Sophie earns $8.00 per hour. To find this, dividends of $18 by 2.25, representing the total hours worked, result in the per-hour earning.
To calculate how much Sophie earns per hour, we need to divide her total earnings by the total number of hours she worked. Sophie earns $18 over 2 1/4 hours.
First, we express the hours worked as an improper fraction or a decimal for ease of calculation. Since 1/4 hour is equivalent to 15 minutes, and 2 1/4 hours are the same as 2 + 0.25 which equals 2.25 hours. Now we divide $18 by 2.25 hours to find the hourly wage:
Hourly Wage = Total Earnings / Total Hours Worked
Hourly Wage = $18 / 2.25 hours
Hourly Wage = $8.00 per hour
So, Sophie earns $8.00 per hour.
Karina has determined that the weight of a newborn elephant increases at a rate of 6% per week for the first 14 weeks. She
needs to determine how much weight a baby elephant will gain on the 14th week if it weighs 92 lbs. at birth. Write the explicit
formula of the geometric sequence that could be used to model this scenario.
This is an exponential growth problem.
The formula is y = a(1+r)^x
Y would be the final answer
a is the starting value
r is the percent of growth
x is the amount of time ( number of weeks)
The equation is:
y(x) = 92(1.06)^x
For 14 weeks replace x with 14:
y(14) = 92(1.06)^14 = 208 pounds.
Answer: W(n) = 92lb*1.06^n
and W(14) = 92lb*1.06^14 = 208lb
Step-by-step explanation:
We know that at the beginning the baby elephant weighs 92Lbs, and for each week it augments by a 6% (or 0.06 in decimals)
Then, at the end of the first week, the weight is:
92lb*1.06 = 97.52lb
at the end of the second week:
(92lb*1.06)*1.06 = 103.37lb
and so on, so you can see that the pattern is:
W(n) = 92lb*1.06^n
where n is the number of weeks after the birth
W(0) = 92lb
W(1) = 97.52lb
...
And we want to know the weight at the end of the 14th week, so we must find:
W(14) = 92lb*1.06^14 = 208lb
2 intersecting lines are shown. A line with points M, H, K intersects a line with points J, H, L at point H. 4 angles are created. Clockwise, from the top, the angles are blank, (x + 15) degrees, blank, (2 x minus 20) degrees.
What is mAngleMHJ?
35°
50°
72.5°
92.5°
Answer:
m∠MHJ = 50°
========================
Step-by-step explanation:
Best explanation is as shown in the attached figure.
As shown in the figure:
x + 15 = 2x - 20 ⇒ vertex angles are congruent
solve for x ⇒ ∴ x = 35°
So, ∠MHJ = 2x - 20 = 2*35 - 20 = 50°
========================================
The measure of all angles will be:
∠MHJ = 2X - 20° = 2 * 35 - 20 = 50°
∠JHK = 180° - ∠MHJ = 180 - 50 = 130°
∠KHL = X + 15° = 35° + 15° = 50°
∠LHM = ∠JHK = 130°
Answer:
B 50 degrees
Step-by-step explanation:
PLEASE HELP!!!!!
the volume of a barrel of sand is 18 cubic feet. how many barrels of sand will be needed to fill a container with a volume of 2 cubic yards
The container with a volume of 2 cubic yards, which is equivalent to 54 cubic feet, would require 3 barrels of sand to fill it up, as the volume of each barrel is 18 cubic feet.
Explanation:To find out how many barrels of sand will be needed to fill a container with a volume of 2 cubic yards, we first need to convert cubic yards to cubic feet, as the measurement of the barrel volume is given in cubic feet. Since 1 cubic yard is equivalent to 27 cubic feet, 2 cubic yards will be 2 * 27 = 54 cubic feet.
Next, we divide the volume of the container by the volume of one barrel of sand. Hence, the number of barrels needed = 54 cubic feet / 18 cubic feet per barrel = 3 barrels.
So, it will take 3 barrels of sand to fill a container with a volume of 2 cubic yards.
