4. The drama club is printing t-shirts for its members. The printing company chargesa certain amount for each shirt plus a setup fee of $40. There are 21 students in the drama club.
a. If there are 21 students in the club and the t-shirt order costs a total of $187, how much does each t-shirt cost? Show your reasoning.
Answer:
$7
Step-by-step explanation:
You want the cost of a shirt when the cost of 21 shirts plus a $40 setup fee is $187.
CostThe total cost of the order is the sum of the setup fee and the extended cost of the shirts.
cost = (setup fee) + (number of shirts) × (cost per shirt)
187 = 40 + 21 × (cost per shirt)
Subtracting 40 gives ...
147 = 21(cost per shirt)
Dividing by 21, we have ...
7 = cost per shirt
Each T-shirt costs $7.
please help . find abc
The required value of ∠ABC in the given triangle is 50°
Explain the relation between interior and exterior angles?The relation between interior and exterior angles of the triangle are related as, the sum two interior angles of triangle is equal to the opposite exterior angle of that triangle.
As we see in the given question, the sum of angle ∠A and ∠B is equal to the exterior angle which is 145°
According to the question:⇒ 2x° + 95° = 145°
⇒ 2x° = 145° - 95°
⇒ 2x = 50°
Thus, required answer of angle ∠ABC is 50°
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Solve this system of linear equations without graphing: {5x+4y=810x−4y=46[tex]Solve this system of linear equations without graphing: {5x+4y=810x−4y=46[/tex]
The solution of given system of linear equations is x = 3.6 and y = 2.5.
A "system" of equations is a collection of equations that you answer all at once. Ax + By + C = 0, where A and B are the coefficients and C is the constant, can be used to describe a linear equation. Non-linear equations are more difficult to comprehend than linear equations.
Solving the equations,
5x +4y = 8
10x − 4y = 46
Adding the above equations, we get
5x + 10x + 4y - 4y = 8 + 46
15x=54
Dividing by 15,
x = 3.6
Now, putting the value of x in second equation,
10(3.6) - 4y = 46
36 - 4y = 46
4y = -10
Dividing by 4, we get
y = -2.5
Therefore, the solution of given system of linear equations is x = 3.6 and y = 2.5.
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Use the following diagram for questions 1-3.
1. Find x.
2. Find y
3. Find z
Answer:
x= 40° y= 66° z=106° ....
The value of angles are x = 40° , y = 66°, z = 106°
Since there are two parallel lines and two intersecting lines forming a triangle we will use the properties of lines and triangles to find out the value of x,y,z. First of all y = 66° because of the vertical angle theorem, which means that adjacent angles formed by the intersection of two lines are supplementary or equal to 180° degrees. The third angle of the triangle formed is 74°. Using the sum of all angles of the triangle is equal to 180° we can find the third angle of triangle x which is equal to 40°. Now z can be found using the property sum of two opposite interior angles which will come out to be 106°. Hence by this, we can find all the angles.
I hope this answer helps.
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Which of the
following best describes the
slope of the line below?
• A. Positive
• B. Negative
• C. Zero
• D. Undefined
Answer:
negative
Step-by-step explanation:
how many different three-letter strings can be formed from the letters a, b, c, d, e (repeats allowed) if the string must contain either all vowels or all consonants?
8 strings can be formed with all vowels from a, b, c, d, e and 27 strings can be formed with all consonants from a, b, c, d and e.
What is permutation and combination?
A permutation is an orderly arrangement of things or numbers.
Combinations are a means to choose items or numbers from a collection or set of items without worrying about the items' chronological order.
The amount of two-letter words that can be created using the letters in a word, like GREAT, is an illustration of permutations: ⁵P₂ = 5!/(5-2)!
How many different ways we may write the words utilizing the vowels in the word GREAT is an example of a combination: ⁵C₂ = 5!/[2! × (5-2)!]
Given, the letters that can be used to create the required three letter word in question: a, b, c, d, e.
