We are asked to evaluate the mathematical expression below;
[tex]8\div2+54\div9\times2\times2[/tex]To do this we would use "PEMDAS". PEMDAS is an acronym for the words parenthesis, exponents, multiplication, division, addition, subtraction.
Given two or more operations in a single expression, the order of the letters in PEMDAS tells you what to calculate first, second, third, and so on, until the calculation is complete.
We will then proceed to solve the expression according to PEMDAS.
[tex]\begin{gathered} 8\div2+54\div9\times2\times2 \\ =\frac{8}{2}+\frac{54}{9}\times2\times2 \\ =4+6\times4 \\ =4+24 \\ =28 \\ \end{gathered}[/tex]Answer: 28
12. Sarah Steenburgh rented a car for seven days at $49.95 per day with unlimited mileage. In
Steenburgh's state, because she already has automobile insurance for her own car, she is
covered for the rental car. She drove 2,465 miles and paid $162.38 in gasoline. How much
did the rental car cost per mile to the nearest cent?
a. $0.19
b. $0.21
c. $0.23
d. $0.25
Answer:
b. $0.21
Step-by-step explanation:
(7·49.95 + 162.38)/2465 = 0.2077
Suppose that there are 150,000,000 people in Yourtown. And, suppose that Yourtown uses 310 × 109cubic meters of water per year. What is the amount of water (in cubic meters) used per person each year in Yourtown?
Given:
The number of people = 150,000,000.
The amount of water used in town = 310 × 109 cubic meters.
Required:
We need to find the amount of water (in cubic meters) used per person each year.
Explanation:
[tex]The\text{ amount of water used per person =}\frac{The\text{ amount of water used}}{The\text{ number of people}}[/tex]Substitute the number of people = 150,000,000 and the amount of water used in town = 310 × 109 cubic meters in the equation.
[tex]The\text{ amount of water used per person =}\frac{310\times109}{150000000}[/tex][tex]The\text{ amount of water used per person =}\frac{33790}{150000000}[/tex][tex]The\text{ amount of water used per person =}\frac{3379}{15000000}[/tex][tex]The\text{ amount of water used per person =}0.000225267\text{ cubic meters}[/tex]Final answer:
[tex]The\text{ amount of water used per person =}0.000225267\text{ cubic meters}[/tex]A cookie factory uses 1 1/3 bags of flour in each batch of cookies. The factory used 6 2/3 bags of flour yesterday. How many batches of cookies did the factory make
Answer: you can get the full fraction by multiplying 6x3 which is 18 so then you add 18 and 2 and you get 20 so now the fraction is 20/3
and you need 11/3 for a batch so now you have 1 whole batch and 9/3 so you just make the 11 a percentage which is 81%
so the answer is 1 whole batch and 81% of another
or 1 9/3
Pythagorean Theorem
Find the length of the third side, write in simplest radical form if needed.
Using Pythagoras's theorem, the length of the third side of the right triangle is 3 units.
How to find the side of a right triangle using Pythagoras's theorem?The length of the third side of the right triangle can be found using Pythagoras's theorem.
The Pythagoras's theorem can be represented as follows:
c² = a² + b²
where
a and b are the legsc is the hypotenuse of the right triangleTherefore, the missing side of the right triangle is the other legs.
b² = (3√5)² - 6²
b² = 45 - 36
b = √9
b = 3
Therefore,
third side of the right triangle = 3 units
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By using Pythagoras' theorem the length of the third side is 3 units
What is Pythagoras's theorem?In a right-angled triangle, the sum of the squares of the smaller two sides of a right-angle triangle is equal to the square of the largest side.
Given, the hypotenuse is 3√5 units and one of the legs is 6 units and assuming the length is x units.
∴ x² = (3√5)² - 6².
x² = 9×5 - 36.
x² = 45 - 36.
x² = 9.
x = ± 3.
As length can not be negative the appropriate value for x is + 3.
