Answer:
The Inequality that shows number of hours Tabitha will need to work to have enough money to buy the tablet is [tex]75+8.5x\geq 306.34[/tex].
Tabitha needs to work at least 28 hours to buy the tablet.
Step-by-step explanation:
Amount earn per hour = $8.50
Amount already saved = $75
Cost of tablet = $289
Sales tax = 6%
We to write and solve the inequality number of hours Tabitha will need to work to have enough money to buy the tablet.
Solution:
Let the number of hours she need to work be 'x'.
First we will find the total amount required to buy tablet.
Amount of sales tax = [tex]\frac{6}{100}\times289 = \$17.34[/tex]
Now Total cost to buy tablet will be equal to sum of Cost of tablet and Amount of sales tax.
framing in equation form we get;
Total cost to buy tablet = [tex]289+17.34 = \$306.34[/tex]
Now we can say that;
Amount already saved plus Amount earn per hour multiplied by Amount earn per hour should be greater than or equal to Total cost to buy tablet.
framing in equation form we get;
[tex]75+8.5x\geq 306.34[/tex]
hence The Inequality that shows number of hours Tabitha will need to work to have enough money to buy the tablet is [tex]75+8.5x\geq 306.34[/tex].
On solving the above Inequality we get;
First we will subtract both side by 75 we get;
[tex]75+8.5x-75\geq 306.34-75\\\\8.5x\geq 231.34[/tex]
Dividing both side by 8.5 we get;
[tex]\frac{8.5x}{8.5}\geq \frac{231.34}{8.5}\\\\x\geq 27.21[/tex]
Hence Tabitha needs to work at least 28 hours to buy the tablet.
The variable x represents the number of long sleeve shirts Nancy bought and the variable y represents the number of short sleeve shirts she bought.
Nancy bought 531 shirts for her business. She bought 2 times as many short sleeve shirts as long sleeve shirts.
How many of each type of shirt did she buy?
Final answer:
Nancy bought 177 long sleeve shirts and 354 short sleeve shirts for her business by solving a system of linear equations based on the provided constraints that she bought a total of 531 shirts and twice as many short sleeve shirts as long sleeve shirts.
Explanation:
The student's question involves solving a system of linear equations to find out how many of each type of shirt Nancy bought for her business. Following the given relationships between long sleeve shirts (x) and short sleeve shirts (y), we understand that Nancy bought a total of 531 shirts and that she bought twice as many short sleeve shirts as long sleeve shirts. The two equations that can represent this scenario are:
Equation 1: x + y = 531
Equation 2: y = 2x
To solve this system, we substitute Equation 2 into Equation 1 to get:
x + 2x = 531
Which simplifies to:
3x = 531
Dividing both sides by 3, we find that:
x = 531 / 3 = 177
Using the value of x to find y from Equation 2, we get:
y = 2 * 177 = 35
Therefore, Nancy bought 177 long sleeve shirts and 354 short sleeve shirts.
A ball is dropped off the side of a bridge. after falling 1.55 s, what is its velocity?
Use the basic kinematic equation of
Final velocity = initial velocity + acceleration * time (shown in image)
simply plug the numbers in to get
Velocity(final) = 0 + -9.80 m/s^2 * 1.55 s
to give us
-15.19 m/s for our final velocity
6(5x-3) distributive property gcf
Answer:
Step-by-step explanation:30x-18
Describe the graph of the system of inequalities:
Step-by-step explanation:
[tex]\left\{\begin{array}{ccc}x>2\\y\leq4\end{array}\right[/tex]
x = 2
This is a vertical line passing through (2, 0) .
y = 4
This is a horizontal line passing through (0, 4).
<, > - dashed line
≤, ≥ - solid line
<, ≤ - shaded to the left (down) from the line
>, ≥ - shaded to the right (up) from the line
Answer:
Below.
Step-by-step explanation:
The shaded area will be to the right of the vertical dotted line x = 2, and below the horizontal continuous line y = 4.
Is 3a a term for expressions
Answer:
yes
Step-by-step explanation
because it is an algebraic expression. 3a + a are called like terms because they both contain the same letter. To simplify an expression we collect together like terms. You can only add or subtract when the letters are the same.
