Answer:
She worked Seven (7) hours.
Step-by-step explanation:
$112.75 is the total
she earned $62 in tips which doesn't count because the questions asked for how long she worked.
Adding tips would make the equation unreliable because how long people work doesn't really affect how much tips you get. You maybe getting 50 bucks of tips in the first and 40 in the next.
solving steps: (where x = number of hours worked)
7.25x + 62 = 112.75 <<<the true equation based on the story
7.25x = 112.75 - 62
7.25x = 50.75
x = 50.75 ÷ 7.25
x = 7
Seven (7) hours worked.
-20 less than or equal to 4x
We will have the following:
[tex]-20\le4x[/tex]When we solve for x we will have
[tex]-\frac{20}{4}\le x\Rightarrow-5\le x[/tex]So, x is equal or grater than -5.
A bank features a savings account that has an annual percentage rate of r=2.8% with interest. compounded quarterly. Benicio deposits $8,000 into the account.
Explanation
From the given question
We are given the formula to compute the amount that a sum of $8000 compounded quarterly will yield after time t at a rate of 2.8%
The formula is given by
[tex]A(t)=a(1+\frac{r}{k})^{kt}[/tex]Part A
[tex]\begin{gathered} a=initial\text{ deposit= \$8000} \\ \\ k=number\text{ of times compounded in a year = 4} \\ \\ r=2.8\text{ \% =0.028} \\ \\ \end{gathered}[/tex]part B
the amount in the account after 7 years will be
[tex]\begin{gathered} A(t)=8000(1+\frac{0.028}{4})^{4\times7} \\ \\ A(7)=\text{ \$}9725.57\text{ } \end{gathered}[/tex]The amount that will be in the account after 7 years will be $9725.57
Part C
APY is given by
In our case we have
[tex]\begin{gathered} APY=(1+\frac{r}{k})^k-1 \\ APY=\left(1+\frac{0.028}{4}\right)^4\:-1 \\ APY=1.02829-1 \\ APY=0.02829 \end{gathered}[/tex]Hence, we will have the APY as
[tex]\begin{gathered} APY=0.02829\times100\text{ \% } \\ APY=2.829\text{ \%} \end{gathered}[/tex]Hence, the APY is 2.829%
Vince is cutting a rectangular piece of pegboard to use in his garage for organization. The width of the pegboard is 8 inches less than half the length. The perimeter of the pegboard is 224 inches. What is the length of the pegboard?
The length of the rectangular pegboard is 80 inches
What is a rectangle?A rectangle is a polygon with four sides in which two opposite sides are parallel and equal
How to find the length of the rectangular pegboard?Since Vince is cutting a rectangular piece of pegboard to use in his garage for organization. The width of the pegboard is 8 inches less than half the length. The perimeter of the pegboard is 224 inches.
Let
L = length of pegboard and W = width of pegboard.Since the width of the pegboard is 8 inches less than half the length, we have that
W = L/2 - 8
Also, since the pegboard is a rectangle, its perimeter, P = 2(L + W)
Now, its perimeter P = 224 inches.
So, 2(L + W) = 224
L + W = 112
Now, substituting the width, W into the equation, we have
L + W = 112
L + L/2 - 8 = 112
L + L/2 = 112 + 8
L + L/2 = 120
3L/2 = 120
L = 120 × 2/3
L = 240/3
L = 80 inches
So, the length of the pegboard is 80 inches
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4x+4≤9x+8
please help
Answer:
x ≥ - [tex]\frac{4}{5}[/tex]
Step-by-step explanation:
4x + 4 ≤ 9x + 8 ( subtract 5x from both sides )
4 ≤ 5x + 8 ( subtract 8 from both sides )
- 4 ≤ 5x ( divide both sides by 5 )
- [tex]\frac{4}{5}[/tex] ≤ x , then
x ≥ - [tex]\frac{4}{5}[/tex]
Answer:
4x + 4 ≤ 9x + 8 Subtract 4x from both sides
4 ≤ 5x + 8 Subtract 8 from both sides
-4 ≤ 5x Divide both sides by 5
≤ x
x ≥
Step-by-step explanation:
a group of 90 students is to be split at random into 3 classes of equal size. all partitions are equally likely. joe and jane are members of the 90-student group. find the probability that joe and jane end up in the same class.
The probability that joe and jane end up in the same class is 0.3258 .
In the question ,
it is given that
90 students is to be split into 3 equal size classes , so ,
the three classes will have 30 students each .
let these classes be Class A , Class B and Class C .
Let Joe and Jane be in Class A .
the total number of ways of selecting 30 students for class A from 90 students is C(90,30) .