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Solve for x: 4 over 5 x + 4 over 3 = 2x x = Write your answer as a fraction in simplest form. Use the "/" symbol for the fraction bar. (2 points)
Answer:
(5 + √115)/15 or (5 - √115)/15
Step-by-step explanation:
4/5x+4/3 = 2x
Multiply each term by the least common multiple of the denominators (15x)
12 + 20x = 30x²
Move all the terms to the left-hand side.
-30x² + 20x + 12 = 0
Multiply each term by -1
30x² - 20x - 12 = 0
Remove the common factor (2)
15x² - 10x - 6 = 0
Solve by using the quadratic formula
a = 15, b = -10, c = -6
[tex]x = \frac{-b\pm\sqrt{b^2-4ac}}{2a}\\\\= \frac{-(-10)\pm\sqrt{(-10)^2-4(15)(-6)}}{2(15)}\\\\= \frac{10\pm\sqrt{100 + 360}}{30}\\\\= \frac{10\pm\sqrt{460}}{30}\\\\= \frac{10\pm\sqrt{4\times115}}{30}\\\\= \frac{10\pm2\sqrt{115}}{30}\\\\= \mathbf{\frac{5\pm\sqrt{115}}{15}}[/tex]
x = (5 + √115)/15 or x = (5 - √115)/15
A florist can make a grand arrangement in 18 minutes or a simple arrangement in 10 minutes. The florist makes at least twice as many of the simple arrangements as the grand arrangements. The florist can work only 40 hours per week .The profit on the simple arrangements is $10 and. the profit on the grand arrangements is $25. hind the number and type of arrangements that the florist should produce to maximize profit.
Answer:
See explanation
Step-by-step explanation:
Let x be the number of simple arrangements and y be the number of grand arrangements.
1. The florist makes at least twice as many of the simple arrangements as the grand arrangements, so
[tex]x\ge 2y[/tex]
2. A florist can make a grand arrangement in 18 minutes [tex]=\dfrac{3}{10}[/tex] hour, then he can make y arrangements in [tex]\dfrac{3}{10}y[/tex] hours.
A florist can make a simple arrangement in 10 minutes [tex]=\dfrac{1}{6}[/tex] hour, so he can make x arrangements in [tex]\dfrac{1}{6}x[/tex] hours.
The florist can work only 40 hours per week, then
[tex]\dfrac{3}{10}y+\dfrac{1}{6}x\le 40[/tex]
3. The profit on the simple arrangement is $10, then the profit on x simple arrangements is $10x.
The profit on the grand arrangement is $25, then the profit on y grand arrangements is $25y.
Total profit: $(10x+25y)
Plot first two inequalities and find the point where the profit is maximum. This point is point of intersection of lines [tex]x=2y[/tex] and [tex]\dfrac{3}{10}y+\dfrac{1}{6}x=40[/tex]
But this point has not integer coordinates. The nearest point with two integer coordinates is (126,63), then the maximum profit is
[tex]\$(10\cdot 126+25\cdot 63)=\$2,835[/tex]
To maximize profit, the florist should produce 1 grand arrangement and 2 simple arrangements. The maximum profit is $45.
Explanation:To maximize profit, the florist should produce a combination of grand and simple arrangements. Let's assume the florist makes x grand arrangements and at least twice as many simple arrangements, which would be 2x or more. Given that the florist can work only a total of 40 hours per week, we can set up the following equation:
18x + 10(2x) ≤ 40
Now, we solve for x to find the number of grand arrangements.
Simplifying the equation, we have 18x + 20x ≤ 40
Combining like terms, we get 38x ≤ 40
Dividing both sides by 38, we find that x ≤ 1.05
Since we can't have a fraction of an arrangement, the florist should produce 1 grand arrangement. From the given information, we know that the florist must produce at least twice as many simple arrangements as grand arrangements. Therefore, the florist should produce at least 2 * 1 = 2 simple arrangements.
The florist's maximum profit can be calculated by multiplying the profit per arrangement by the number of corresponding arrangements.
The profit for the grand arrangement is $25, so the total grand arrangement profit is 1 * $25 = $25. The profit for the simple arrangement is $10, so the total simple arrangement profit is 2 * $10 = $20. Therefore, the maximum profit is $25 + $20 = $45.
