Answer:
f(4) = 11
Step-by-step explanation:
f(x) = 3 x -1
Let x = 4
f(4) = 3*4 -1
= 12-1
= 11
f (x) = 3x - 1
f (4) = 3 × 4 - 1
f (4) = 12 - 1
f (4) = 11
Hope Helpful :-;
Caleb worked his 40 regular hours last week, plus 6 overtime hours at the time-and-a-half rate. His gross pay was $1,063. What was his hourly rate?
If Caleb worked his 40 regular hours last week, plus 6 overtime hours at the time-and-a-half rate. His gross pay was $1,063. His hourly rate is : $21.69.
What is hourly rate?Hourly rate can simply be defined as the wages earn per hour.
Given data :
Regular hours = 40
Over time = 6 ( 1.5 ) = 9
Gross pay = $1,063
Hence,
let h represent the hourly rate
So,
1.5h = overtime rate
Now let determine the hourly rate
40h + 6(1.5h) = 1,063
40h + 9h = 1,063
49h = 1,063
Divide both side by 49h
h = 1,063/ 49
h = $21.69
Therefore the hourly rate is the amount of $21.69.
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One summer, an ice cream truck driver sold 2,994 Popsicles and 515 ice creams. How many
treats did the driver sell in all?
Answer:2479
Step-by-step explanation: subtract 2,994 and 515 and you would get 2479
Answer: 3509 treats
Step-by-step explanation:
If I'm understanding correctly, we need to add the desserts together right?
[tex]2994+515\\=3509[/tex]treats in total
A solid glass cylinder, which is used in an expensive laser amplifier, has a volume of 75vm^3. The cost of polishing the surface area of this glass cylinder is £2 per cm² for the curved surface area and £3 per cm^2 for the circular top and base areas. Given that the radius of the cylinder is r cm, (a) show that the cost of the polishing, £C, is given by C = 6πr² + 300/r
The cost of the polishing, £C, is given by C = 6πr² + 300/r.
The volume of the solid cylinder is 75 m³.
Formula for volume of cylinder = πr²h.
Where R is rhe radius of cylinder and h is the height of the cylinder.
So we can write,
πr²h = 75
h = 75/πr².
So the height of the cylinder is 75/πr² centimeters.
Curved surface area of the cylinder is 2πrh m².
Cost of polishing the curved surface area is £2/cm².
Total cost of polishing the curved surface area = £2×2πrh
Area of the base and the top is 2(πr²).
Cost of polishing base and top is £3/cm².
Cost of polishing 1m² of the base and top,
Cost of area of base and top = £3/cm².
Total Cost of polishing base and top area = £3×2(πr²)
The total cost C of polishing the whole glass,
C = 4πrh + 6πr²
Puting the value of h = 75/πr²
C = 4πr(75/πr²) + 6πr²
C = 6πr² + 300/r.
Hence it is proved that the total cost of polishing is,
C = 6πr² + 300/r.
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a professor rolls a fair, six-sided die. using the classical method of probability, what is the probability that at least five spots will be showing up on the die?
The probability that at least five spots will be showing up on the die is 1/3.
It is given that a professor rolls a fair, six-sided die.
We need to find the probability that at least five spots will be showing up on the die.
Total possible outcomes = {1,2,3,4,5,6}
Number of total outcomes = 6
At least five spots will be showing up on the die. So,
Favorable outcomes = {5,6}
Number of favorable outcomes = 2
Formula for probability:
Probability = [tex]\frac{Number of Favorable Outcomes}{Number of Total Outcomes}[/tex]
On substituting Number of favorable outcomes and Number of total outcomes in the formula of Probability, we get
Probability = 2/6
Probability = 1/3
Therefore, the required probability is 1/3.
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You have 2 different savings accounts. For Account A, the simple interest earned after 3 months is $1.75. For Account B, the simple interest earned after 21 months is $17.50. If the interest rate is 3.5% for Account A and 2.5% for Account B, how much is the principal in each account? Which account earned you the most interest the first month? Explain your answer.