Since , we have fixed Joe and Jane in Class A , the remaining 28 spots of class A can be filled by remaining 88 students in C(88,28) ways ,
So , the probability that Joe and Jane end up in the same class is
= C(88,28)/C(90,30) .
Since there are three classes ,
the required probability is 3*C(88,28)/C(90,30) .
= 3×[tex]\frac{88!}{28!*60!}[/tex]×[tex]\frac{60!*30!}{90!}[/tex]
= 29/89
= 0.3258
Therefore , the probability that joe and jane end up in the same class is 0.3258 .
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please help me , and can you explain what i shluld study to understand this
x = 12° and y = 7° are the value of linear angles.
What is linear pair of angles?
When two lines meet at a single point, a pair of linear angles is created. If, following the junction of the two lines, the angles are next to one another, they are said to be linear. A linear pair's angles add up to 180° in all cases.8x° = 96°
x = 96/8
x = 12°
8x° = 11y + 19
8 * 12° = 11y + 19
96 = 11y + 19
11y = 96 - 19
11y = 77
y = 77/11
y = 7°
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15 points to help me out.
Answer:
can't answer the first two questions as figure is not mentioned in picture
3. -3
4. 6
5. 3/4
6. -3
7. 5
8. 3
Step-by-step explanation:
answer all ........................................................................................................................................................................................................................................................................................................................................1
Answer:
1. 39, 46
2. 180
Step-by-step explanation:
1. count up by 7
2. not sure..
a package boodins weighs 6.2 ounces. A package of rews weighs 9.97 ounces. how much more does a package of rews weigh than a package of boondins
passes through (1,4) and perpendicular to y=2x-7
The equation of the line is found as y = -x/2 + 9/2.
What is meant by the equation of the line?This is an x and y equation for whom solution set is just a line in the (x,y) plane. The "slope-intercept" form is the most commonly used in algebra. y = mx + b. In effect, x is used as a parameter, and y is written as just a function of x: y = f(x) = mx+b.For the given question;
The equation of the perpendicular line is given as;
y = 2x - 7
Compare the equation with the standard form of slope intercept.
y = mx + c
m = slope and c is the y intercept.
m1 = 2
Now, the line is perpendicular, thus the relation between both slopes is;
m1 × m2 = -1
m2 = -1/2
The passing coordinates of the line is (1. 4).
Find the equation using formula.
y - y1 = m2(x - x1)
y - 4 = (-1/2) (x - 1)
Simplifying,
y = -x/2 + 9/2
Thus, the equation of the line is found as y = -x/2 + 9/2.
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railroad accidents a researcher wishes to study railroad accidents. he wishes to select 4 railroads from 15 class i railroads, 2 railroads from 8 class ii railroads, and 1 railroad from 7 class iii railroads. how many different possibilities are there for his study?
Different possibilities for the given case are, 267540
4 railroads chosen from 15 class I railroads
2 railroads chosen from 8 class II railroads
1 railroad chosen from 7 class III railroads
So total combinations = ¹⁵C₄ ˣ ⁸C₂ ˣ ⁷C₁
= (15!)/(4!*11!) x (8!)/(2!6!) x (7!)/(1!6!)
= 15 x 7 x 13 x 4 x 7 x 7 = 267540
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In the Mediterranean, the Mycenaeans rose to prominence by a mix of military prowess, economic connections, and cultural sway.
Thus, Military Might: The Mycenaeans had a strong military force and were expert warriors. They used sophisticated bronze weapons and chariot warfare as a tactic.
They were able to increase their influence and take control of neighbouring territories thanks to their military might.
Control over Trade Routes: The Mycenaeans had complete control over key trade routes in the Mediterranean, particularly those that extended from the Aegean to the eastern Mediterranean and beyond.
Thus, In the Mediterranean, the Mycenaeans rose to prominence by a mix of military prowess, economic connections, and cultural sway.
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the interest rate on a five-year certificate of deposit (cd) for banks in south florida in 2018 was normally distributed with a mean of 2.28 percent and a standard deviation of 0.37 percent. 1. what proportion of these banks had an interest rate less than 2.5 percent?
The proportion of these banks that had an interest rate less than 2.5 percent is 0.724.
For a normally distributed set of data, given the mean and standard deviation, the probability can be determined by solving the z-score and using the z-table.
