Answer:
$65/hour
Step-by-step explanation:
Let C(h) represent the total amount payable to the plumber. Then:
C(h) = $75 + (rate)(2 hr) = $205. Solve for the "fixed hourly rate."
Subtracting $75 from both sides, we get:
(rate)(2 hr) = $130.
Dividing both sides by (2 hr) results in (rate) = $65/hour
The total bill of $205 is composed of a $75 fixed charge and $130 for the 2 hours worked. This implies that the plumber charges an hourly rate of $65. A representative tape diagram would show these components separately, with 2 equal blocks for the hourly rate totaling to the overall cost of $205.
Explanation:The situation described is a basic arithmetic problem dealing with a fixed cost ($75) and a variable cost (hourly rate, represented as h). The equation that represents this problem is 75+2h=205, derived from the fixed cost plus two times the hourly rate (since the plumber worked for 2 hours). To solve for h (the hourly rate), we subtract 75 from both sides which leaves us with 2h=130, then divide by 2, giving us h=65. This means the hourly rate, h, the plumber charges is $65.
Without seeing the options A, B, C, and D, I can't explicitly say which tape diagram would best represent this situation. However, ideally, the tape diagram should illustrate $75 as a fixed cost and then two equal blocks (each equivalent to $65) to represent the cost of each hour worked. The total of all blocks combined should equal $205, the total cost.
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Are being a student and preferring “pirate” independent events? Why or Why not?
Answer:
The answer is:
No, they are not independent because P(student)≈ 0.82 and P(student|pirate) ≈0.94
Step-by-step explanation:
so the answer is B
No, they are not independent because P(student) = 0.82 and P(Student|pirate) = 0.94
What is called independent events?One event doesn't affect the other event, the two events are said to independent events.The probability of being student P(student) = 0.82
The probability of perferring pirate P(pirate) = 0.94
These two events are not independent events.
Hence, they are not independent because P(student) = 0.82 and P(Student|pirate) = 0.94
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The bake stars picked 907 apples last weekend at local orchard. They made caramel apples and sold them in the bakery in trays of 6. How many trays of caramel apples did they have to sell and how many apples were left over?
Answer:
151 trays, 1 left over
Step-by-step explanation:
907/6 = 151 remainder 1
The Bake Stars could sell 151 trays of caramel apples with 1 apple left over.
The Bake Stars picked 907 apples and sold them in trays of 6.
To determine how many trays they can sell, divide the total number of apples by the number of apples in each tray:
907 apples / 6 apples per tray = 151 trays with 1 apple remaining (since 907 = 151 * 6 + 1).
a) explain how you can write and solve equations to find the measure of each angle
b) then find the measure of each angle.
Answer:
A) For line l = (2x + 8°) + (5x - 10°) = 180° ....... (i)
For line k = (3x + 42°) + (x + 34°) = 180° ....... (ii)
B) In line l, two angles are = 60° and 120°
In line k, two angles are = 120° and 60°
Step-by-step explanation:
Requirement A
To find the measure of each angle, we have to use equation.
According to the graph, line l and k are parallel, therefore, both are straight angle. We know that a straight angle is equal to 180°. Therefore, line l and k are 180°. As both the line are intersected by line j, the lines are separated by two angles. So, the equation for line l is -
(2x + 8°) + (5x - 10°) = 180° ....... (i)
the equation for line k is -
(3x + 42°) + (x + 34°) = 180° ....... (ii)
Requirement B
For line "l "
By solving the equations, we can measure the angles
(2x + 8°) + (5x - 10°) = 180°
or, 2x + 8° + 5x - 10° = 180°
or, 7x - 2° = 180°
or, 7x = 180° + 2°
or, 7x = 182°
or, x = 182° ÷ 7 [Dividing both the sides by 7]
or, x = 26°
Therefore, 2x + 8° = 2 × 26° + 8° = 52° + 8° = 60°
the other angle is = 5x - 10° = 5 × 26° - 10° = 130° - 10° = 120°
For line "k "
(3x + 42°) + (x + 34°) = 180°
or, 3x + 42° + x + 34° = 180°
or, 4x + 76° = 180°
or, 4x = 180° - 76° [Deducting 76° from the both the sides]
or, 4x = 104°
or, x = 104° ÷ 4
Hence, x = 26°
Therefore, 3x + 42° = 3 × 26° + 42° = 78° + 42° = 120°
The other angle is = x + 34° = 26° + 34° = 60°
1000(1+0,05 )^4 *x=1500
The answer is supposed to be x=ln(1.5)/4ln(1.0125)
I'm currently at 4log¹'⁰¹²⁵(1.0125)=log¹'⁰¹²⁵(1.5)
What did I do wrong?