The principal of account A is $20.83 and the principal of account B is $58.33. Account 2 earned the most interest rate in the first month.
The formula to calculate Simple interest, Simple interest = Principal × rate of interest × time.
The principle for Account A would be,
2 = Principal × 3.2% × 3
So, the principal is $20.83
The principle for account B would be,
38.50 = Principal × 2.2% × 30
So, the principal is $58.33,
The interest rate for both accounts is now as follows:
For account 1
= $20.83 × 3.2%
= $0.67
And, for account 2
= $58.33 × 2.2%
= $1.28
Account 2 has the greatest interest rate, thus it is taken into account.
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please help, if you can answer this correctly and put your explanation i will give brainliest
The error Julius made in his explanation is using the area of a rectangle as the longest side instead of area of a square.
Pythagorean theoremPythagorean theorem is the sum of the square of opposite and adjacent sides which result in the sum of the square of the hypotenuse of a triangle.
c² = a² + b²
Where,
c = hypotenusea = oppositeb = adjacentThe error Julius made in his explanation is using the area of a square as the hypotenuse. The figure he used to represent the longest side (hypotenuse) is a rectangle.
The correct working should be:
c² = area of square a + area of square b
c² = 25 + 16
c² = 41
find the square root of both sidesc = √41
c = 6.40312423743
Approximately,
c = 6.4
In conclusion, Julius made the mistake of representing the longest side with area of a rectangle instead of a triangle.
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a ladder 25 feet long is leaning against the wall of a building. initially, the foot of the ladder is 7 feet from the wall. the foot of the ladder begins to slide at a rate of 2 ft/sec, causing the top of the ladder to slide down the wall. the location of the foot of the ladder, its x coordinate, at time t seconds is given by x(t)
The approximate value of x(t), which indicates the location of coordinate the ladder's foot at time t seconds, is 6.85. 7
What in math is a coordinate?Coordinates are numerical lengths or angles that uniquely identify locations on two-dimensional (2D) surfaces or in three-dimensional (3D) space ( 3D ). Mathematicses, scientists, and engineers frequently employ a variety of coordinate systems.
The location in the cartesian plane will be determined by the coordinate points. A point's distance from the y axis is known as the x-coordinate, also known as the abscissa, and its distance from the x-axis is known as the y-coordinate, also known as the ordinate.
based on the information provided,
x = the distance between the wall and the bottom of the ladder
y = distance of the top of the ladder from the ground
x² + y² = 25²
x² + 7² = 25²
x² = 625 -49 = 429
y = √576
Differentiating the equation with respect to time t gives
2x dx/dt + 2y dy/dt = 0
dx/dt = -y dy/dt / x
= -√576 * (2) / 7
= 6.85 feet per second approximately.
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URGENT!! ILL GIVE
BRAINLIEST! AND 100 POINTS
Answer:
B) To make a right triangle in the center, the area of the smaller two square must add to equal the area of the largest square
Step-by-step explanation:
1) add the area of the two smaller squares together
f^2= 9
g^2 = 16
9+16=25
2) compare the sum of the two squares to the larger square (the hypotonus)
h^2= 25 so, f^2 + g^2 = h^2
3) The area of the smaller squares is equal to the area of the larger square, therefore b is the correct answer.
2x+50=3xljb volugvluclkjhvlyotcltc
Answer:
subtract 2x from 3x thats x so 50=x
Step-by-step explanation:
Answer:x=50
Step-by-step explanation:bring 3x over on one side with 2x and bring 50 over on the other side by itself.
The equation becomes 2x-3x=-50
2x-3x is -x
so the equation is -x=-50
there are two negatives in the equation so you make the equation positive because a negative and a negative equals a positive
Therefore the answer is x=50
Select the correct answer.
If the graph of f (x) = |x| is shifted to the left 2 units, which function describes the graph of the new function?