First, solve for the z-score using the formula below.
z-score = (x – μ) / σ
where x = individual data value = 2.5
μ = mean = 2.28
σ = standard deviation = 0.37
z-score = (2.5 - 2.28) / 0.37
z-score = 0.22 / 0.37
z-score = 0.5946
To get the proportion, find the probability that corresponds to the z-score in the z-table. (see attached images)
z-score = 0.5946
By interpolating the values,
probability = 0.724
proportion = 0.724
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the radius of a right circular cone is increasing at a rate of 5 inches per second and its height is decreasing at a rate of 4 inches per second. at what rate is the volume of the cone changing when the radius is 50 inches and the height is 10 inches?
The rate at which the volume of the cone is changing is -5235.98 inches³/s when the radius of the circular cone is 50 inches and the height is 10 inches.
The formula for the circular cone can be given as;
V = 1/3 πr²h
Now we take the derivative with respect to time as follows;
V = 1/3 πr²h
dV/dt = 1/3π d/dt(r²h)
dV/dt = 1/3π [2r(dr/dt) × h + r²(dh/dt)]
Now we substitute the values in this equation as follows;
dV/dt = 1/3π [2 × 50 × 5 × 10 + (50²) (-4)]
dV/dt = 1/3π [ 5000 - 10000]
dV/dt = 1/3π [-5000]
dV/dt = -5235.98
Hence the negative sign indicates that the volume is decreasing over time and the rate of change is calculated to be -5235.98 inches³/s.
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A coffee shop is having a sale on prepackaged coffee and tea. Yesterday they sold 11
packages of coffee and 50 packages of tea, for which customers paid a total of $288. The day
before, 12 packages of coffee and 38 packages of tea was sold, which brought in a total of
$248. How much does each package cost?
The most appropriate choice for Simultaneous linear equation will be given by -
8 packages of coffee and 4 packages of tea are sold.
What is simultaneous linear equation?
At first it is important to know about linear equation
Equation shows the equality between two algebraic expressions by connecting the two algebraic expressions by an equal to sign.
A one degree equation is known as linear equation.
Two or more linear equations, which can be solved together to obtain common solution are known as simultaneous linear equation.
Here,
A coffee shop sold 11 packages of coffee and 50 packages of tea, for which customers paid a total of $288
So,
11x + 50y = 288 ...............(1)
The day before, 12 packages of coffee and 38 packages of tea was sold, which brought in a total of $248
So,
12x + 38y = 248
2(6x + 19y) = 248
6x + 19y = [tex]\frac{248}{2}[/tex]
6x + 19y = 124 ....................(2)
Multiplying (1) by 6 and (2) by 11,
66x + 300y = 1728
66x + 209 y = 1364
Subtracting above two equations,
91 y = 364
[tex]y = \frac{364}{91}[/tex]
y = 4
Putting the value of y in (2),
6x + 19[tex]\times[/tex]4 = 124
6x + 76 = 124
6x = 124 - 76
6x = 48
[tex]x = \frac{48}{6}\\x = 8[/tex]
8 packages of coffee and 4 packages of tea are sold.
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The most appropriate choice for Simultaneous linear equation will be given by -
8 packages of coffee and 4 packages of tea are sold.
What is simultaneous linear equation?
At first it is important to know about linear equation
Equation shows the equality between two algebraic expressions by connecting the two algebraic expressions by an equal to sign.
A one degree equation is known as linear equation.
Two or more linear equations, which can be solved together to obtain common solution are known as simultaneous linear equation.
Here,
A coffee shop sold 11 packages of coffee and 50 packages of tea, for which customers paid a total of $288
So,
11x + 50y = 288 ...............(1)
The day before, 12 packages of coffee and 38 packages of tea was sold, which brought in a total of $248
So,
12x + 38y = 248
2(6x + 19y) = 248
6x + 19y =
6x + 19y = 124 ....................(2)
Multiplying (1) by 6 and (2) by 11,
66x + 300y = 1728
66x + 209 y = 1364
Subtracting above two equations,
91 y = 364
y = 4
Putting the value of y in (2),
6x + 194 = 124
6x + 76 = 124
6x = 124 - 76
6x = 48
8 packages of coffee and 4 packages of tea are sold.
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What is the answer to this question
Eric has 23 cookies, but she ate 19 cookies,
How many does eat cookies left.
(100 POINTS)
Answer: 23 - 19 = 4
Step-by-step explanation:
Answer:
how many does eat cookies left??? what
Step-by-step explanation:
anyway, it should be 4 cookies i guess?
23 - 19 = 4
...unless this is like a trick question with bad grammar
1. What is the center of the hyperbola?
(y+3)^2/9 − (x−2)^2/2 = 1
Enter your answer by filling in the boxes.