Total number of letters that can be used = 5
Total number of vowels in the available letters to be used = 2 ('a' and 'e')
Total number of consonants in the available letters to be used = 3 ('b', 'c' and 'd')
Case 1: A three letter word having all vowels where letters can be repeated
Here, since two letters are to put in three empty positions, the total number of ways to form this word = 2³ = 2 × 2 × 2 = 8
Case 2: A three letter word having all consonants where letters can be repeated
Here, since three letters are to put in three empty positions, the total number of ways to form this word = 3³ = 3 × 3 × 3 = 27
Thus, 8 strings can be formed with all vowels from a, b, c, d, e and 27 strings can be formed with all consonants from a, b, c, d and e.
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What is the equation of the line that passes through the point (6,-5) and has a slope of -{1}{3}?
Answer:
y = - [tex]\frac{1}{3}[/tex] x - 3
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
here m = - [tex]\frac{1}{3}[/tex] , then
y = - [tex]\frac{1}{3}[/tex] x + c ← is the partial equation
to find c substitute (6, - 5 ) into the partial equation
- 5 = - 2 + c ⇒ c = - 5 + 2 = - 3
y = - [tex]\frac{1}{3}[/tex] x - 3 ← equation of line
(car sales) of the cars sold during the month of july, 90 had air conditioning, 102 had automatic transmission, and 72 had power steering. 7 cars had all three of these extras. 22 cars had none of these extras. 25 cars had only air conditioning, 61 cars had only automatic transmissions, and 33 cars had only power steering. 11 cars had both automatic transmission and power steering. how many cars had exactly two of the given options?
There were 58 cars sold with exactly two of the given options.
1. There were 90 cars sold with air conditioning.
2. There were 102 cars sold with automatic transmission.
3. There were 72 cars sold with power steering.
4. There were 7 cars sold with all three options.
5. There were 22 cars sold with none of the options.
6. There were 25 cars sold with only air conditioning.
7. There were 61 cars sold with only automatic transmission.
8. There were 33 cars sold with only power steering.
9. There were 11 cars sold with both automatic transmission and power steering.
Let's just count the number of cars that have exactly two of the given options:
Air Conditioning & Automatic Transmission: 25
Air Conditioning & Power Steering: 22
Automatic Transmission & Power Steering: 11
So there are 25 + 22 + 11 = 58 cars that have exactly two of the given options.
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Translate the sentence into an inequality. The sum of a number times 3 and 23 is greater than 25.
Translation of the given sentence with variable y into inequality is given by 3y + 23 > 25.
As given in the question,
Given sentence is :
Let the number be represented by y.
The sum of y times of 3 and 23 is greater than 25.
Translation of the given sentence into inequality is given by :
y times 3 is represented by 3y
Sum of y times 3 and 23 is given by 3y + 23
Sum is greater than 25
3y + 23 > 25
Simplify the inequality we get,
3y > 25 -23
⇒3y > 2
⇒y > 2/3
Therefore, translation of the given sentence with variable y into inequality is given by 3y + 23 > 25.
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g(x)= x^2-5 9x-17 (x+1)(x-5) g(7)=
The solution for g(7) in the piecewise function g(x) = (x + 1)(x - 5) is 16
How to determine the solution for the function?From the question, we have the equation that can be used in our computation to be a piecewise function
This piecewise function is represented as g(x)
Also from the question, we have the following function that we are to compute
g(7)
This means that the value of x is 7, and we calculate g(x) when x = 7
To do this, we make use of an equation in the piecewise function, where the domain occupies x = 7
This domain is x c (2, oo)
And the function is
g(x) = (x + 1)(x - 5)
Substitute the known values in the above equation, so, we have the following representation
g(7) = (x + 1)(x - 5)
So, we have the following equation
g(7) = (7 + 1)(7 - 5)
There is no constant to add or subtract to both sides of the equation
Also, there is no factor to multiply or divide from both sides of the equation
So, we have the following representation
g(7) = (7 + 1)(7 - 5)
Solving further, we have
g(7) = 16
Hence, the solution is 16
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the augusta national golf club in augusta, georgia is an 18-hole course that consists of par-3 holes, par-4 holes, and par-5 holes. a golfer who shoots par has a total of 72 strokes for the entire course. there are two more par-4 holes than twice the number of par-5 holes, and the number of par-3 holes is equal to the number of par-5 holes. find the numbers of par-3, par-4, and par-5 holes on the course.