A) g(x) = |x| + 2
B) g(x) = |x| - 2
C) g(x) = |x + 2|
D) g(x) = |x - 2|
The correct option is D) g(x) = |x - 2| for the shifting of graph of f (x) = |x| is shifted to the left 2 units.
What is described as the translation of function?In geometry, translation refers to a function which moves an element a specified distance. The element is not otherwise altered. It has not been rotated, mirrored, or resized.Every point of an element must be transitioned in the exact same direction and at the same distance during a translation.When performing a translation, this same initial object is referred to as the pre-image, as well as the object after translation is referred to as the image.For the given question, the function is given as;
f(x) = |x|
There is a shifting of 2 units towards the left, it means there is shift on the x-axis toward the negative x-axis.
Then, value of x will be reduced by 2 units, which is given by function.
g(x) = |x - 2|.
Thus, the function which correctly described shifting of 2 units left is g(x) = |x - 2|.
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Answer:The correct option is D) g(x) = |x - 2| for the shifting of graph of f (x) = |x| is shifted to the left 2 units.
Step-by-step explanation: I did it on plato.
Which represents the restrictions on the radical inequality [tex]\sqrt[4]{2x+1} \ \textgreater \ 3[/tex]?
A. [tex]2x+1\geq 0[/tex]
B. [tex]\sqrt{2x+1} \ \textgreater \ 0[/tex]
C. [tex]2x+1\leq 0[/tex]
D. There are no restrictions.
there are no restrictions other than 2 x + 1 > 81 on the radical inequality.
We are given the radical inequality as:
⁴√ 2 x + 1 > 3
We need to find the restriction on this inequality.
For this we will first put x on one side and other constant on the other side.
So, we get that:
2 x + 1 > 3⁴
2 x + 1 > 81
So, the restriction is not from the given options.
But, the value of 2 x + 1 should be greater than 81 for the inequality to be true.
Therefore, we get that, there are no restrictions other than 2 x + 1 > 81 on the radical inequality.
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What are “a” and “b” for each of the following exponential function
1. y= -4•2^x a= b=
2. y= (0.2)^x. a= b=
Answer:
Step-by-step explanation:a-t457 =e36_0uh
find the circumference and area of circle A if each unit on the graph im measures 1 centimeter, round answers to the nearest tenth,
circumference: ___ cm
area: ___cm^2
The circumference of the given circle will be 18.84cm and its area will be 28.26cm²
the center of the given circle is A with coordinates (2,3)
we are given that each block on the graph represents 1cm,
on observing the graph we can conclude that the radius of the circle is 3cm.
circumference of the circle is given by the formula,
2πr
taking pi as 3.14 and substituting r=3 in the above formula we get,
2*3.14*3
=18.84cm
thus the circumference of the circle will be 18.84 units.
Similarly, area of a circle can be calculated using the formula,
πr²
taking π as 3.14 and substituting r=3 in the above formula,
3.14*3²
=28.26cm²
What is the difference between area and perimeter?
Perimeter is - "distance around the outside of a shape" while area is - "measures of the space inside a shape."
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The area of a trapezoid is given by the formula A=12(b1+b2)h. Solve the equation for b2.
In a case whereby the area of a trapezoid is given by the formula A=12(b1+b2)h then the equation for b2 is b2= (A - 12hb1)/12h.
How can the value of the term b2 be expressed?
The formula for the trapezoidis given as A=12(b1+b2)h , where the value of term b2 is been exdpected to be found.
firstly, we need to open the bracket as :
A=12(b1+b2)h
A= 12hb1 + 12hb2
Then this can be simplified as 12hb2= (A - 12hb1)
Then we can try to make the b2 the subject of the formula as
b2= (A - 12hb1)/12h.
Therefore, the value of the term b2 can be written as b2= (A - 12hb1)/12h.
