft, 24 ft, 30 ft C D
Answer:
B. 10 yd., 14 yd., 17 yd.
Step-by-step explanation:
In a right triangle, the squares of the sums of the two shorter sides must equal the square of the longer side(which is the hypotenuse)
From the combinations given only the set 10 yd, 14 yd. and 17 yd does not obey this rule
10² + 14² = 296
17² = 298
So this does not match
Which of the following sets of ordered pairs does not satisfy a linear function?
(2, 5), (3, 7), (4, 9), (5, 11), (6, 13)
(2, 6), (3, 9), (4, 12), (5, 15), (6, 18)
(2, 5), (4, 9), (6, 13), (7, 15), (9, 17)
(2, 6), (4, 8), (6, 10), (8, 12), (10, 14)
Answer:
(2, 6), (4, 8), (6, 10), (8, 12), (10, 14)
1. How do you translate a point R(x, y) using T h,k
2. After translating L(2,-5) using T-3, -4 , what will the coordinates of L' be?
3. For question below , identify the image point bases on the transformation given.
4.Preimage: U(-1, -3); Translate using T-6,5
The coordinates of the image point would be U'(5,2).
What is coordinates?Coordinate is a pair of numbers used to identify the position of a point in a plane or in space. It is mostly used in mathematics, science, and engineering. Coordinates are used to define locations on maps, to plot graphs, and to identify points on a two-dimensional plane. By knowing the coordinates of two points, one can calculate the distance between them.
To translate a point R(x, y) using T h,k, you take the x-coordinate of R, subtract h, and add k to the y-coordinate of R. Therefore, the coordinates of the point L' after translating L(2, -5) using T-3, -4 would be L'(-1, -9).
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x2 + y2 − 5px = 0 polar form
Please help me, this is linear equations.
The slope of line A is 6 and the slope of line B is 2
Line A is greater than the slope of line B
What is the diameter of the
circle?
C = 7.6 m
Answer:
2.42
Step-by-step explanation:
To find the diameter divide by 3.14 or pi. That equals 2.42038216561 but 2.42 is the rounded answer (if you are rounding to the hundredths place)
Which of the following expressions are written in standard form? Choose ALL that apply.
Answer:
[tex]A. \;x^2 -7x + 1[/tex]
[tex]B.\;5x^2 + 2x[/tex]
Step-by-step explanation:
Standard Form of Polynomial
Standard form of a polynomial is written in the descending order of the power of the variable.
The standard form of polynomial is given by
[tex]f(x) = a_nx^n + a_{n-1}x^{n-1}+....... + a_1x + a_0[/tex]
where [tex]x[/tex] is the variable and [tex]a_i,\; i = 0...n[/tex] are coefficients.
The only two expressions in standard form are
[tex]A. \;x^2 -7x + 1[/tex]
and
[tex]B.\;5x^2 + 2x[/tex] (here the constant a₀ is 0)
Suppose that the distance a car travels varies directly with the amount of gasoline it uses. A certain car uses 12 gallons of gasoline to travel 288 miles. How
many miles can the car travel if it has 9 gallons of gasoline?
Answer:
Step-by-step explanation:
225 miles because you have to divide 100 by 4 that would give me 25 MPG and be asked, how many miles can the car travel using? Nine gallons of gasoline? So that would be right here, And that's at 225 Miles that it can travel with nine gallons of gasoline.
Write an inequality to represent the graph. a solid line passing through points 0 comma 2 and 4 comma negative 1 with shading below the line Group of answer choices y is greater than or equal to negative four thirds times x plus 2 y is less than or equal to negative three fourths times x plus 2 y is greater than or equal to negative three fourths times x plus 2 y is less than or equal to negative four thirds times x plus 2
The solution to the inequality is x ≤ 1.
What is inequality?Inequality in mathematics is when two values are not equal. It can be expressed using symbols such as >, <, ≥ and ≤. This can be used to compare two values, express a range of values, or indicate that one value is greater or less than another. Inequality is a powerful tool for solving mathematical problems, as it can be used to deduce relationships between different variables.
To solve this inequality, we must first perform the operations on the left side of the equation to get an expression equal to 4. We can start by simplifying the fraction on the left side of the equation. We can multiply both the numerator and denominator by x, which will give us 5x - 3 = x + 2x. We can then add 3 to both sides to get 5x = 3 + 2x, which can then be simplified to 3x = 3. Finally, we can divide both sides by 3 to get x = 1. Therefore, the solution to the inequality is x ≤ 1.