A hammer thrower is competing in a track and field meet. He rotates exactly 5 times in 2π seconds, and the motion of his hammer is represented by a sine function.
Which function rule could model this situation?
f(x)=5 sin x
f(x)= sin(5x)
f(x)=5π sin x
f(x)= sin(1/5x)
Answer:
Therefore the correct option is sin(5x).
Step-by-step explanation:
i) The hammer thrower rotates exactly 5 times in 2[tex]\pi[/tex] seconds.
Therefore one rotation is completed in [tex]\frac{2\pi }{5}[/tex] seconds.
ii) Since the motion of the hammer is represented by a sine function therefore
one rotation is considered to be one full cycle and the time period of that cycle
is given in equation i) and it is T = [tex]\frac{2\pi }{5}[/tex] seconds.
iii) the equation of a sine function is given by sin(2[tex]\pi[/tex][tex]\frac{1}{T}[/tex]) which in this case would
be sin(2[tex]\pi[/tex] × [tex]\frac{1}{\frac{2\pi }{5}}[/tex] × x) = sin(5x)
iv) Therefore the answer is sin(5x)
What’s the common denominator for 4 and 3
e^2x + 3e^x - 18 = 0
Solving e²ˣ + 3eˣ- 18 = 0 involves substituting y = ex to transform it into a quadratic equation. Solving this quadratic equation yields a valid solution, y = 3, leading to x = ln(3). Therefore, the solution is x = ln(3).
To solve the equation e²ˣ + 3eˣ- 18, we perform a substitution to convert it into a quadratic form.
Let y =eˣ. Then the equation becomes:
y² + 3y - 18 = 0.This quadratic equation can be solved using the quadratic formula:This gives us two solutions for y:
y = 3 and y = -6.Since y = eˣ, and eˣ must be positive:
y = -6 is not valid. Thus, y = 3.Finally, solve for x:
eˣ = 3 ⟹ x = ln(3).Therefore, the solution to the equation e²ˣ + 3eˣ- 18 = 0 is x = ln(3).
Convert 5/16 to a decimal using long division
Answer: 0.3125
Step-by-step explanation:
Convert the fraction to a decimal by dividing the numerator by the denominator.
A sphere has a radius of 16 in. Which statements about the sphere are true? Check all that apply.
The sphere has a diameter of 8 in.
The volume of the sphere is StartFraction 2,048 Over 3 EndFraction pi inches cubed.
The sphere has a diameter of 32 in.
The radius’s length is one-half the length of the diameter.
The volume of the sphere is StartFraction 16,384 Over 3 EndFraction pi inches cubed.
The diameter’s length is one-half the length of the radius.
Answer:
The sphere has a diameter of 32 in. CORRECT: the diameter of a sphere doubles its radio, so if the radio equals 16,the diameter measures the double, in this case, 32.The radius' lenght is one half the length of the diameter. CORRECT: , by definition, the diameter is the maximum distance between two opposite points on the surface of the sphere, and its lenght equals twice the radius because the radius is the distance between the center of the sphere and any point of the frontier of the sphere (then, one colud imagine that the distance between two opposite points in a sphere can be united by two radius, or a diameter).The volume (V) of a sphere can be calculated as [tex]\frac{4\pi r^3}{3}[/tex], where r is the radio. In this case, the volume of the sphere will be [tex]\frac{4\pi\times16^3}{3}=\frac{4\pi\times4096}{3}[/tex], which is also equal to [tex]\frac{16384\times\pi}{3}[/tex].Answer:
The True statements are:
The sphere has a diameter of 32 in.
The radius’s length is one-half the length of the diameter.
The volume of the sphere is StartFraction 16,384 Over 3 EndFraction pi inches cubed.
Step-by-step explanation:
The sphere has a diameter of 8 in. FalseThis is false because a radius is half of a diameter. Half of the given diameter of 8 in is 4 in whereas the radius in the question is 16 in.
The volume of the sphere is StartFraction 2,048 Over 3 EndFraction pi inches cubed. FalseThis is false because the volume of the sphere is 4πr³/3 = (16,384/3) π cubic inches.