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After excavating a lot, workers removed an estimated 7,000 cubic yards of dirt from the area. If this dirt were spread in an even layer over an empty lot with dimensions 30 yards by 64 yards, about how deep, in yards, would the layer of dirt be?
A.Less than 1
B.Between 1 and 2
C.Between 2 and 3
D.Between 3 and 4
E.More than 4
The layer of dirt would be between 3 and 4 yards and precisely 3.6458 yards.
Given the volume of the lot is 7000 cubic yards.
After spreading to an even layer
The dimension is 30 yards and 64 yards
The volume of the lot can be given as Length x Width x Depth
Let us say the depth of the lot is x
Which means
30 x 64 x X = 7000
1920 x X = 7000
X = 3.6458
Hence the depth of the lot is 3.6458 which is between 3 and 4.
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Grace's height is 1.45 m. Jackson is 0.2 m shorter than Grace. What is
Jackson's height? Give your answer in metres (m).
By using the method subtraction, Jackson's height is 1.25m.
What is subtraction?To subtract in mathematics is to take something away from a group or a number of objects. The group's total number of items decreases or becomes lower when we subtract from it. The components of a subtraction issue are the minuend, subtrahend, and difference. An arithmetic operation called subtraction simulates the process of deleting items from a collection. The action of subtracting a matrix, vector, or other quantity from another according to predetermined rules in order to find the difference.
Given that,
Grace's height is 1.45 m.
Jackson is 0.2 m shorter than Grace.
Jackson's height is 1.45 -0.2 = 1.25
Therefore, Jackson's height is 1.25m.
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complete the pattern 0, 20, 40, 60, _, _
Step-by-step explanation:
0 20 40 60 80 100.................
what will be the value of k so that the equation [tex]kx^{2} -4x+1[/tex] has two equal roots (same roots)
The value of k that will make the quadratic equation kx² - 4x + 1 = 0 to have two equal roots is; k = 4
What are the roots of the Quadratic Equation?The general form of representing a quadratic equation is;
ax² + bx + c = 0
Now, we are given the quadratic equation which is;
kx² - 4x + 1 = 0
Now, for a quadratic equation to have 2 equal roots, it means that;
b² = 4ac
Thus, applying that to our given quadratic equation gives us;
(-4)² = 4(k * 1)
4k = 16
k = 4
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Rachel is making premade 3-inch by 5-inch tile rectangles for her driveway. If it takes her 6 minutes to position each rectangle, how many hours will it take her to create a 2-foot by 4-foot pattern drive? Write your answer as a decimal.
This is a Metric conversion problem. Note that it will take 38.4 minutes to create a 2-foot by 4-foot pattern drive. See the explanation below.
What is the calculation justifying the above answer?There are several ways to do this. Let's use the area of the times and that of the pattern drive.
Note that the area of the 3inch by 5-inch tile =
Area of a rectangle
L x B =
3 x 5
= 15inches
Applying the same rule to the pattern drive, we have
2 x 4
= 8 foot
Note that 1 foot = 12 inches
For convenience, thus, we convert the area of the pattern drives into inches. This gives us:
8 x 12
= 96 inches
To get how many minutes it will take to create a 2 by 4-foot pattern drive, we have
Recall that it takes 6 minutes to lay a 3x5 which is 12 inches in area.
Hence,
96/15
= 6.4
6.4 x 6
= 38.4 minutes.
Hence, it will take Rachel 38.4 minutes to lay a 2 by 4-foot pattern drive given the parameters above.
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A 35-inch ribbon was cut into 8 equal lengths how long was each piece?
Answer:
4⅜ or 4.375 inches.
Step-by-step explanation:
35 ribbon into 8 pieces is:
35/8 = 4⅜ or 4.375 inches.
One plus one plus 278 times 67 divided by 782
Answer:25.8184143223
1+1+278*67/782
1+1+18626/782
2+23.8184143223
25.8184143223
can anyone please help me with quetion c
Answer: The arrow is pointing to 76.5.