The correct answer is [tex]\( x = \frac{\ln(1.5)}{4\ln(1.05)} \).[/tex]
Let's analyze the given equation step by step:
Given the equation [tex]\( 1000(1+0.05)^4 \cdot x = 1500 \)[/tex], we want to solve for [tex]\( x \).[/tex]
First, simplify the left side of the equation by calculating
[tex]\( (1+0.05)^4 \):\( (1+0.05)^4 = (1.05)^4 \).[/tex]
Now, the equation becomes:
[tex]\( 1000 \cdot (1.05)^4 \cdot x = 1500 \).[/tex]
Next, divide both sides by [tex]\( 1000 \cdot (1.05)^4 \) to isolate \( x \):[/tex]
[tex]\( x = \frac{1500}{1000 \cdot (1.05)^4} \).[/tex]
Simplify the right side by dividing 1500 by 1000:
[tex]\( x = \frac{1500}{1000} \cdot \frac{1}{(1.05)^4} \),[/tex]
[tex]\( x = 1.5 \cdot \frac{1}{(1.05)^4} \).[/tex]
Now, to express [tex]\( x \)[/tex] in terms of natural logarithms, we take the natural logarithm of both sides:
[tex]\( \ln(x) = \ln(1.5 \cdot \frac{1}{(1.05)^4}) \).[/tex]
Using the property of logarithms that [tex]\( \ln(ab) = \ln(a) + \ln(b) \)[/tex], we can split the right side:
[tex]\( \ln(x) = \ln(1.5) - \ln((1.05)^4) \).[/tex]
Applying the power rule of logarithms, [tex]\( \ln(a^b) = b\ln(a) \)[/tex], we get:
[tex]\( \ln(x) = \ln(1.5) - 4\ln(1.05) \).[/tex]
To solve for [tex]\( x \)[/tex], exponentiate both sides to remove the natural logarithm:
[tex]\( e^{\ln(x)} = e^{\ln(1.5) - 4\ln(1.05)} \),[/tex]
[tex]\( x = e^{\ln(1.5)} \cdot e^{-4\ln(1.05)} \),[/tex]
[tex]\( x = 1.5 \cdot \frac{1}{e^{4\ln(1.05)}} \),[/tex]
[tex]\( x = 1.5 \cdot \frac{1}{(e^{\ln(1.05)})^4} \),[/tex]
[tex]\( x = 1.5 \cdot \frac{1}{(1.05)^4} \).[/tex]
Now, we have arrived back at the expression we had for [tex]\( x \)[/tex] earlier:
[tex]\( x = 1.5 \cdot \frac{1}{(1.05)^4} \).[/tex]
To find the numerical value of [tex]\( x \)[/tex], we can use the expression involving natural logarithms:
[tex]\( x = e^{\ln(1.5) - 4\ln(1.05)} \).[/tex]
This is equivalent to:
[tex]\( x = \frac{e^{\ln(1.5)}}{e^{4\ln(1.05)}} \),[/tex]
[tex]\( x = \frac{1.5}{1.05^4} \).[/tex]
Finally, to express [tex]\( x \)[/tex] as a single logarithm, we can use the change of base formula for logarithms:
[tex]\( x = \frac{\ln(1.5)}{\ln(1.05^4)} \),[/tex]
[tex]\( x = \frac{\ln(1.5)}{4\ln(1.05)} \).[/tex]
This is the correct expression for [tex]\( x \)[/tex] in terms of natural logarithms. The mistake in the original attempt was likely in the manipulation of the logarithms, where the properties of logarithms were not correctly applied. The correct step is to use the quotient rule of logarithms, [tex]\( \ln(\frac{a}{b}) = \ln(a) - \ln(b) \)[/tex], and the power rule, [tex]\( \ln(a^b) = b\ln(a) \)[/tex], to arrive at the correct expression for [tex]\( x \).[/tex]
Otis and Andrew each bought a hot dog. Andrew also bought a $3 drink. Write an expression to represent how much they spent if h is the cost of a hot dog
Answer:
2h+3 Because they bought 2 hot dogs and h represents the amount they cost. And the 3 represents the drink he purchased
9-4b+(8+7b+5c) what is the answer to this
Answer:
17+3b+5c
Step-by-step explanation:
9-4b+(8+7b+5c)
9-4b+8+7b+5c
9+8-4b+7b+5c
17+3b+5c
The reciprocal of 7/4
Answer:
4/7
Step-by-step explanation:
you just flip the numbers across the division/fraction sign
Heya.