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Consider the following functions.f = {(-5, 2), (2, -5), (-1, -3)}and g = {(-1, 1), (-5,3)}Step 1 of 4: Find (f + g)(-1)
To calculate (f g)(-1), we use the definition:
[tex](f+g)(x)=f(x)+g(x)[/tex]This is true if x is defined for f and g. Now, for our problem:
[tex](f+g)(-1)=f(-1)+g(-1)=-3+1=-2[/tex][tex]undefined[/tex]I'll give brainliest!
The numbers written in correct scientific notation format are-
7 x 10⁻⁹
3 x 10⁻⁶
0.1 x 10⁻⁸
What is Scientific Notation?Scientific notation is a techniques of writing a large number or small number in a simple form. It involves expressing a number by the multiplication of 10 raise to the specific exponent.
Given are the set of numbers.
In order to classify the given numbers based on the correct syntax of scientific notation, it is necessary to understand the rules for writing the correct syntax.
The base to which exponent is raised should always be 10.The exponent should be a non-zero integer. (It can be both positive or negative integer)The absolute value of the coefficient is greater than or equal to 1 but it should be less than 10Based on the above rules, we can classify the correct scientific notation as -
7 x 10⁻⁹
3 x 10⁻⁶
0.1 x 10⁻⁸
Therefore, the numbers written in correct scientific notation format are-
7 x 10⁻⁹
3 x 10⁻⁶
0.1 x 10⁻⁸
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A bicycle has a listed price of $522.95 before tax. If the sales tax rate is 7.75%, find the total cost of the bicycle with sales tax included. Round your answer to the nearest cent, as necessary.
$_____
If a bicycle has a listed price of $522.95 before tax and the sales tax is 7.75%, then the total cost of the bicycle with sales tax included is $563.47
The listed price of bicycle = $522.95
The sales tax percentage = 7.75%
We know
C = p(t×p)
Where C is the total cost
p is the listed price
t is the sales tax percentage
Substitute the values in the equation
C = 522.95+((7.75/100)×522.95)
= 522.95+40.53
= $563.47
Hence, if a bicycle has a listed price of $522.95 before tax and the sales tax is 7.75%, then the total cost of the bicycle with sales tax included is $563.47
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Write the correct inequality for the following statement and then solve for the given number of
yards.
You have found a used car and your parents have agreed to pay the first
$750 for you. You have a summer job mowing yards for $25 per yard.
Write and inequality that will calculate the number of yards (y) you will
have to mow to get to at least the cost (C) of the car.
If the car cost a total of $4500 how many yards will you have to mow?
Step-by-step explanation:
You have found a used car and your parents have agreed to pay the first $750 for you. You have a summer job mowing yards for $25 per yard. Write and inequality that will calculate the number of yards (y) you will have to mow to get to at least the cost (C) of the car.
25y + 750 = C
If the car cost a total of $4500 how many yards will you have to mow?
25y + 750 = 4,500
subtract 750 from both sides:
25y + 750 - 750 = 4,500 - 750
25y = 3,750
divide both sides by 25:
25y/25 = 3,750/25
y = 150
Must mow 150 yards.
check:
25(150) + 750 = 4,500
3,750 + 750 = 4,500
4,500 = 4,500
There is a mound of g pounds of gravel in a quarry. Throughout the
day, 400 pounds of gravel is added to the mound. Two orders of 600 pounds are sold and the gravel is removed from
the mound. At the end of the day, the mound has 1,200 pounds of gravel.
There is a mound of 2000 pounds of gravel in a quarry
Quantity of gravel added in the mound throughout the day = 400 pounds
Quantity of orders sold from the mound = 600*2 = 1200 pounds
Quantity of gravel left in the mound at the end of the day = 1200 pounds
Let g represent the pounds of gravel in the quarry
Formulating the equation we get the following:
Mounds of gravel in the quarry + Gravel added in the mound - Gravel sold from the mound = Gravel left at the end of the day
g + 400 - 600(2) = 1200
g + 400 - 1200 = 1200
g = 2000
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Help plssssssssssssssssssssssssssssssss
Answer: [tex]y=-2x+3[/tex]
Step-by-step explanation:
Perpendicular lines have slopes that are negative reciprocal slopes, so the slope of the line we want to find is -2.