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Meg dilated triangle W by a factor less than 1. Then she performed other transformations that were not dilations to create similar triangle W′.
Which could be the vertices of triangle W?
A. X(–2, 2), Y(–10, 2), Z(–6, 10)
B. X(2, 2), Y(4, 2), Z(3, 4)
C. X(0, 2), Y(4, 2), Z(2, –6)
D. X(2, 2), Y(2, 6), Z(4, 6)
Answer:
A. X(–2, 2), Y(–10, 2), Z(–6, 10)
Step-by-step explanation:
This looks a bit tough, but knowing that scale factors less than 1 are ½, ¼, etcetera, I come to this answer, also knowing that in the end, they must have an unproportional relationship.
I hope this is correct, and as always, I am joyous to assist anyone at anytime.
The angles X degree and (90-x degree) are
Answer:
Complementary angles
Step-by-step explanation:
Complementary angles sum to 90°, that is
x + 90 - x = 90°
Thus x and (90 - x) are complementary angles
Use the order of operations to evaluate the expression below.
15- [14 = (15-8) + 13 - 14 - 10
The method to solve the expression is given.
What is PEMDAS?The abbreviation PEMDAS is used to indicate the sequence of steps to be taken when resolving expressions with multiple operations. P is for "parentheses," E is for "exponents," M is for "multiplication," D is for division, A is for addition, and S is for subtraction.
The given expression,
15- [14 = (15-8) + 13 - 14 - 10
First, we solve the parenthesis.
15-14 = 7 + 13 - 14 -10
Now, adding the terms.
15-14 = 21 - 24
Subtracting the terms.
1 = -3
Which is contradiction.
Therefore, the expression is wrong.
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given matrix A is 2x3 matrix, matrix C is a 2x1 matrix and A x B = C. what are the demensions of matrix B?
The dimensions of matrix B must be 3x1 to satisfy the given matrix multiplication where a 2x3 matrix A is multiplied by B to result in a 2x1 matrix C.
The student is asking about the dimensions of a matrix B that when multiplied by a given 2x3 matrix A, results in a 2x1 matrix C. In matrix multiplication, the product of an mxn matrix A and an nxp matrix B yields an mxp matrix C. The resulting matrix, C, has the same number of rows as the first matrix (A) and the same number of columns as the second matrix (B). Additionally, the number of columns in the first matrix must match the number of rows in the second matrix. Therefore, since matrix A has 3 columns, matrix B must have 3 rows for the multiplication to be defined. And since matrix C has 1 column, matrix B must have 1 column as well. So, the dimensions of matrix B are 3x1.
Michelle is a server in a restaurant. On a weekend night, Michelle earned $4 an hour and $65 in tips She made a total of $93 Write and solve an equation to determine how many hours she worked
Answer:worked 7 hours
Step-by-step explanation:
93 - 65 = 28
28/4 = 7 hours
Michelle worked for 7 hours on the weekend night based on the equation 4h + $65 = $93, where h represents the number of hours worked.
How many hours she worked?Let's denote the number of hours Michelle worked as "h". She earned $4 per hour for her work, so the total amount she earned from her hourly wage is 4h. Additionally, she earned $65 in tips.
So, the total amount she made can be represented by the equation:
Total earnings = Hourly wage + Tips
$93 = 4h + $65
Now, we can solve for the number of hours Michelle worked:
4h + $65 = $93
Subtract $65 from both sides:
4h = $93 - $65
4h = $28
Now, divide both sides by 4 to solve for "h":
h = $28 / 4
h = 7
Michelle worked for 7 hours on that weekend night.
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What is -c - d
c = -3 and d = -6
Answer:
-3
Step-by-step explanation:
-(-3) = 3
-(-6) = 6
-3 - (-6) = 3
-c - d
c = -3
-3 - d
d = -6
-3 - (-6)
=-3+6
=3
Answer:
Step-by-step explanation:
-3 - (-6) = x (u would use Keep Change Flip [KCF] to solve)
-3 + 6 = x
3=x
so the answer is 3
Hope this helps!!