First, let us learn about reciprocals.
Basically, it's the fraction flipped. Easy as 1, 2, 3!
Let's do an example:
We have an equation that says Find the reciprocal of 5/2.
1. Flip the fraction.
2. We then have 2/5 as a final answer.
Now onto the question:
1. We need to flip the equation.
2. This results as 4/7.
Therefore, our answer is "4/7".
#BrainlyOn!
What is the greatest number of right angles a triangle can contain?
O A. O
O
B. 3
O c. 1
OD.2
SUBMIT
Answer:
1
Step-by-step explanation:
Only 1 right angle can be in any triangle.
(4x^2-2x+8)+(x^2+3x-2)
Answer:
Step-by-step explanation:
(4x^2-2x+8)+(x^2+3x-2)
Collect like terms
5x^2+x+6
5x^2+x+6 dont know if you need to siplify it any more
Jordan is driving to a concert and needs to pay for parking. There is an automatic fee of $11 just to enter the parking lot, and when he leaves the lot, he will have to pay an additional $4 for every hour he had his car in the lot. How much total money would Jordan have to pay for parking if he left his car in the lot for 2 hours? How much would Jordan have to pay if he left his car in the lot for
t
t hours?
Answer:
11+(2×4)
11+8
$19....
Answer:
Cost for 2 hours=19, Cost for 2 hours=11+4t
9. A home improvement store advertises 60 square
feet of flooring for $253.00, plus an additional $80.00
installation fee. What is the cost per square foot for
the flooring?
A. $4.95
B. $5.25
C. $5.55
D. $6.06
Answer:
C. $5.55
Step-by-step explanation:
Total cost of installing 60 square feet of flooring
= $253.00 + $80
= $333
Total number of square feet for flooring = 60
Now cost per square foot of the flooring
= total cost/total number of square feet
That’s
$333/60 = $5.55
Each square foot cost $5.55
Roberto has 1 3/4 pies he wants to give to two friends. Show two ways he could split the pies between the friends
Answer:
7/8
Step-by-step explanation:
Simplify the following:
(1 + 3/4)/2
Put 1 + 3/4 over the common denominator 4. 1 + 3/4 = 4/4 + 3/4:
(4/4 + 3/4)/2
4/4 + 3/4 = (4 + 3)/4:
((4 + 3)/4)/2
4 + 3 = 7:
(7/4)/2
7/4×1/2 = 7/(4×2):
7/(4×2)
4×2 = 8:
Answer: 7/8
What are the solutions of x^2-2x+5=0
Answer:
1 + 2i and 1 – 2i
What is the quotient for the equation above?
Answer:
The correct answer is 32.5
8 divided by 6040 fill in the blank
Answer:
0.00132450331
Step-by-step explanation:
just divide lol
To solve 8 divided by 6040, perform the division, resulting in approximately 0.0013245.
To solve the problem of 8 divided by 6040, follow these steps:
1. Recognize this as a division problem: 8 ÷ 6040.2. Since 8 is smaller than 6040, the quotient will be less than 1.3. Perform the division by dividing 8 by 6040: 8 ÷ 6040 ≈ 0.0013245Therefore, 8 divided by 6040 equals 0.0013245.Factor the quadratic expression completely
8x2 – 18x – 5 =
Final answer:
To factor the quadratic expression 8x² – 18x – 5 completely, one finds factors of the coefficient product (–40) that sum to the x coefficient (–18). These factors are -20 and +2, which are used to rewrite and group the middle term, allowing us to factor by grouping into (4x + 1)(2x – 5).