Step-by-step explanation: It's pointing to 76.5 because there are 10 spaces between 75 and 80 so in that case, each line is .5, and since it's on the third line that means it is 1.5 more than 75 so 76.5.
Answer:
C) The arrow points to 76.5.
Step-by-step explanation:
The number line is divided into 10 parts equally.
We can find out the distance between each point by taking the difference between the largest and smallest number on the number line and dividing the difference by 10.
80 - 75 = 5
5/10 = .5
So, the distance between each number/mark on the line is .5
Now, we can label each point by adding .5 to each mark as we go. Then, we'd get this.
*see attachment below
Since the number line constructed here has all the values, we can now tell which value the arrow is pointing to.
The answer is therefore 76.5.
let’s say you have a four-digit personal identification number (pin). each digit can be 0, 1, 2, 3, 4, 5, 6, 7, 8, or 9, giving a total of 10 possible numbers for each digit. if a pin is 4 digits, each digit can be any one of the 10 possible numbers, how many different possible combinations are there?
If each digit can be 0, 1, 2, 3, 4, 5, 6, 7, 8, or 9, giving a total of 10 possible numbers for each digit. if a pin is 4 digits, each digit can be any one of the 10 possible numbers, The different possible combinations are there is : 10,000.
Different possible combinationGiven :
Digit = 0, 1, 2, 3, 4, 5, 6, 7, 8, or 9
Possible number = 10
Pin = 4 digits
Now let determine the different possible number
Possible number combination = 10 x 10 x 10 x 10
Possible number combination = 10,000
Therefore the combination is 10,000.
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A random number generator is used to create a list of 150 single-digit numbers. Of those 150 numbers, 72 are odd and
78 are even. The number 9 was generated 15 times.
To the nearest whole percent, what is the experimental probability of an odd number other than 9 being generated?
The experimental probability of an odd number other than 9 being generated is 0.38.
What is probability?Probability refers to potential. A random event's occurrence is the subject of this area of mathematics. The range of the value is 0 to 1. Mathematics has incorporated probability to forecast the likelihood of various events.
According to the probability formula, the probability of an event occurring, or P(E), is equal to the proportion of positive outcomes to all outcomes. P(E) is defined mathematically as favorable outcomes divided by total outcomes.
Given Data
A random number generator is used to create a list of 150 single-digit numbers. Of those 150 numbers, 72 are odd and 78 are even. The number 9 was generated 15 times.
Total numbers generated = 150
Odd numbers = 72
Even numbers = 78
Generation of number 9 = 15
Number of odd numbers except 9 itself
= 72 -15
= 57
Probability = [tex]\frac{Odd numbers except 9 itself}{total munbers}[/tex]
Probability = [tex]\frac{57}{150}[/tex]
Probability = 0.38
The experimental probability of an odd number other than 9 being generated is 0.38.
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Find the equation of the line that contains The given point and is perpendicular to the given line. Write the equation in slope intercept form, if possible. (14,21); y = -7x + 4
Answer: [tex]y=\frac{1}{7}x+19[/tex]
Step-by-step explanation:
Perpendicular lines have slope that are negative reciprocals, so the slope of the line we want to find is 1/7.
The equation in point-slope form is [tex]y-21=\frac{1}{7}(x-14)[/tex].
Rearranging into slope-intercept form,
[tex]y-21=\frac{1}{7}x-2 \\ \\ y=\frac{1}{7}x+19[/tex]
Rounded to the nearest hundreth. This one is 2 answers.
Installing custom glass windows costs $400 for the install and $30 per square foot of
glass needed for your windows. The total charge for your window installation was
$4900. Translate this information into an equation using a to represent the number of
square feet of glass used for your windows.
Using your equation, determine the number of square feet of glass used for your
windows.
Please help ASAP really bad at math and can’t afford a tutor.
Part 1
[tex)400+30x=4900[/tex]
Part 2
[tex]30x=4500 \\ \\ x=150[/tex]
So, the answer is 150 ft².