The center of the hyperbola given as (y + 3)²/9 − (x − 2)²/2 = 1 is (2, -3)
How to determine the center of the hyperbola?From the question, the equation of the hyperbola is given as
(y + 3)²/9 − (x − 2)²/2 = 1
As a general representation, a hyperbola is represented as
(y - k)²/a² − (x − h)²/b² = 1
From the above general representation, the coordinates of the center of the hyperbola is
Center = (h, k)
By comparing the equations (y - k)²/a² − (x − h)²/b² = 1 and (y + 3)²/9 − (x − 2)²/2 = 1, we have the following representstion
(h, k) = (2, -3)
This means that
Center = (2, -3)
Hence, the center is (2, -3)
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Answer:
(2,-3) See question 10
Step-by-step explanation:
the sum of the digits in a three digit mumber is 9. the tens digit is half the sum of the other two amd the hundreds digit is half the unit digit. fond the number.
The number is 234.
Step-by-step explanation:
Let the 3 digits be H , T and U so the number is HTU.
H + T + U = 9
T = 0.5H + 0.5U
U = 2H
So from the last 2 equations
T = 0.5H + 0.5(2H)
T = 0.5H + H
T = 1.5H
So substituting for T and H is the first equation:
H + 1.5H + 2H = 9
4.5H = 9
H = 2.
So T = 1.5*H = 1.5 *2 = 3.
[tex]x + 49 \ \textgreater \ 28[/tex]I need it now please
To solve an inequation for x you have to follow the same procedure you follow when solving equations, with exception that when you multiply/divide by a negative number the direction of the inequality gets inverted.
So to solve the given inequelity for x, you have to pass "+49" to the other side of the expression. To do so, subtract it from both sides of the expression:
[tex]\begin{gathered} x+49-49>28-49 \\ x>-21 \end{gathered}[/tex]The result of the inequality is x > -21
The midpoint of UV is (5,−11). The coordinates of one endpoint are U(3,5). Find the coordinates of endpoint V.
Using the mid point, the coordinates of the end point V is (7, -27)
How to find the coordinate using the mid point?A midpoint is a point lying between two points and is in the middle of the line joining the two points.
In other words, the midpoint of a line segment is a point that lies halfway between 2 points.
Therefore, the coordinates of the endpoint V can be found as follows:
using the mid point,
(xₙ, yₙ) = (x₁ + x₂ / 2, y₁ + y₂ / 2)
Therefore,
(5, -11) = (3 + x₂ / 2, 5 + y₂ / 2)
Hence,
5 = 3 + x₂ / 2
cross multiply
10 = 3 + x₂
10 - 3 = x₂
x₂ = 7
Hence,
- 11 = 5 + y₂ / 2
-22 = 5 + y₂
-22 - 5 = y₂
y₂ = - 27
Therefore, the coordinates of V is (7, -27)
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y+1=3/2(x-1) in slope intercept form
Answer:
y=[tex]\frac{3}{2}[/tex]x - [tex]\frac{5}{2}[/tex]
Step-by-step explanation:
To get slope intercept form (y=mx+b), simplify and solve for y.
y+1=[tex]\frac{3}{2}[/tex](x-1)
Simplify
y+1=[tex]\frac{3}{2}[/tex]x - [tex]\frac{3}{2}[/tex]
Solve for y
y=[tex]\frac{3}{2}[/tex]x - [tex]\frac{5}{2}[/tex]
How to solve this question, I have an idea of what to do but I’m confused on solving it
ANSWER
R1, R2, R3, R4, G1, G2, G3, G4. Option B.
what is the probability that when a coin is flipped six times in a row, it lands heads up every time? (enter the value of probability in decimals. round the answer to three decimal places.)
The probability that the coin lands heads up six times in a row is 0.016
Probability is the term used in mathematics to understand how likely an event is to happen or can also be described as how likely it is that a proposition is true.
It can be determined by dividing the favorable outcomes or events by the total number of outcomes.
As the coin has two sides, the probability that when the coin lands, it lands heads up is determined as follows;
Probability = 1 / 2
Now the probability that the coin lands heads up six times in a row can be calculated as follows;
Probability = (1^6) / (2^6)
Probability = 1 / 64
Probability = 0.015625
Rounding it to three decimal places as follows;
Probability = 0.015625 = 0.016
Therefore, the probability that the coin lands heads up six times in a row is calculated to be 0.016
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Stephanie has 5 pizzas. She shares 4-
of the pizzas with her friends. Estimate how much pizza Stephanie has left.
8
16
02/20
pizzas
O2 pizzas
O
01/P
pizzas
01 pizza
After subtraction we can see Stephanie has only 1 pizzas left.
What is subtraction?