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Chose the equation that matches the graph(image)
The exponential function that best matches the graph is given as follows:
E. y = 4^(x + 1).
How to define an exponential function?An exponential function, with horizontal asymptote at y = 0, is defined as follows:
y = ab^x.
In which:
a is the initial value.b is the rate of change.From the graph, when x = 0, y = 4, hence the parameter a is given as follows:
a = 4.
When x = -1, y = 1, meaning that when x increases by one, y is multiplied by 4, hence the parameter b is given as follows:
b = 4.
Hence the function is defined as follows:
y = 4(4)^x
y = 4^(x + 1).
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In isosceles trapezoid ABCD, AB || CD. If m
Given the Figure shown below is, ΔABC~ΔAXY if so, what is the scale factor between the two triangles?
Given the Figure shown below is, ΔABC~ΔAXY if so, 1.67 is the scale factor between the two triangles.
What is scale factor?The ratio between the scale of an original thing and a new object that is a representation of it but has a different size is known as a scale factor (bigger or smaller).
Consider two comparable squares as an illustration. One has a side length of 2 inches, while the other has a side length of 4 inches. This results in a scale factor of 1: 2 from the small square to the huge square. The scale factor between these two comparable squares is 1: 2, or tiny square to huge square.
Given that,
12 / 20 = 17 / x
or, 12 x = 340
or, x = 28.33
on the other hand,
25 / 15 = 1.66
20 / 12 = 1.66
28.33 / 17 = 1.66
now, scale factor = 1.67
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Find the value of x from the adjoining figure
The value of x from the adjoining figure given as pentagon is 85°.
What is angle?An angle is a geometric figure formed by two rays, or lines, that share a common endpoint, called the vertex. The measure of an angle is typically expressed in degrees, radians, or other units of angular measurement, and it represents the amount of rotation between the two rays. Angles are often used in geometry, trigonometry, physics, and other fields to describe the orientation of objects and the relationships between them. Some common types of angles include acute angles (less than 90°), obtuse angles (greater than 90°), and right angles (exactly 90°).
Here,
This is a pentagon with sum of angle as 540 degrees.
50+x=180
x=130°
x+80+120+125+130=540
x=540-455
x=85°
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Find the geometric mean of 4 and 8
Answer:
[tex]4\sqrt2[/tex]
Step-by-step explanation:
1) a=4 and b=8
2) Let geometric mean is g. [tex]g=\sqrt ab[/tex] or you can do [tex]g=\sqrt 4 times8[/tex]
3) g=[tex]4\sqrt2[/tex]
How many positive odd integers less than 10000 can be written using the digits 3 4 6 8 and 0.
Answer:
Step-by-step explanation:
125.
Triangle ABC is an equilateral triangle. CD bisects AB.
find x and y.
A
(4x + 2)°
C
x= type your answer.....
y type your answer...
1 point
4y
6y + 24
D
B
Answer:
Step-by-step explanation:
Given AB = AC = BC (all sides of equilateral triangle are equal)
BC = 6y + 4
AD = 4y
as D is midpoint of AB, so AB = 2 x 4y = 8y
Since AB = BC
Hence, 8y = 6y + 24
Or, 8y - 6y = 24
Or, 2y = 24
Or, y = 24/2 = 12
Now, Angle ACB = 60 degree (all angles of an equilateral triangle measure 60 degree)
And CD being bisector of side opposite C so it is angular bisector of angle ACB
So, angle ACD = 1/2 of angle ACB
Or, 4x + 2 = 30
Or, 4x = 30 - 2 = 28
Or, x = 28/4 = 7 degree
Answer:
Correct options are A) , B) and D)
A median of a triangle is a line segment that joins the vertex of a triangle to the midpoint of the opposite side.
Suppose that the fish population P(t) in a lake is attacked by a disease at time t = 0, with the result that the fish cease to reproduce (so that the birth rate is B = 0) and the death rate S (deaths per week per fish) is thereafter proportional to 1/sqrt(P). If there was initially 900 fish in the lake and 441 were left after 6 weeks, how long did it take all the fish in the lake to die?
Using Integration, we can find out that all the fish in the lake died after 20 weeks.