Under her cell phone plan, Genesis pays a flat cost of $40.50 per month and $5 per gigabyte, or part of a gigabyte. (For example, if she used 2.3 gigabytes, she would have to pay for 3 whole gigabytes.) She wants to keep her bill under $55 per month. What is the maximum whole number of gigabytes of data she can use while staying within her budget?
Using mathematical operations, the maximum whole number of gigabytes of data Genesis can use while staying within her budget is 2GB.
What are mathematical operations?Mathematical operations are used in mathematical functions to produce a defined output.
Some of the mathematical operations include addition, subtraction, multiplication, division, exponentiation, and modulus operations.
In this situation, we used the mathematical operations of subtraction, division, addition, and multiplication to determine Genesis's data maximum usage that does not exceed her budget.
Fixed cost per month = $40.50
Usage rate per gigabyte or part thereof = $5
Budgeted bill = $55 per month
Maximum gigabyte usage per month = 2.9 {($55 - $40.50) ÷ $5}
But Genesis cannot use 3GB but only 2GB because 3GB will make her total bill exceed her budget.
Check:
Cost of using 3GB = $55.50 ($40.50 + $5 x 3)
Cost of using 2GB = $50.50 ($40.50 + $5 x 2)
Thus, for Genesis to maintain her data plan within budget, the maximum she can spend is 2GB.
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SOLVE ASAP PLEASE TAKING A TEST!!!
The equation of the circle with the centre (5,7) and containing the point p (1,9) is [tex]\sqrt{20} =(x-5){2}+(y-7){2}[/tex]
How to find the equation of a circle ?The equation for a circle in standard form is [tex](x-x1){2}[/tex]+ [tex](y-y1){2}[/tex] = [tex]r{2}[/tex], where (x, y) denotes arbitrary coordinates on the circle's perimeter, r denotes the circle's radius, and (x1, y1) denotes the coordinates of the circle's centre.
The equation of a circle with centre (x1,y1)
[tex](x-x1){2}[/tex]+ [tex](y-y1){2}[/tex] = [tex]r{2}[/tex]
we know the centre , which is (5,7) so the equation changes to:
[tex](x-5){2}[/tex]+ [tex](y-7){2}[/tex] = [tex]r{2}[/tex]
putting the values of the point p we get
[tex](1-5){2}[/tex] [tex]+ (9-7){2}[/tex][tex]= r{2}[/tex]
r=[tex]\sqrt{20}[/tex]
so the equation of the circle will be:
[tex]\sqrt{20} =(x-5){2}+(y-7){2}[/tex]
Therefore the equation that satisfies the given condition of a circle with centre (5,7) and containing point p (1,9) is [tex]\sqrt{20} =(x-5){2}+(y-7){2}[/tex]
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Consider matrix A.
A =[-3 5 2 8 -1 3]
What matrix results from the elementary row operations represented by -3R2 + 4R₁?
Enter your answer by filling in the boxes.
The resultant matrix after elementary row operation is:
[tex]A = \left[\begin{array}{ccc}-12&20&8\\-24&3&-9\end{array}\right][/tex]
What is elementary row operation?
In mathematics, the elementary row operation is a method in which the two rows exchanged. In this, the rows are either multiplied, added or division. Sometimes, single row is multiplied by some constant.
According to the question, the given matrix A is written below:
[tex]A = \left[\begin{array}{ccc}-3&5&2\\8&-1&3\end{array}\right][/tex]
Now, performing elementary row operations represented by [tex]-3R_{2} +4R_{1}[/tex]
The given matrix becomes after elementary row operations:
[tex]A = -3R_{2} + 4R_{1} = \left[\begin{array}{ccc}-12&20&8\\-24&3&-9\end{array}\right][/tex]
Hence, the resultant matrix after elementary row operation is::
[tex]A = \left[\begin{array}{ccc}-12&20&8\\-24&3&-9\end{array}\right][/tex]
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