Explanation:
To factor the quadratic expression 8x2 − 18x − 5 completely, we need to find two binomials that when multiplied together give us the original quadratic expression. This process generally involves finding two numbers that multiply to give us the product of the coefficient of x2 term (8) and the constant term (-5) and also add to give the coefficient of the x term (-18).
The product of the coefficient of x2 and the constant term is -40 (8 × -5). We need to find factors of -40 that will add up to -18. After testing several combinations of factors, we see that -20 and 2 work since -20 + 2 = -18. Now we rewrite the middle term using these two numbers:
8x² − 20x + 2x − 5
Next, we group the terms to facilitate factoring by grouping:
=(8x² − 20x) + (2x − 5)
Now we factor out the common factors from each group:
=4x(2x − 5) + 1(2x − 5)
At this point, we have a common binomial factor (2x − 5) that can be factored out:
=(4x + 1)(2x − 5)
This is the expression factored completely.
Plz help I can’t understand this at all or know how to do it
Answer:
1. 6100
2. 1150
3. 60
4. 50
Step-by-step explanation:
evie had 3/8 gallon of blue pint, 1/4 gallon of red, and 2/5 of green paint. How paint does she have in all?
Answer: 1 1/40.
Step-by-step explanation:
A box in the shape of a rectangular prism has a volume of 72 cubic feet. The box has a length of x feet, a width of (x − 1) feet, and a height of (x + 9) feet. Find the dimensions of the box.
72 = l . w . h
72 = x . (x - 1) . (x + 9)
72 = (x² - x) . (x + 9)
72 = x³ + 9x² - x² - 9x
72 = x³ + 8x² - 9x
0 = x³ + 8x² - 9x - 72
0 = x² (x + 8) - 9 (x + 8)
0 = (x² - 9)(x + 8)
0 = (x - 3)(x + 3)(x + 8)
x = 3 or x = -3 or x = -8
so, x = 3
length = x = 3
width = x - 1 = 2
height = x + 9 = 12
Final answer:
To find the dimensions of the rectangular prism, set up an equation using the volume formula and solve for x. The dimensions of the box are 3 feet, 2 feet, and 12 feet.
Explanation:
To find the dimensions of the box, we need to set up an equation using the volume formula for a rectangular prism. The volume of a rectangular prism is given by V = length x width x height.
So, we have the equation x(x - 1)(x + 9) = 72.
Simplifying this equation, we get x³ + 8x² - 9x - 72 = 0.
Using factoring or synthetic division, we find that x = 3 is a solution to the equation. Therefore, the length of the box is 3 feet, the width is 2 feet, and the height is 12 feet.
Please help me out! I will mark brainliest!!!
Answer:A. 36
Step-by-step explanation:2x+16=×+20 x=4
4+8=12. 4+20=24
12+24=36
Ratios equivalent to 4:8
Answer:
8:36
Step-by-step explanation:
Answer:
Step-by-step explanation:
2/8
If the area of a triangle with a base measuring 22 feet is 93.5 square feet, find its height
Answer:
I think it is 8.5
Step-by-step explanation:
The height of the triangle is 8.5 feet
To find the height of a triangle when the area and the base are known, we use the formula Area = 1/2 x base x height, where A is the area, b is the base, and h is the height. Given that the area of the triangle is 93.5 square feet and the base measures 22 feet, we can rearrange the formula to solve for h: h = 2 × Area/Base
h = 2×93.5/22
h=187/22
h = 8.5 feet
Therefore, the height of the triangle is 8.5 feet.
A science class has a total of 34 students. The number of females is 16 less than the number of males. How many males and how many females are in the class?
Answer:
25 and
9
Step-by-step explanation:
Let the number of males be A and that of females be B
Total number of students = 34
Number of females B = A - 16
Remember males and females = 34
That’s
A + B = 34
We now have two equations
Equation one:B = A - 16
Equation two: A + B = 34
Substitute A - 16 for B in equation 2
We have,
A + B = 34
A + A - 16 = 34
2A - 16 = 34
Add 16 to both sides
2A - 16 + 16 = 34 + 16
2A = 50
Divide both sides by 2
2A/2 = 50/2
A = 25
Now put 25 as A in any of the equations to get B
Using equation one , we have
B = A - 16
B = 25 - 16
B = 9
There are 25 males and 9 females in the class
The graph of the parent function f(x) = x3 is transformed such that g(x) = f(–2x). How does the graph of g(x) compare to the graph of f(x)
The graph of g(x) = f(–2x) will be a horizontally stretched and reflected version of the graph of the parent function f(x) = x^3. The reflection occurs over the y-axis, and the stretch is by a factor of 1/2.