To avoid a service fee, your checking account balance must be at least $500 at the end of each month. Your current balance is $529.57. You use your debit card to spend $126.08. What possible amounts can you deposit into your account by the end of the month to avoid paying the service fee?
Answer:
$96.51
Step-by-step explanation:
529.57 - 126.08 = 403.49
500 - 403.49 = 96.51
The possible amount you deposit into your account by the ed of the month to avoid paying the service fee would be $96.51
Answer:
$96.51
Step-by-step explanation:
Please need help on this
Answer:
there is an 88% chance it will land on teal, because if you do 16/18, you get 0.8 repeating. then, you multiply by 100 and get 88%
How to write 12,430,000 in expanded form?
The following expression models the total cost of the field trip ,where x represents the number of students 80r What does the constant term in the above expression represents?
Answer:
no of students by cost per student?
Answer:The cost of the if 0 students signed up
Step-by-step explanation:I got the answer right :)
ILL MARK BRAINLIEST ASAP IF CORRECT Write the equation of the quadratic function with roots -9 and and -3 and a vertex at (-6, -1).
Answer:
see explanation
Step-by-step explanation:
The equation of a parabola in vertex form is
y = a(x - h)² + k
where (h. k) are the coordinates of the vertex and a is a multiplier
here (h, k) = (- 6, - 1), thus
y = a(x + 6)² - 1
To find a substitute one of the roots into the equation
Using (- 3, 0), then
0 = a(- 3 +6)² - 1
0 = 9a - 1 ( add 1 to both sides )
1 = 9a ( divide both sides by 9 )
a = [tex]\frac{1}{9}[/tex], thus
y = [tex]\frac{1}{9}[/tex](x + 6)² - 1 ← in vertex form
Expand factor and simplify
y = [tex]\frac{1}{9}[/tex] (x² + 12x + 36) - 1 ← distribute
y = [tex]\frac{1}{9}[/tex] x² + [tex]\frac{4}{3}[/tex] x + 4 - 1
= [tex]\frac{1}{9}[/tex] x² + [tex]\frac{4}{3}[/tex] x + 3 ← in standard form
If you solve using the equation for the constant of proportionality, y/x = k, with k=4/5 and y = 2/3, what is the value of x?
A. X = -2/15
B. X = 8/15
C. X = 5/6
D. X = 1 1/5
[tex]\bf \cfrac{y}{x}=k\qquad \begin{cases} k=\frac{4}{5}\\ y=\frac{2}{3} \end{cases}\implies \cfrac{~~\frac{2}{3}~~}{x}=\cfrac{4}{5}\implies \cfrac{2}{3}(5)=4x\implies \cfrac{10}{3}=4x \\\\\\ \cfrac{10}{12}=x\implies \cfrac{5}{6}=x[/tex]
In this problem, we solve for 'x' in the equation for constant of proportionality, 'y/x = k', given that 'y' is 2/3 and 'k' is 4/5. Substituting these values in the equation and solving for 'x' gives the result 5/6.
Explanation:The question refers to the concept of the constant of proportionality which is a key topic in mathematics. We have an equation, y/x = k, where k is the constant of proportionality. Here, we have been given that y = 2/3 and k = 4/5. If we substitute these values into the equation, we will be able to solve for x.
To solve for x, we rearrange the equation by multiplying both sides by x and then dividing by k. This leaves us with an equation in terms of x: x = y/k. Substituting the given values, we get x = (2/3) / (4/5) = 5/6. So, the correct answer according to the provided options is C. X = 5/6.
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Factorise fully 5x-15
To factorise fully the expression 5x-15, we must search for the greatest common factor (GCF) that can be taken out of both terms. The expression 5x - 15 can be factorised fully by finding the greatest common factor, which is 5. So the expression factorised fully is 5(x - 3).
Explanation:To factorise fully the expression 5x-15, we must search for the greatest common factor (GCF) that can be taken out of both terms.
The GCF of 5x and 15 is 5. Thus, we can pull 5 outside of the equation and divide each term by 5.
The equation becomes: 5(x - 3).
So, the expression 5x - 15 factorised fully is 5(x - 3).