What do you mean by integration?Integration is the process of connecting the parts to create the whole. In the integral calculus, we find a function whose derivative is known. Integration is therefore the opposite of distinction. Integration is used to define and calculate the area enclosed by the function graph. The basic calculus methods used to address arithmetic issues are differentiation and integration.
We first determine the growth rate of the fish, let it be D.
The death rate factor S is to be multiplied by P to get the death rate, so the term is:
- SP = - k P/√P
= - k√P
Given, birth rate, S is 0.
P' = -k√P
Now, we can separate and integrate it:
P'/√P = -k
∫dP'/√P = ∫-k dt
2√P = -kt + c
Applying the data that we have:
P (0) = 900
2 (30) = 0 + c
⇒ c = 60.
At t = 6,
P = 441
= (21) ²
So, 2(21) = 60 - 6k
⇒ 6k = 18
⇒ k = 3.
Finally, we set t = 0 and we solve it for t:
2(0) = 60 - 3t
⇒ t = 20.
Therefore, the fish in the lake died after 20 weeks.
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Last year at a certain high school, there were 50 boys on the honor roll and 80 girls on the honor roll. This year, the number of boys on the honor roll increased by 20% and the number of girls on the honor roll increased by 10%. By what percentage did the total number of students on the honor roll increase? Round your answer to the nearest tenth (if necessary).
Answer:
the total number of students on the honor roll increased by 13.8%.
Step-by-step explanation:
Last year, there were a total of 50 + 80 = 130 students on the honor roll.
This year, the number of boys on the honor roll increased by 20%, which means there are now 1.2 * 50 = 60 boys on the honor roll.
The number of girls on the honor roll increased by 10%, which means there are now 1.1 * 80 = 88 girls on the honor roll.
The total number of students on the honor roll this year is 60 + 88 = 148.
The percentage increase in the total number of students on the honor roll is (148-130)/130 * 100% = 13.8%.
Rounding to the nearest tenth, we get that the total number of students on the honor roll increased by 13.8%.
Find AnB if A= 3,6 9,12 and B = 2,4 6,8 10,12
Answer:
A ∩ B = {6, 12}
Step-by-step explanation:
A ∩ B means only the terms A and B have in common.
Therefore, A ∩ B = {6, 12}
biostatistics questions help to solve
The following table lists numbers in their standard and scientific notations. Fill in the missing values.
The first two have been completed for you as examples.
Standard Notation
The numbers are written in their standard and scientific notations as follows. Fill in the missing values accordingly.
3.0 * 10⁴ = 3000
6.79 * 10⁻³ = 0.00679
0.0216 = 2.16 * 10⁻²
9.02 * 10⁷ = 90200000
1000000 = 10⁶
1.02 * 10⁻⁵ = 0.0000102
0.000723 = 7.23 * 10⁻⁴
9.99 * 10⁹ = 990000000
56000 = 5.6 * 10⁴
How to express the number using scientific notation?Scientific notation is a way of expressing numbers that are too large or too small (usually would result in a long string of digits) to be conveniently written in decimal form. It is also called standard form or standard index form e.g 1000000 = 10⁶ and 0.0001 = 10⁻⁴
3.0 * 10⁴ = 3.0 * 10000 = 3000
6.79 * 10⁻³ = 6.79 * 0.001 = 0.00679
0.0216 = 2.16 * 10⁻²
9.02 * 10⁷ = 9.02 * 10000000 = 90200000
1000000 = 10⁶
1.02 * 10⁻⁵ = 1.02 * 0.0001 = 0.0000102
0.000723 = 7.23 * 10⁻⁴
9.99 * 10⁹ = 990000000
56000 = 5.6 * 10⁴
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For the following equation, determine the values of the missing entries. Reduce all fractions to lowest terms.
4x−2y=12
Note: Each column in the table represents an ordered pair. If multiple solutions exist, you only need to identify one.
Therefore , the solution of the given problem of equation comes out to be (1, -4) is a solution to the equation 4x - 2y = 12.
How do equations work?The equivalent sign (=) is used in arithmetic equations to signify the equality of two propositions. It is shown that it is possible to compare various numerical factors by using mathematical techniques, which have served as manifestations of reality. For instance, the equal sign divides the number 12 even the solution y + 6 = 12 in two distinct portions. How many characters also are present from either end of such a character can be calculated. Conflicting symbol readings are prevalent.