Explanation:The student's question involves a transformation of a cubic parent function. The original function, f(x) = x3, represents a standard cubic graph, which is symmetric about the origin and increases from negative infinity to positive infinity as x does the same. The transformation g(x) = f(–2x) modifies the parent function in two notable ways. First, the multiplication by –2 reflects the graph over the y-axis (because of the negative sign) and also stretches it horizontally by a factor of 1/2 (because the absolute value of the number is greater than 1).
To visualize this, if we consider specific points on the graph of f(x) such as (1,1), (2,8), and (3,27), you would find their corresponding points on g(x) at (-0.5,1), (-1,8), and (-1.5,27), respectively. This indicates that every point on g(x) is twice as far from the y-axis as it is on f(x), and on the opposite side due to the reflection.
The effect of this transformation demonstrates the result of horizontal stretching and reflection when contrasts with the original function f(x), providing insight into how linear transformations affect the shape and position of graphs.
Point X (-3, -2) is translated using the rule (x, y) = (x+3, y + 4), then reflected over the x-axis. What is
the coordinate of X”?
(a) (0,2)
(c) (-2,0)
(b) (0,-2)
(d) (2,0)
The resulting coordinate of X is (0, -2)
TransformationGiven the coordinate point X (-3, -2). If the coordinate is translated using the rule (x, y) = (x+3, y + 4), the resulting coordinate will be (-3+3, -2+4) = (0, 2)
If the result is reflected over x-axis, hence the resulting coordinate will be (0, -2)In conclusion, the resulting coordinate of X is (0, -2)
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After translation and reflection, the coordinate of X" is (0, -2).
Explanation:To find the coordinate of X" after a translation and reflection, we need to first apply the translation rule to point X (-3, -2). Using the rule (x, y) = (x+3, y + 4), we add 3 to the x-coordinate and add 4 to the y-coordinate:
x' = -3 + 3 = 0
y' = -2 + 4 = 2
After the translation, the new coordinates are (0, 2). To reflect over the x-axis, we change the sign of the y-coordinate, giving us the final coordinate of X" as (0, -2).
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The city of Arachna has a spider population that has been doubling every year. If there are about 100,000
spiders this year, how many will there be 4 years from now?
Answer:
1,600,000
Step-by-step explanation:
100,000x2x2x2x2
Answer:160000
Step-by-step explanation:
,
PLEASE HELP
The total cost f(x), in dollars, for renting a moving van for a week and driving it x miles is shown below:
f(x) = 90 + 0.13x
What is the value of f(200), and what does f(200) represent?
Answer:
f(200) =116
f(200) is the cost to rent the moving van and drive it 200 miles
Step-by-step explanation:
f(x) = 90 + 0.13x
Let x = 200
f(200) = 90+ .13(200)
=90+26
=116
f(200) is the cost to rent the moving van and drive it 200 miles
In ΔPQR, the measure of ∠R=90°, the measure of ∠Q=38°, and RP = 72 feet. Find the length of PQ to the nearest tenth of a foot.
Answer:74
Step-by-step explanation:
Since RP is 72, you would divide 72 by 2. The quotient you would get is 36. So then Q=38, you would add 36+38 and get 74.
Answer:
116.9FT
Step-by-step explanation:
What is greater than 1/12?
Answer(s): 1/2, 1, 1/3, 1/4
Any of these could work. Any number beyond 1 could work. The fraction 1/12 is pretty small, and the bigger the number in fractions, the smaller they get.
Example: 1/24 is bigger than 1/64
Because 64 is a bigger number, you'd have to cut it up more and more, getting smaller pieces.
So, any number smaller than 12 in a fraction could work- EXCEPT negatives. All whole numbers work as well.
is an equilateral triangle also a rhombus
yes is an equilateral triangle also a rhombus
Answer:
ues it is a equilateral triangle
Step-by-step explanation:
from the meaning of equilateral, equilateral means all sides are equal in length.
a rrhombus has all its side equal.and therefore it s an equilateral triangle