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Step by step answer for
1/2n +3/4n=1/2
let's keep in mind that we have denominators of 2, 4 and 2, and thus we can use their LCD of 4, and multiply both sides by that LCD to do away with the denominators, let's proceed,
[tex]\bf \cfrac{1}{2}n+\cfrac{3}{4}n=\cfrac{1}{2}\implies \stackrel{\textit{multipying both sides by }\stackrel{LCD}{4}}{4\left( \cfrac{1}{2}n+\cfrac{3}{4}n \right)=4\left( \cfrac{1}{2} \right)}\implies 2n+3n=2 \\\\\\ 5n=2\implies n=\cfrac{2}{5}[/tex]
1 MP Reason There are 12,600 insects on display at the new
Science Center exhibit. Explain how you can use base-ten
blocks to show the value of the digit 2 in 12,600.
Answer:
The value of the digit 2 in the number 12,600 is 2,000
Step-by-step explanation:
we have the number 12,600
Rewrite the number in expanded form (write the number in its digits value)
[tex]12,600=10,000+2,000+600[/tex]
so
The value of the digit 1 in the number is 10,000
The value of the digit 2 in the number is 2,000
The value of the digit 6 in the number is 600
A function that has y-values with more than one corresponding x-value is
called a:
Answer:
Im not sure what the answers are on your test but its usually called a domain.
-
-
-
Let me know what the possible answers are if it is a multiple choice question!
Step-by-step explanation:
Answer: many-to-one function
Step-by-step explanation:
Calcular el volumen en m3 de la esfera en el que el área de uno de sus círculos maximos es 36pim2
Answer:
The volume of the sphere is [tex]V=288\pi\ m^3[/tex]
Step-by-step explanation:
The question in English is
Calculate the volume in m^3 of the sphere in which the area of one of its maximum circles is 36pi m^2
we know that
The radius of the maximum circle in the sphere is equal to the radius of the sphere
Step 1
Find the radius of the maximum circle
The area of the circle is
[tex]A=\pi r^{2}[/tex]
we have
[tex]A=36\pi\ m^2[/tex]
substitute and solve for r
[tex]36\pi=\pi r^{2}[/tex]
Simplify
[tex]36=r^{2}[/tex]
take the square root both sides
[tex]r=6\ m[/tex]
Step 2
Find the volume of the sphere
The volume of the sphere is
[tex]V=\frac{4}{3}\pi r^{3}[/tex]
substitute the value of r
[tex]V=\frac{4}{3}\pi (6)^{3}[/tex]
[tex]V=288\pi\ m^3[/tex]
Callie and Madison went to buy concert tickets for themselves and their five friends. The
tickets for the closest section were $45 each, and $30 for each ticket in the other section. They
ended up spending a total of $210. How many tickets of each type did they buy?
Answer:
They bought 0 ticket of closest section and 7 tickets of other section
Step-by-step explanation:
- Callie and Madison went to buy concert tickets for themselves and
their five friends
- That mean they are 7
- Tickets for the closest section were $45 each
- Tickets for other section were $30 each
- They ended up spending a total of $210
- Assume that they buy x tickets for closest section and y tickets for
the other section
∵ They want 7 tickets
∴ x + y = 7 ⇒ (1)
∵ The cost of the closest section ticket was $45
∵ The cost of the other section ticket was $30
∵ They spent $210 on them
∴ 45x + 30y = 210
- All terms have common factor 15, then divide them by 15
∴ 3x + 2y = 14 ⇒ (2)
* Now we have a system of equations to solve
- Multiply equation (1) by -2 to eliminate y
∴ -2x - 2y = -14 ⇒ (3)
- Add equations (2) and (3)
∴ x = 0
- substitute the value of x in equation (1) to find y
∴ 0 + y = 7
∴ y = 7
∵ x represents the number of tickets of the closest section and y
represents the number of tickets in the other section
∴ They bought 0 ticket of closest section and 7 tickets of other
section
Write a word problem with the information below.
89 x 2 = 178
178 + 89 = 267
Both doctors saw 267 patients altogether.