Here,
To find the values of missing entries, we can pick any arbitrary value of x and solve for y. Let's take x=1.
4(1) - 2y = 12
Simplifying the equation, we get:
-2y = 8
Dividing both sides by -2, we get:
y = -4
So, when x=1, y=-4. Therefore, the missing entries in the table are (1, -4).
Using this value, we can also check that the equation 4x - 2y = 12 is satisfied:
4(1) - 2(-4) = 4 + 8 = 12
So, (1, -4) is a solution to the equation 4x - 2y = 12.
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Determine whether the variable is qualitative or quantitative. Model of car driven Is the variable qualitative or quantitative? A. The variable is quantitative because it is an attribute characteristic. B. The variable is qualitative because it is an attribute characteristic. C. The variable is qualitative because it is a numerical measure.
D. The variable is quantitative because it is a numerical measure.
A variable in mathematics is a number that can change depending on the issue. Several mathematical statements and equations use the generic letters x, y, and z. In other words, a variable is a symbol that stands for an unknowable numeric value. Say that x Plus 5 equals 10. The "x" variable is used here.
The variable "model of car driven" is qualitative because it is an attribute characteristic. Qualitative variables are those that are not numerical in nature but rather represent characteristics or categories that can be observed or measured through attributes. In this case, the model of the car driven is a type of attribute that describes the make and model of the car, such as Honda Civic, Toyota Corolla, etc.
Therefore, option B is the correct answer.
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Optiοn B, "The variable is qualitative because it is an attribute characteristic," is the cοrrect answer.
What is a qualitative variable?A qualitative variable is a type οf variable in statistics that describes a characteristic οr quality οf an οbject οr phenοmenοn. It is alsο called a categοrical variable, and it can be nοminal οr οrdinal. Nοminal variables have categοries that have nο inherent οrder, while οrdinal variables have categοries with a natural οrder οr ranking.
The variable "Mοdel οf car driven" is qualitative because it is an attribute characteristic. Qualitative variables are variables that are nοt numerical in nature but are based οn attributes οr characteristics. In this case, the mοdel οf the car driven is a categοrical variable that describes a particular characteristic οf the car, such as its make οr mοdel. This variable cannοt be measured quantitatively οr numerically, but rather it can be categοrized based οn specific attributes οr features.
Therefοre, οptiοn B, "The variable is qualitative because it is an attribute characteristic," is the cοrrect answer.
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Help me with number 7 please
Answer:
Are we supposed to give the answer in fractions?
Please help me answer this question ASAP!!
The surface area of the rectangular prism, found by summing the surface areas of the six rectangular faces is about 2,600 square inches
What is a rectangular prism?A rectangular prism is a three dimensional solid with six rectangular faces, such that faces of the prism that face each other are parallel and congruent.
The surface area of the rectangular prism is the sum of the surface areas of the six rectangular faces of the prism
The area of the rectangles that make up the surface are;
A₁ = 8 inches × 36 inches = 288 square inches
A₂ = 23 inches × 8 inches = 184 square inches
A₃ = 23 inches × 36 inches = 828 square inches
A₄ = 23 inches × 8 inches = 184 square inches
A₅ = 8 inches × 36 inches = 288 square inches
A₆ = 23 inches × 36 inches = 828 square inches
The surface area of the rectangular prism, A, is therefore;
A = A₁ + A₂ + A₃ + A₄ + A₅ + A₆
Therefore;
A = 288 + 184 + 828 + 184 + 288 + 828 = 2600
The surface area of the rectangular prism is 2,600 square inches
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Given w=8, x=-5, y =-12 as a mixed number, what is the value of xy/3x
Answer:
-4
Step-by-step explanation:
-5 x -12/ 3 x -5
60/-15
-4
The function h(x) is a continuous quadratic function with a domain of all real numbers. The table lists some of the points on the function. x h(x) −6 12 −5 7 −4 4 −3 3 −2 4 −1 7 What are the vertex and range of h(x)?
The vertex of the parabola is at the point (-3/2, -21/4) and the range of the function would be (-21/4, infinity).
What is the quadratic function?
A quadratic function is a function of the form [tex]f(x) = ax^2 + bx + c,[/tex] where a, b, and c are constants, and a is not equal to 0. It is a type of polynomial function that can be graphed as a parabola, which is a symmetric curve that opens either upwards or downwards.