The y-intercept is given to be 3, so the equation is [tex]y=-2x+3[/tex].
A smiley face (orange) and its image (open) are graphed on the coordinate plane below. Which sequence of transformations maps the solid smiley face onto the open smiley face?A. reflect over x-axis, rotate 270° counterclockwiseB. rotate 270° counterclockwise, translate right 8 unitsC. translate up 8 units, reflect over y-axisD. reflect over y-axis, rotate 90° counterclockwise
The only way to check which one is the correct answer is to perform each set of transformations and check which one is the correct one. First, note that the initial position of the smiley face is the third quadrant. So, we will first apply vaguely the transformations to check to which one is the smiley face located in the first quadrant once we are done with the transformations.
So, let us analyze each set of transformations separately.
Option A
After reflexing over the x axis, the smiley face position would be
so, once rotated 270° counterclockwise, the position of the smiley face would be
so option A is not the correct answer
Option B
if we rotate 270° counterclockwise, the smiley face's position would be
and by translating 8 units to the right, it would be
so option B is the correct answer
What is the answer to this or is the answer right
Answer:
(c) corresponding angles
Step-by-step explanation:
You want to know the description of the marked angles in the given diagram.
Interior anglesInterior angles are between the "parallel" lines. Angle 5 is interior, but angle 1 is not, so they cannot be described as interior angles.
Exterior anglesExterior angles are both outside the "parallel" lines. Angle 1 is exterior, but angle 5 is not, so they cannot be described as exterior angles.
Corresponding anglesCorresponding angles are both in the same direction from the point of intersection of the "parallel" lines with the transversal. Here, both angles 1 and 5 are "northwest" of the intersection point, so are corresponding angles.
Alternate anglesAlternate angles are on opposite sides of the transversal. Consecutive, or same-side, angles are on the same side of the transversal. Angles 1 and 5 are not alternate angles, as they are both on the same side of the transversal.
What are the solutions of the equation (x + 2)2-2(x + 2)-15 = 0? Use u substitution to solve.
O x=-7 and x = 1
O x = -5 and x = 3
O x=-3 and x = 5
O x= -1 and x = 7
The solution for the given equation is x = -5 and x = 3.
How to solve a quadratic equation by substitution?
The equation is first transformed into a more familiar form. Replace the substitutions with the original variables after factoring the problem. The difference of squares equation is used to finish the factorization and locate the answers for x.
Given, the equation for solving is: (x + 2)² - 2(x + 2) - 15 = 0 --(i)
Let in the equation, y = x + 2 --(ii)
Equating (i) and (ii), we get:
y² - 2y - 15 = 0 ⇒ y² - 5y + 3y - 15 = 0 ⇒ y(y - 5) + 3(y - 5) = 0
⇒ (y + 3)(y - 5) = 0 ⇒ y = -3, 5 (by solving the equations)
Thus, from (ii) and value of y obtained above, we get,
x + 2 = -3 ⇒ x = -3 -2 = -5 and x + 2 = 5 ⇒ x = 5 - 2 = 3
Thus, (b) x = -5 and x = 3 is the correct answer.
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Describe a series of transformations Matt can perform to device if the two windows are congruent
We can generate congruent shapes by combining the three types of transformations: rotations, reflections, and translations. Actually, using a combination of one or more of these three transformations, any pairs of congruent shapes can be matched to one another.
What are transformations?A point, line, or geometric figure can be transformed in one of four ways, each of which affects the shape and/or location of the object. Pre-Image refers to the object's initial shape, and Image, after transformation, refers to the object's ultimate shape and location.
Given Data
We now understand that the size and shape of the figures are preserved during stiff transformations (reflections, translations, and rotations). Pre-image and image are always congruent with one another.
Series of transformation Matt can perform:
Reflection (Flip)
Because the equivalent points from the pre-image to the image remain at the same distance from the line of reflection, a reflection maintains its original shape.