No. of par-3 holes be represented by = 5
No. of par-4 holes be represented by = 8
No. of par-5 holes are represented by = 5
Total number of courses in the club= 18 (given in the question)
Total shot taken by golfer=72 (given in the question)
Let par-3 holes be represented by t
Let par-4 holes be represented by f
Let par-5 holes be represented by v
forming equations:
f+2=2v
t=v
f + v + t = 18
f+2=2v
f=2v-2 -(i)
t=v -(ii)
f + t + v=18
putting values from (i) and (ii)
(2v-2) + v + v=18
2v-2+2v=18
4v=18+2
4v=20
v=20/4
v=5
Number of par-5 holes=5
from (i)
f=2v-2
putting value
f=2(5)-2
f=10-2
f=8
Number of par-4 holes=8
from (i)
t=v-
putting value
t=5
t=5
Number of par-3 holes=5
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a music store buys instruments and then sells them for more than they paid. during a off sale, the store offers a clarinet for . how much did the store pay for the clarinet?
The current price of the clarinet and the various discounts and markups illustrate that the amount the store paid was $90.
How to calculate the price?First find out the selling price of the clarinet:
= Discounted price / ( 1 - discount rate)
= 93.60 / ( 1 - 20%)
= $117
This selling price is 30% more than what the store paid so the price the store paid was:
= Selling price / ( 1 + rate of increase)
= 117 / ( 1 + 30%)
= $90
In conclusion, the amount the store paid was $90.
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Complete question
A music store buys instruments and then sells them for 30% more than they paid. During a 20% off sale, the store offers a clarinet for $93.60.
How much did the store pay for the clarinet?
Solve for the value of v.
123°
(2v+1)°
Step-by-step explanation:
the angles between 2 intersecting lines must be the same on both sides of either line, they are just left-right mirrored.
so,
123 = 2v + 1
2v = 122
v = 61
if the interest for 5 years on Rs 3000 is Rs 525, find the interest on Rs 2200 for 6 years at the same rate of interest.
Using the formula of simple interest, the interest on Rs 2200 for 6 years at the same rate of interest is Rs 462.
In the given question,
The given principal amount = Rs 3000
The given time = 5 years
Interest amount = 525
Now finding the rate of interest.
As we know that the formula of simple interest.
I = P*R*T/100
525 = 3000*R*5/100
Multiply by 100 on both side we get
52500 = 15000*R
Divide by 15000 on both side
R = 52500/15000
R = 3.5
In the question we have to find the interest on Rs 2200 for 6 years at the same rate of interest.
To find the interest put the value in I = P*R*T/100
As given P=2200, R=3.5%, T=6 years
I = P*R*T/100
I = 2200*3.5*6/100
I = 462
Hence, the interest on Rs 2200 for 6 years at the same rate of interest is Rs 462.
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help meeeeeeeeeeeeeeeeeee pleaseeee rn rnnnnnnnnnn!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
help meeeeeeeeeeeeeeeeeee pleaseeee rn rnnnnnnnnnn!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Lat week, Lia old 20 hand-engraved watch band, earning a total profit of $105. 0. She plan to make 50 engraved watch band to ell at the community art fair. If he ell all 50 watch band, how much profit can Lia expect to earn?
$
If Lisa sells 50 watch bands, she gets a profit of $262.50.
A unitary method is defined.
Mathematicians use the unitary method to solve problems by first determining the value of a single unit, or 1, (by dividing), and then determining the necessary value by multiplying the value of the single unit.
We must first ascertain the cost of one watch band.
To determine this, we simply divide $105 by 20, which equals $5.25.
We can divide $5.25 by 50 because she sells all 50 watchbands.
50 multiplied by $5.25 equals $262.50.
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Bacteria colonies can increase by 73% every 2 days. If you start with 55 bacteria microorganisms, how large would the colony be after 10 days?
Answer:
In order to complete the equation we need to use this method :
Future Amount = I(1+r)^t
I=Initial Amount
R=Growth rate
T=Time periods
Now that we know that....
Letsss seee:
You started with 55 so
Future Amount = 55(1+r)^t
The growth rate is 73% so we have to convert to decimal so
Future Amount=55(1+.73)^t
Time period is 73% every 2 days and you want to see how large the colony would be after 10 days so you do 10/2:
Future Amount=55(1+.73)^5
Future Amount therefore equals 852.301407 BUT You have to round to the nearest whole number Sooo
The Answer is 852.Step-by-step explanation:
Hope this helpss you Tony!