Given the table of points for the continuous quadratic function h(x), we can find the vertex and range of the function. Since the function is quadratic and continuous, it can be represented in the standard form [tex]f(x) = a(x - h)^2 + k[/tex], where (h, k) is the vertex of the parabola.
To find the vertex, we can use the fact that the x-coordinate of the vertex is given by -b/2a, where a and b are the coefficients of the quadratic term and the linear term, respectively. In this case, a = 1 (since the function is continuous and quadratic), and b can be found using any two points on the parabola:
[tex]b = (h(x2) - h(x1))/(x2 - x1) = (4 - 7)/(-2 + 1) = 3[/tex]
Therefore, the x-coordinate of the vertex is x = -b/2a = -3/2. To find the y-coordinate of the vertex, we can evaluate the function at this value of x:
[tex]h(-3/2) = (1)(-3/2 - h)^2 + k[/tex]
To solve for k, we can use one of the points on the parabola, say (-6, 12):
[tex]12 = (1)(-6 - h)^2 + k[/tex]
Expanding and simplifying, we get:
[tex]12 = (h - 6)^2 + k[/tex]
Substituting -3/2 for h, we get:
[tex]12 = (-(3/2) - 6)^2 + k\\\\12 = 81/4 + k\\\\k = -21/4[/tex]
Therefore, the vertex of the parabola is at the point (-3/2, -21/4).
To find the range of the function, we can look at the shape of the parabola. Since the coefficient of the quadratic term is positive, the parabola opens upwards, and the vertex is the lowest point on the graph. Therefore, the range of the function is all real numbers greater than or equal to the y-coordinate of the vertex, which is -21/4. In interval notation, we can write the range as (-21/4, infinity).
Hence, the vertex of the parabola is at the point (-3/2, -21/4) and the range of the function would be (-21/4, infinity).
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Please heeelp i have 30 minutes
The mathematical model that can be used to express the verbal statement of the proportional relationships are;
10. y = k/x²
11. P = k/V
12. P = k·V·I
What are proportional relationships?A proportional relationship is one in which the output variable is a multiple of the input variable and a constant (the constant of proportionality).
10. The verbal statement is; y varies inversely as the square of x
The inverse relationship indicates that a variable is related to the reciprocal of the other variable, therefore;
The mathematical model for the statement can be presented as follows;
y ∝ 1/x²
The constant of proportionality k can therefore be applied as follows;
y = k/x²11. The verbal statement is; For a constant temperature, the pressure P of a gas is inversely proportional to the volume V of the gas
The mathematical model of the proportional relationship is; P ∝ 1/V
Therefore;
P = k/V
12. The verbal statement is; The electric power P of a direct current circuit is jointly proportional to the voltage V and the electric current I
The mathematical model is therefore;
P ∝ V·I
Therefore;
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Which equations represent circles that have a diameter of 12 units and a center that lies on the y-axis? Select two options. x2 + (y – 3)2 = 36 x2 + (y – 5)2 = 6 (x – 4)² + y² = 36 (x + 6)² + y² = 144 x2 + (y + 8)2 = 36
Answer: x^2 + (y – 3)^2 = 36
Step-by-step explanation:
The standard equation of a circle with center at (h, k) and radius r is
(x - h)^2 + (y - k)^2 = r^2.
If the center lies on the y-axis, then h = 0: (x - 0)^2 + (y - k)^2 = r^2
If the circle diameter is 12, then the circle radius is 6, and so r^2 = 36
So, among the given equations, your
x^2 + (y – 3)^2 = 36 is correct
In a sample of 900 U.S. adults, 192 think that most celebrities are good role models. Two U.S. adults are selected from this sample without replacement.
The probability that both adults think most celebrities are good role models is 0.046
What is probability?Probability is a branch of mathematics that deals with the study of random events or processes. It is the measure of the likelihood or chance of an event or outcome occurring, expressed as a number between 0 and 1, where 0 represents an impossible event and 1 represents a certain event.
Given that the probability that the celebrities are good role models is 192/900
Then if we pick two adults without replacement; 192/900 * 192/899
= 0.046
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Missing parts;
In a sample of 900 U.S. adults, 192 think that most celebrities are good role models. Two U.S. adults are selected from this sample without replacement.Find the probability that both adults think most celebrities are good role models.