Answer:
there were 2 doctors. first doctor saw 89 patient. Second doctor saw the twice of first doctor. calculate how much patient did second doctor saw
What is the simplified expression for 3 power 3 multiplied by 3 power 3 over 3 power 4? 30 31 32 34
Answer:
The simplest form of the expression is 3² ⇒ 3rd answer
Step-by-step explanation:
- The expression is 3 power 3 multiplied by 3 power 3 over 3 power 4
∵ 3 power 3 = 3³
∵ multiplied by 3 power 3 = × 3³
∵ over 3 power 4 = ÷ [tex]3^{4}[/tex]
- Lets write all of them in one expression
∴ The expression = [tex]\frac{3^{3}*3^{3}}{3^{4}}[/tex]
- All the numbers in the expression is 3 to the power
∴ The expression have the same base 3
- Remember: if we have numbers of same base multiplied then we
add their powers and if divided then we subtract their powers
[tex]\frac{a^{m}*a^{n}}{a^{q}}=a^{m+n-q}[/tex]
- Lets use this rule to simplify the expression
∵ The expression = [tex]\frac{3^{3}*3^{3}}{3^{4}}[/tex]
- Use the rule of the same base above
∴ [tex]\frac{3^{3}*3^{3}}{3^{4}}[/tex] = [tex]3^{3+3-4}=3^{6-4}=3^{2}[/tex]
∴ The simplest form of the expression is 3²
Answer:
3 to the 2nd power.
Step-by-step explanation:
please help 21 points!!!!!
Step-by-step explanation:
The measure of angle y is 62°.
I solve this by
We know: Measures of interior angles in a triangle add up to 180°.
Therefore we have the equation:
60° + 58° + y = 180°
118° + y = 180° subtract 118° from both sides
118° - 118° + y = 180° - 118°
y = 62°
The measure of angle x is 122°.
I solve this by
Angles 58° and x are supplementary angles.
Supplementary angles add up to 180°.
Therefore we have the equation:
x + 58° = 180° subtract 58° from both sides
x + 58° - 58° = 180° - 58°
x = 122°
what is the total amount?
Total amount of what?
$8.75 * 7.5
about $65.63
Forgive me if I'm wrong
Hope this helps!
X over 4 greater than or equal to negative 8
x/4 >= -8
Multiply both sides by 4.
x >= (-8)(4)
x >= -32
The value of X is greater than or equal to -32.
Explanation:To solve the inequality X/4 ≥ -8, we need to isolate the variable X. Firstly, we can multiply both sides of the inequality by 4 to get rid of the denominator: X ≥ -32. This means that the value of X is greater than or equal to -32. In interval notation, we can represent this as (-32, ∞).
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50pts!! Which expression is equivalent to the polynomial given below? 54x+30
A.) 9(5x+5)
B.) 6(9x+30)
C.) 6(9x+5)
D.) 6(9x+4)
Answer:
6(9x+5)
Step-by-step explanation:
6*9x = 54x
6*5 = 30
The expression should be 6(9x+5)
Given information;The equation is 54x + 30
Calculation of an expression:A polynomial represents an expression that comprises of indeterminates and coefficients, which includes only the operations of addition, subtraction, multiplication, and a non-negative integer.
So,
= 54x + 30
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Which property of real numbers is shown below?
-6+6=0
associative property of addition
commutative property of addition
identity property of addition
inverse property of addition
O
Answer:
The inverse property of addition.
Step-by-step explanation:
The number 6 is added to its inverse -6.
The property of real numbers (-6) + 6 = 0 will be Inverse property of addition. Then the correct option is D.
What are the properties of the Addition?Any of the many numerical laws governing how values are added.
Some Addition properties are as follows:
Associative property of addition – The total is unchanged when the order of the sub-blocks is changed.
For example, (2 + 3) + 4 = 2 + (3 + 4)
Commutative property of addition – No matter how the addends are arranged, the result remains constant.
For example, 4 + 2 = 2 + 4
Identity property of addition – The integer is that summation of 0 and that value.
For example, 0 + 4 = 4
Inverse property of addition – Zero is the result of adding any integer to its inverse.
For example, a + (-a) = 4
The property of real numbers -6+6=0 will be Inverse property of addition.
Then the correct option is D.
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