Rotations as a Transformation of Congruence
A rotation is when a figure turns. Although the figure is the same size and shape, it appears to have fallen over. A clock is a fantastic example of a rotation in the real world. Every hour or every day, the connecting arms of a clock revolve around its central point. The degree of rotation is used to characterize a rotation; popular rotations include 90 degrees, 180 degrees, and 270 degrees. The figure returns to its original position after a full 360-degree spin. A rotation must additionally include the direction, either clockwise or counterclockwise. A rotation's degree amount and direction can be computed using this information.
Congruence transformation through translation
When we move an object or shape from one location to another without changing its size, shape, or orientation, we call that movement a translation. A translation, often known as a slide, involves moving each point on an object or shape by the same amount and in the same direction.
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A personal trainer offers two different plans. Plan A costs $25 per session and Plan
B costs $50 per session. If the trainer coaches 18 sessions this week and earns $625
dollars, how many sessions of each type did he coach?
The personal trainer took 11 plan A and 7 plan B classes.
Let the number of sessions of plan A be x. So, the number of sessions of plan B be (18 - x). Now forming the equation as per the mentioned information.
25×x + 50 (18 - x) = 625
Performing multiplication on Left Hand Side of the equation
25x + 900 - 50x = 625
Rearranging the equation
900 - 625 = 50x - 25x
Performing subtraction on both the sides of the equation
275 = 25x
Shifting 25 to other side of equation
x = 275/25
Performing division to find the value of x
x = 11
Number of plan A classes = 11
Number of plan B classes = 18 - 11
Number of plan B classes = 7
Thus, the number of plan A classes is 11 and plan B classes is 7.
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write equations for total edge length E, total surface area A, and volume V of a cube with side lengths of s.
side length--volume
3. 9
5. 25
9.5. 90.25
s. s*3^2
If the length of a side of cube is "s", then total edge length (E = 12s), total surface area (A = 6s²) and Volume (V = s³).
As per the question statement, the length of a side of cube is "s".
We are required to write down the equations for total edge length "E", total surface area "A" and Volume "V" of the cube with respect to "s".
To solve this question, we need to know a couple of basic structural properties of a cube, that is,
There are 12 edges in a cube, all of equal length,
And, there are 6 faces in a cube, all of equal surface area.
[A reference image is attached hereby for better understanding;
The 12 edges of the cube are: AB, BC, CD, AD, CG, DH, BF, AE, EF, FG, GH and EH,
And, the 6 Faces of the cube are: ABCD, ABEF, CDGH, BCFG, ADEH and EFGH]
Therefore, total edge length (E) = (12 * s) = 12s,
Or, (E = 12s)
Total surface area (A) = [6 * (s)²] = 6s²,
Or, (A = 6s²)
[Since, area of a square of edge length "s" = s², and every face of a cube is a square]
Finally, Volume (V) of the cube = [s * s * s] = s³,
Or, (V = s³).
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Alexandria a car dealer, earns 1/25 commission of her luxury vehicle sales. Last year, her sales were $480,000. What was the total dollar amount of her commission last year?
The total dollar amount of her commission last year equals to $19,200.
What is a sales commission?This refers to the percentage of the value of a sale that a sales associate or representative may earn.
To start, we must analyze the data we have. Given that Alexandria's total sales were $ 480000, and the commission received is 1/25 of that sales.
The commission earned from the sales:
= 1/25 * $480000
= $19,200
Therefore, the total dollar amount of her commission last year equals to $19,200.
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Let g(x)=x^2-64 and h(x)=root(8x+512). Find each combination and state its domain. 1. (h/g)(x)(Number one has a fraction) 2. (h・g)(x)3. (g・h)(x)Show work please!
Given the functions:
[tex]\begin{gathered} g(x)=x^2-64 \\ h(x)=\sqrt[]{8x+512} \end{gathered}[/tex]1. (h/g)(x)
[tex](\frac{h}{g})(x)=\frac{h(x)}{g(x)},\text{ g(x)}\ne0[/tex]We substitute the functions and solve:
[tex](\frac{h}{g})(x)=\frac{\sqrt[]{8x+512}}{x^2-64}[/tex]Factor the common term 8:
[tex]=\frac{\sqrt[]{8(x+64)}}{x^2-64}[/tex]And we have:
[tex]\begin{gathered} x^2-64\ne0 \\ x^2-64+64\ne0+64 \\ x^2\ne64 \\ x\ne8\text{ and x}\ne-8 \end{gathered}[/tex]What is the length of segment SR?