Answer:
How large would the colony be after 10 days?
852 is the answer.
Step-by-step explanation:
3n=1/9 Find the value of n.
PLEASE HELP
Answer: n=1/27=0.037
Step-by-step explanation:
Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation : 3*n-(1/9)=0
Simplify 1/9
3n - 1/9 = 0
Rewrite the whole as a fraction using 9 as the denominator :
3n 3n • 9
3n = —— = ——————
1 9
Equivalent fraction : The fraction thus generated looks different but has the same value as the whole
Common denominator : The equivalent fraction and the other fraction involved in the calculation share the same denominator
2.2 Adding up the two equivalent fractions
Add the two equivalent fractions which now have a common denominator
Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:
3n • 9 - (1) 27n - 1
———————————— = ———————
9 9
End of step 2
27n - 1
——————— = 0
9
Start of step 3
When a fraction equals zero ...
Where a fraction equals zero, its numerator, the part which is above the fraction line, must equal zero.
Now,to get rid of the denominator, Tiger multiplys both sides of the equation by the denominator.
Here's how:
27n-1
————— • 9 = 0 • 9
9
Now, on the left hand side, the 9 cancels out the denominator, while, on the right hand side, zero times anything is still zero.
The equation now takes the shape :
27n-1 = 0
Solving a Single Variable Equation:
3.2 Solve: 27n-1 = 0
Add 1 to both sides of the equation :
27n = 1
Divide both sides of the equation by 27:
n = 1/27 = 0.037
Given: ABCD trapeziod, AB=DC, BK - altitude, AB=8, AK=4
Find: m
The value of angle A and B are 60° and 120° respectively.
How to calculate the angles?It is important to note that in isosceles trapezoid, the angles adjacent to the bases are congruent.
Therefore A = D
B = C
When in the right angle, the hypothenuse is twice the leg, the angle opposite it will be:
ABK = 30°
Also, KBC = 90°
Therefore, B = 30° + 90° = 120°
A = D = 180° - 120° = 60°
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Complete question:
Given: ABCD trapeziod, AB=DC, BK - altitude, AB=8, AK=4
Find: mA and mB.
Help please
74°
94°
100°
106°
Answer:
106
Step-by-step explanation:
180-74=106
You can find x by looking at the corresponding angle under it and we know a straight line is 180 degrees and the other side of the x is 74 degrees then we just subtract to find the x angle
Hopes this helps please mark brainliest
a variable t follows a uniform probability distribution where t is between 0 and 8 what is the probability that the random variable has a value greater than 5?
There is a 1/3 chance that random variable will have a value higher than 5.
Define the term random variable?A random variable is called with an unknown value or a function that gives values to each of the results of an experiment. Random variables are similarly defined by letters and fall into one of two categories: continuous variables, which can take on any value within a continuous range, or discrete variables, which have specified values.For the variable t, which follows uniform probability distribution.
0 ≤ t ≤ 8
Total variables = 9.
For the probability of value greater than 5 for the random variable.
P(t > 5) = P(t = 6) + P(t = 7) + P(t = 8)
P(t > 5) = 1/9 + 1/9 + 1/9
P(t > 5) = 3/9
P(t > 5) = 1/3
Thus, there is a 1/3 chance that random variable will have a value higher than 5.
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[tex]x^{2}-6x+1=0[/tex]
Solve the quadratic equation using the quadratic formula.
Show exact answers in simplified radical form; no rounded decimals.
The solutions of the quadratic equation using the quadratic formula is x = 3 + 2√2 and x = 3 - 2√2
Solving Quadratic equation using the Quadratic formulaFrom the question, we are to solve the given quadratic equation using the quadratic formula
The given quadratic equation is
x² - 6x + 1 = 0
Using the quadratic formula,
x = [-b±√(b² - 4ac)] / 2a
a = 1, b = -6, and c = 1
Thus,
x = [-(-6) ±√((-6)² - 4(1)(1))] / 2(1)
x = [6 ±√(36 - 4)] / 2
x = [6 ±√(32)] / 2
x = [6 ± 4√2] / 2
x = [2(3 ± 2√2)] / 2
x = 2(3 ± 2√2) / 2
x = (3 ± 2√2)
x = 3 + 2√2 and 3 - 2√2
Hence, the roots are 3 + 2√2 and 3 - 2√2
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Jonshelle is developing a new bread recipe. The relationship between cups of water, w, and cups of flour, f, is a=2/5b. What is the scale factor of flour to
water?