The sphere has a diameter of 32 in. TrueThis is True because a radius is half of a diameter. Half of the given diameter of 32 in is 16 in and the radius in the question is also 16 in.
The radius’s length is one-half the length of the diameter. TrueThis is True because a radius is half of a diameter
The volume of the sphere is StartFraction 16,384 Over 3 EndFraction pi inches cubed. TrueThis is True because the volume of the sphere is 4πr³/3 = (16,384/3) π cubic inches.
The diameter’s length is one-half the length of the radius. FalseIt is the radius’s length that is one-half the length of the diameter
Suppose that a code consists of 5 digits, none of which is repeated. ( A digit is one of the 10 numbers 0,1,2,3,4,5,6,7,8,9.) How many codes are possible?
Answer:
30240
Step-by-step explanation:
There are two primary ways to approach this problem - the logical and the mathematical.
The logical way is very simple:
Since you know that there are 5 digits and each must be different, start with the first digit and work your way up.
The first digit can be any of 10 digits (0–9).
However, the second digit can be any of only 9 digits as 1 digit has already been used and cannot be repeated.
Similarly, applying the same logic, there are only 8 options for the third digit, 7 for the fourth digit, and 6 for the fifth and final digit.
Now, multiply all these numbers together to get the total number of configurations like so:
10⋅9⋅8⋅7⋅6=30240
The more mathematically inclined way requires the use of a special formula. Since in this particular scenario, the order of the numbers matter, we can use the Permutation Formula:
P(n,r)=n!(n−r)!
where n is the number of numbers in the set and r
is the subset.
Since there are 10 digits to choose from, we can assume that n=10
.
Similarly, since there are 5 numbers that need to be chosen out of the ten, we can assume that r=5
.
Now, plug these values into the formula and solve:
=10!(10−5)!
=10!5!
=10⋅9⋅8⋅7⋅6
=30240
Will Mark as Brainliest whoever answers first
Round 37,748 to the tens
Answer:
37750
Step-by-step explanation:
Please help!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answer:
[tex]y=\sqrt[3]{x+3}+3[/tex]
Step-by-step explanation:
The S-shaped curve is that of the cube root function (choices C or D). The parent function has its critical point at the origin. Here, that has been moved 3 units left and 3 units up.
Replacing x with x-a will move a function's graph to the right by "a" units. Here, we have a=-3, so we expect to see ∛(x-(-3)) = ∛(x+3). The graph of that is moved up 3 units by adding 3 to the function value. This gives ...
y = ∛(x+3) +3 . . . . . matches choice D
Which of the following equations represents a line that is parallel to y = 3x +2
and passes through the point, (1, 6)?
O A. y = 3x +6
O B. y = 3x +9
O c. y=-3x+2
O D. y = 3x+3
The correct equation of the new line parallel to y = 3x + 2 and passing through (1, 6) is y = 3x + 3.
Explanation:To find the equation of the line that is parallel to the given line y = 3x + 2 and passes through the point (1, 6), we first need to acknowledge that parallel lines have the same slope.
Therefore, the slope of the new line will also be 3. We can use the point-slope form of the equation y - y1 = m(x - x1) to find the equation. Substituting the given point into the equation, we get y - 6 = 3(x - 1).
Simplifying the equation, we find y = 3x + 3. So, the equation of the line that is parallel to the original line and passes through the given point is y = 3x + 3.
Does the graph represent a function? Yes or NO
In a video game,you score p game points and b triple bonus points. An expression for your score is p+3b. What is your score when you earn 245 games points and 20 triple bonus points
Your score in the game is 305 points.
Step-by-step explanation:
Given,
Expression used for score = p + 3b
p = game points
b = triple bonus points
Game points earned by you = p = 245 games point
Triple bonus points = b = 20
Putting these values in given expression
Total points = [tex]245+3*20[/tex]
Total points = [tex]245+60[/tex]
Total points = 305 points
Your score in the game is 305 points.
Keywords: addition, expression
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At a local fitness center, members pay a $12 membership fee and $3 for each aerobics class. Nonmembers pay $4 for each aerobics class. For what number of aerobics classes will the cost for members and nonmembers be the same?