____ units
The value of the length of the segment SR is; 12 units.
What is a line segment?A line segment is a straight line with finite length, and thus, have to endpoints(points on either ends).
According to the diagram at point it makes the angle of 90° with both triangles, thus;
SR = SQ
2x + 8 = 8x - 4
And to find the value of x, we will find the value of line segment SR
8x -2x = 8+4
6x = 12
x = 12/6
x = 2
Then we will put the value of x in SR ;
SR = 2x + 8 = 2(2) + 8 = 4 + 8 = 12
SR = 12
Hence, The value of the length of the segment SR is; 12 units.
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Find the length of the side labeled x. Step by step.
Answer: 72.4
Step-by-step explanation:
soh-cah-toa
cos(25)= adjacent/hypotenuse
cos(25)= adjacent/48
adjacent= 48 * cos(25)
tan(59) = opposite/adjacent
tan(59) = x / 48 * cos(25)
x = 72.4
pls be quick or is do Friday
Use the drawing tools to form the correct answer on the graph.
Draw a point that belongs to the solution region of this system of inequalities.
y > 1.5x + 4
y < 2/3x + 4
A point that belongs to the solution region of this system of inequalities is (0, 4).
What is an inequality?An inequality can be defined as a mathematical relation that compares two (2) or more integers and variables in an equation based on any of the following arguments (symbols):
Greater than (>).Less than (<).Greater than or equal to (≥).Less than or equal to (≤).What is a graph?A graph refers a type of chart that's generally used to graphically represent data points on both the horizontal and vertical lines of a cartesian coordinate, which are the x-axis and y-axis.
In this scenario, a graph which represent the solution to the given system of inequalities is shown in the image attached below.
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what is a word problem for [tex]18 \div 6[/tex]
Given the expression:
[tex]18\div6[/tex]The answer = 3
The word problem for the given expression will be:
What is the 18 divided by 6?
. A line is parallel to the line y = -x +9 and passes through the point of intersection of
x+y = 10 and 3x - 4y + 12 = 0. Determine the equation of the line.
Answer:
Step-by-step explanation:
point of intersection of the equations: (4,6)
The line parallel to the given line would be y = -x + k
the line passes through (4,6)
putting the values, we get, 6 = -4 + k ⇒ k = 10
Required equation⇒ y = -x + 10
assume a pool measuring 26 meters by 12 meters is surrounded by a path of uniform width as shown in the figure Express the area in the past A in Square meters as a function of its width X in meters
We know that
• The dimensions of the pool are 26 meters by 12 meters.
,• The uniform surrounding path has a width of ,x, meters.
To find a function of x to express the whole area, we have to define the width and length including the path.
The width would be-
[tex]w=26-2x[/tex]The length is
[tex]l=12+2x[/tex]The total area is
[tex]\begin{gathered} A=w\cdot l \\ A(x)=(26-2x)(12+2x) \end{gathered}[/tex]We use the distributive property to show the function in the simplest form.
[tex]A(x)=312+52x-24x-4x^2[/tex]Then, we reduce like terms. So, the function is
[tex]A(x)=-4x^2+28x+312[/tex]An auto mechanic charges $55 for a house call plus $40 per hour for any work done. The client can spend no more than $250 for the call to the mechanic. Write ✍️ the inequality that represents this scenario.
Solution
Houe Call = $55
Workdone call per hour = $40
Let h denotes the number of hours used
Total charges on the call
[tex]55+40h[/tex]The client can spend no more than $250 for the call to the mechanic
[tex]55+40h\leq250_{}[/tex]The inequality is
[tex]55+40h\leq250_{}[/tex]Find the average rate of change of the function f(x) = x² + 8x from x₁ = 1 to x₂ = 2.