The definition of subtraction is subtracting one number or amount from another. It is addition's opposite operation. Subtraction subtracts a number from another to find the difference, whereas addition adds or groups numbers to find the sum. The word "subtract" can also mean to compare two values to determine how many factors account for a value's difference from another. That is the most fundamental concept behind the term "difference" for the solution to a subtraction problem.
We are given that,
Stephanie has 5 pizzas, Also she shared 4 of the pizzas with her friends
Hence she is left with 5-4= 1 pizza
Hence Stephanie has left with 1 pizza
Therefore the correct option is option D)
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Cuanto es 25 dividido en 386,4
HELP ME PLEOPLE THIS IS SO CONFUSING HELP ME I WILL GET SUSPENDED IF I DON"T ANSWER THIS HELP ME PLEASE HELP I WILL GET A 0 AND SUSPENDED HELP
You have a TV that is 30 inches tall and 40 inches wide. What is the length of the diagonal of the TV. (The measure from bottom left to top right of the TV) 2500 inches/ 1250 inches/ 50 inches/ 26.5 inches
The length of the diagonal of the TV is 2500 inches
Calculating your TV size is less complicated than you might think. A TV's size refers to its diagonal length, which comes from measuring from the upper left hand corner of the actual TV screen to the lower right hand corner.
How do you measure the diagonal of a TV?TV that is 30 inches tall and 40 inches wide.
The length of the diagonal of the TV of the equation is
[tex]30^{2} + b^{2} =40^{2}[/tex]
Then
[tex]30^{2} +40^{2} =2500[/tex]
so
The length of the diagonal of the TV is 2500 inches
Calculating your TV size is less complicated than you might think. A TV's size refers to its diagonal length, which comes from measuring from the upper left hand corner of the actual TV screen to the lower right hand corner. Most are expressed in inches.
The screen surface's diagonal length is calculated from one corner to the other corner (bottom left to top right or top left to bottom right)
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question
A group of friends’ dinner bill before tax is $122.75. The sales tax rate is 8%. They want to leave an 18% tip after tax. What is their total dinner bill, including tax and tip, rounded to the nearest cent?
Responses
The cost of the total bill for the friends is $154.665.
What is a tax?This implies a levy that's paid to the government by individuals and firms.
From the information, the.group of friends’ dinner bill before tax is $122.75, sales tax rate is 8% and they want to leave an 18% tip after tax.
The total bill will be:
= Cost of food + Tax + Tip
= $122.75 + (8% × $122.75) + (18% × $122.75)
= $122.75 + $9.82 + $22.095
= $154.665
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Find the volume of this object.Use 3 for π.Volume of a CylinderV= πr²h4 ft9 ft5 ft5 ft5 ftVolume of aRectangular PrismV = whV ≈ [?]ft³Enter
Mathematics → Solid Figures → Volume
The volume of a cylinder is:
[tex]V=\pi r^2h[/tex]In this question,
r = 2 ft (4/2 =2)
h = 5 ft
Then, the volume of the cylinder is (Vc):
[tex]\begin{gathered} Vc=\pi *2^2*5 \\ Vc=\pi *4*5 \\ Vc=20\pi \end{gathered}[/tex]Using π = 3:
[tex]\begin{gathered} Vc=3*20 \\ Vc=60ft^3 \end{gathered}[/tex]The volume of a rectangular prism (Vr) is:
[tex]Vr=lwh[/tex]In this question:
l = 9 ft
w = 5 ft
h = 5 ft
Then, the volume of the rectangular prism is:
[tex]\begin{gathered} V=9*5*5 \\ V=225ft^3 \end{gathered}[/tex]The volume of the object (V) is the sum of the volumes:
[tex]\begin{gathered} V=Vc+Vr \\ V=60+225 \\ V=285ft^3 \end{gathered}[/tex]Answer: 285 ft³.
How do you solve this problem?
The area of the figure given below is 56.6 units² .
In the question ,
a figure is given
where there is one rectangle and two semicircles .
the length of the rectangle is given as 11 units
and the breadth of the rectangle is = 4 units
we know that the area of the rectangle is = length × breadth
on substituting the values ,
we get
area = 11 × 4
area = 44 units²
the radius of the semicircle = 2 units
the are of the semi circle = (1/2)*π*r²
since there are two semicircle , the area of the two semi circle will be
= 2 * (1/2)πr²
= π*r²
On substituting , the value of radius = 2 ,
we get the area is = 3.14*(2)² = 12.56 using π = 3.14
so the area of the complex figure is = 44 + 12.56 = 56.56
≈ 56.6
Therefore , The area of the figure given below is 56.6 units² .
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