For 12 number of aerobics classes, cost for members and nonmembers is same
Solution:
Let "x" be the number of aerobic classes
At a local fitness center, members pay a $12 membership fee and $3 for each aerobics class
Therefore,
Members pay = 12 + 3(number of classes)
Members pay = 12 + 3x ------- eqn 1
Nonmembers pay $4 for each aerobics class
Nonmembers pay = 4x ------- eqn 2
For cost for members and nonmembers be the same, eqn 1 must be equal to eqn 2,
12 + 3x = 4x
4x - 3x = 12
x = 12
Thus for 12 number of aerobics classes, the cost for members and nonmembers will be same
a total of 345 tickets were sold for the school play. they were either adult tickets or student tickets. the number of student tickets sold was two times the number of adult tickets sold. how many adult tickets were sold?
Answer:
115
Step-by-step explanation:
a + s = 345
s = 2a
a + 2a = 345
3a = 345
a = 345/3
a = 115 <===== adult tickets
s = 2a
s = 2(115)
s = 230......student tickets
Can someone please help me with this question? :)
Answer:
Step-by-step explanation:
[tex]\frac{h*(a+b)}{2}=\frac{6.7*(7+10.4)}{2}\\\\=\frac{6.7*17.4}{2}=\frac{116.58}{2}=58.29[/tex] cm²
Tina lives in a state that charges her 4.5% state income tax on her federal taxable income. If her federal taxable income is $61,600, how much does Tina pay in state income tax?
$ 2772 is paid in state income tax
Solution:
Given that, Tina lives in a state that charges her 4.5% state income tax on her federal taxable income
Federal taxable income = $61,600
To find: Amount paid by Tina in state income tax
Tax rate = 4.5 %
Which means, 4.5 % of $61,600 is paid as tax
[tex]Tax\ Rate = 4.5 \% \text{ of } 61600[/tex]
Here, "of" means multiplication or product
[tex]Tax\ Rate = 4.5 \% \times 61600\\\\Tax\ Rate = \frac{4.5}{100} \times 61600\\\\Tax\ Rate = 0.045 \times 61600\\\\Tax\ Rate = 2772[/tex]
Thus $ 2772 is paid in state income tax
4.5% of 61,600
0.045(61,600) = 2772
Chase purchased a sweatshirt from the clearance rack. The price of the sweatshirt after the discount is represented by the expression 0.75x, where x represents the original price of the sweatshirt.
Which expression also represents the discounted price of the sweatshirt?
A
(0.75 − 0.25)x
B
(0.75 + 0.25)x
C
x – 0.25x
D
x + 0.25x
Answer:B(0.75+0.25)x
Step-by-step explanation:
Is a discount of 0.75 was given the d real value of the sweatshirt would be a whole number
Which is 1-0.75=0.25
Graph the line that has a slope of 1/9 and includes the point (0,8)
Answer:
Step-by-step explanation:
y = mx + b
slope(m) = 1/9
y int (b) = 8.....or (0,8)
y = 1/9x + 8.....this is ur equation
ur x intercept is : (can be found by subbing in 0 for y
0 = 1/9x + 8
-1/9x = 8
x = 8 * -9
x = - 72....or (-72,0)
The equation of line is y = ( 1/9 )x + 8
What is an Equation of a line?
The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept
And y - y₁ = m ( x - x₁ )
y = y-coordinate of second point
y₁ = y-coordinate of point one
m = slope
x = x-coordinate of second point
x₁ = x-coordinate of point one
The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )
Given data ,
Let the equation of line be represented as A
Now , the value of A is given by
The slope of the line m = 1/9
So , Slope m = 1/9
The point on the line is given by P = P ( 0 , 8 )
Now , the equation of line is y - y₁ = m ( x - x₁ )
Substituting the values in the equation , we get
y - 8 = ( 1/9 ) ( x - 0 )
y - 8 = ( 1/9 ) x
On simplifying the equation , we get
Adding 8 on both sides of the equation , we get
y = ( 1/9 )x + 8
Therefore , the value of A is y = ( 1/9 )x + 8
Hence , The equation of line is y = ( 1/9 )x + 8
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factorise
24p2 + pq - 23q²
24p² + pq - 23q² =
= 24p² + 24pq - 23pq - 23q²
= 24p(p + q) - 23q(p + q)
= (p + q)(24p - 23q)
The required factorization of the given expression is given as (24p - 23q)(p + q).