The average rate of change of the function f(x) = x² + 8x from x₁ = 1 to x₂ = 2. is 16
what is average rate of change ?The average rate of change expresses how frequently one quantity changes in relation to another. It provides an idea of the amount the function changed per unit throughout the specified time period. In order to calculate the rate of change, one simply divides the amount of change in one thing by the comparable amount of change in another.
The average rate of change of a continuous function,
f(x) , on a closed interval [a,b] is given by
F(x)=[tex]\frac{F(b)-F(a)}{b-a}[/tex]
[tex]\frac{25 -9}{1}\\ \frac{16}{1}\\ =16[/tex]
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Assume that when human resource managers are randomly selected, 43% say job applicants should follow up within two weeks. If 6 human resource managers are randomly selected, find the probability that exactly 3 of them say job applicants should follow up within two weeks.
The probability is 0.9204 that exactly 3 of them say job applicants should follow up within two weeks.
Binomial probability distribution
P(X = x) = [tex]C_{n,x}[/tex] . [tex]p^{x}[/tex] .[tex](1-p)^{n-x}[/tex]
[tex]C_{n,x}[/tex]= n!/ x!(n - x)!
The parameters are:
n is the number of trails.
x is the number of successes.
p is the probability of success on a single trial.
In this problem:
43% say job applicants should follow up within two weeks, thus p = 0.43
6 managers are selected, thus n= 6.
The probability that at least 3 of them say job applicants should follow up within two weeks is P(X≥ 3), which is given by:
P(X ≥3) = 1 -P(X < 3)
In which:
P(X < 3 ) = P(X = 0) + P(X = 1) + P(X = 2)
Then:
P(X = x) = [tex]C_{n,x}[/tex]. [tex]p^{x}[/tex]. [tex](1-p)^{n-x}[/tex]
P(X = 0) = [tex]C_{6,0}[/tex] [tex](0.43)^{0}[/tex]. [tex](0.57)^{6}[/tex] = 0.0342
P(X = 1) = [tex]C_{6,1}[/tex](0.43) . [tex](0.57)^{5}[/tex] = 0.0259
P(X = 2) = [tex]C_{6,2}[/tex](0.43)² [tex](0.57)^{4}[/tex] =0.0195
P(X<3) = P(X = 0) + P(X = 1) + P(X =2) = 0.0342 + 0.0259 + 0.0195
= 0.0796
P(X≥3) = 1 - P(X<3) = 1- 0.0796 = 0.9204
0.9204 is the probability that at least 3 of them say job applications should follow up within two weeks.
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E Homework: HW 9.3Question 7, 9.3.17HWотFind the area of the shaded regionInside the square and between thetwo circles. Use x 3.1410 m10 mThe area of the shaded region is approximatelym?(Type an integer or decimal)
Area of shaded region = 168.56 [tex]m^2[/tex]
What is area of square and semicircle?
Area of square is the total space taken by the square.
If the side of square is a units, then area of square is calculated by
Area of square = [tex]a \times a[/tex] sq units
Area of semicircle is the total space taken by the semicircle
If the radius of semicircle is r units, then area of semicircle is calculated by
Area of semicircle = [tex]\frac{1}{2}\times \pi \times r^2[/tex] sq units
Here,
Side of square = 28 m
Area of square = [tex]28 \times 28 = 784 m^2[/tex]
Radius of circle = [tex]\frac{28}{2} = 14 m[/tex]
Area of two semicircles =
[tex]2 \times \pi \times r^2 \times \frac{1}{2}\\3.14 \times 14 \times 14\\615.44 m^2[/tex]
Area of shaded region = [tex](784 - 615.44) m^2[/tex]
= 168.56 [tex]m^2[/tex]
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Complete Question
The figure has been attached here.
3(x+4) -4 = 2(x+4) + x
Answer: Infinite Solution
Step-by-step explanation:
3x+12-4=2x+8+x
3x+8=3x+8
Answer:
All real numbers
The answer to this equation is 0=0
Step-by-step explanation:
3(x+4)-4= 2(x+4)+x
3x+12-4= 2x+8+x
3x+8=3x+8
3x-3x=8-8
0=0 Answer