Answer: the i8 49
Step-by-step explanation:98493
There are 15 circles and 6 squares. What is the simplest ratio of squares to total shapes?
Answer:
2/7Step-by-step explanation:
There are 15 circles and 6 squares.
Total shapes:
15 + 6 = 21Ratio of squares to total shapes:
6/21 = 2/7Answer:
the answer is 2:7
Step-by-step explanation:
6÷3 : 21÷3
=2:7
-7 + 5x = 5x + 9 help me pls
Answer:
solve for x 7 (5x+9)=- (x-9) 7(5x + 9) = −(x − 9) 7 ( 5 x + 9) = - ( x - 9) Simplify 7(5x+9) 7 ( 5 x + 9). Tap for more steps... 35x+63 = −(x−9) 35 x + 63 = - ( x - 9) Simplify −(x−9) - ( x - 9).
Step-by-step explanation:
Rewrite 0+0+7(5x+9)= -(x----9)
Apply the distributive property. 7 (5x) + 7.9= - (x-9)
nikolai and teresa are trying to decide which restaurant they should take their friend thomas to for his birthday. nikolai wants to take thomas to a vietnamese restaurant (which serves generous portions of inexpensive but delicious food), and teresa wants to take thomas to a french restaurant (which serves expensive and beautifully presented food). to resolve the issue, they decide to flip a coin. if nikolai wins the coin toss they will take thomas to the vietnamese restaurant and the next time a friend of theirs has a birthday they will take her or him to the french restaurant teresa likes. if teresa wins the coin toss, they will go to the french restaurant first and the vietnamese restaurant later. the conflict style they used is best described as:
The conflict style they used is Collaboration.
Given, that Nikolai wants to take Thomas to a Vietnamese Restaurant (which serves generous portions of inexpensive but delicious food), and Teresa wants to take Thomas to a French restaurant (which serves expensive and beautifully presented food)
To resolve the issue, they decide to flip a coin.
If Nikolai wins the coin toss they will take Thomas to the Vietnamese restaurant and the next time a friend of theirs has a birthday they will take her or him to the French restaurant Teresa likes and If Teresa wins the coin toss, they will go to the French restaurant first and the Vietnamese restaurant later.
Here, we can see that this is a win-win situation as both can go to their favorite restaurant.
So, the conflict style they used is Collaboration. As, Collaboration generates solutions that satisfy both the parties’ needs.
Hence, the conflict style they used is Collaboration.
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I need help like asap !!!
only numbers and decimal points
Now we have to,
→ find the required value of b.
Formula we use,
→ (AC)² = (BC)² + (AB)²
Then the value of a will be,
→ (10.5)² = b² + (3)²
→ 110.25 = b² + 9
→ b² = 110.25 - 9
→ b = √101.25
→ [ b = 10.06 in ]
Hence, value of b is 10.06 in.
A rectangle has width 2x + 0.6 and width x -0.4. The perimeter of the rectangle is
51.4 cm. What are the length and width of the rectangle?
Answer:notsure
Step-by-step explanation:
the rabbit population in a certain area is 200%of last years population. There are 700 rabbits this year how many were there last year
Answer:
the answer is 350
Step-by-step explanation:
if it increased by 200% that means it doubled
so when x is doubled we get 700
so: 2x=700
x=700/2
x=350
A football team lost 5 yards on each of 3 plays. Explain how you could use a number line to find the team's change in field positive after the 3 plays. Then find and interpret the change in position.
The total spots moved, after the 3 plays is 15 spots to the left.
What is the unitary method?The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.
Given that the football team lost 5 yards on each 3 plays.
Assume that a number line to be able to see how far in the field did they lost in 3 games.
Therefore,
1 : 5 (1 game is to 5 yards)
3 : 15 (3 games is to 15 yards )
After the first play, we would move to the left on the line 5 spots (to simulate 5 yards lost) and then make a dot to show your new position.
The total spots moved, after the 3 plays is 15 spots to the left.
Hence, All they lost 15 yards in 3 games.
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