What are the factors?A number or algebraic expression that evenly divides another number or expression—i.e., leaves no remainder—is referred to as a factor.
Given expression in the quesiton is 24p2 + pq - 23q², we have to factorize the given expression,
So,
24p² + pq - 23q²,
Substituting pq = 24 pq - 23pq
= 24p² + 24pq - 23pq - 23q²
= 24p(p + q)-23q(p + q)
= (24p - 23q)(p + q)
Thus, the required factorization of the given expression is given as (24p - 23q)(p + q).
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Liam has $7.50 How much does liam earn in a 35 hour work week (gross pay without benefits)
Answer:
7.50*35=262.50
Step-by-step explanation:
What is the value of x?
5 cm
3 cm
Enter your answer in the box
40 cm
2x + 10
Answer: 7cm
Step-by-step explanation:
Answer: the answer is 7
Step-by-step explanation:
1. Suppose that AB and EF are corresponding sides of similar triangles. AB = 6 and the scale factor is 3, what is EF?
A. 3
B. 6
C. 9
D. 18
Answer:
d
Step-by-step explanation:
since since the scale factor is 3 angle ab abyou multiply 6 * 3 to get 18
The length of the Side EF is 18.
What is the scale factor?A scale factor is defined as the ratio between the scale of a given original object and a new object.
Given that corresponding sides are AB and EF, and EF is a side of the larger (second) triangle.
scale factor 3 means each length of the second is 3 times as long as the first.
Therefore, the length of the side EF when the length of side AB is 6 units is,
EF = 3 x AB
= 3 x 6 units
= 18 units.
Therefore, Side EF is 18.
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A store advertises a 35% discount on a $951 computer system.
For this case we propose a rule of three:
$ 951 -------------> 100%
x -------------------> 35%
Where "x" is the variable that determines the amount of the discount equivalent to 35%.
[tex]x = \frac {35 * 951} {100}\\x = \frac {33285} {100}\\x = 332.85[/tex]
Thus, the discount is $332.85.
The new price of the computer system is:
$951- $332.85 = $617.5
Answer:
The new price of the computer system is: $617.5
When Elmer empties his bank, he found 17 pennies, 4 nickels, 5 dimes, and 2 quarters. What was the value of the coins in his bank?
Elmer's bank contained coins totaling $1.37, calculated by summing the value of each type of coin separately.
Explanation:To find the total value of the coins in Elmer's bank, we need to calculate the value of each type of coin separately and then sum them up. The value of coins is counted based on their denomination, with pennies being worth 1 cent, nickels 5 cents, dimes 10 cents, and quarters 25 cents.
Pennies: 17 pennies × 1 cent = 17 centsNickels: 4 nickels × 5 cents = 20 centsDimes: 5 dimes × 10 cents = 50 centsQuarters: 2 quarters × 25 cents = 50 centsAdding these amounts gives us a total value of 17 + 20 + 50 + 50 = 137 cents. Therefore, the value of the coins in Elmer's bank is $1.37.
The value of the coins in Elmer's bank is $2.17.
17 pennies = $0.17
4 nickels = $0.20
5 dimes = $0.50
2 quarters = $0.50
Adding these amounts together: $0.17 + $0.20 + $0.50 + $0.50 = $2.17.
Which basic construction if shown here?
A) bisect an angle
B) bisect a like segment
C) construct a parallel line
D) copy a line segment
Answer:
A
Step-by-step explanation:
Consider triangle OAM and OBM. In these triangles,
OA is congruent to OB as radii of one circle;AM is congruent to BM as radii of two congruent circles;OM is congruent to OM by reflexive property (this side is common).Thus, triangles OAM and OBM are congruent by SSS postulate.
Congruent triangles have congruent corresponding parts, so
[tex]\angle AOM\cong \angle BOM[/tex]
Hence, OM is angle AOB bisector.
Answer:
a
Step-by-step explanation:
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