Doug have 30 quarters and 15 dimes.
Step-by-step explanation:
Given,
Number of coins = 45
Worth of coins = $9.00 = 9.00*100 = 900 cents
Each quarter = 25 cents
Each dime = 10 cents
Let,
x be the number of quarters
y be the number of dimes
According to given statement;
x+y=45 Eqn 1
25x+10y=900 Eqn 2
Multiplying Eqn 1 by 10
[tex]10(x+y=45)\\10x+10y=450\ \ \ Eqn\ 3[/tex]
Subtracting Eqn 3 from Eqn 2
[tex](25x+10y)-(10x+10y)=900-450\\25x+10y-10x-10y=450\\15x=450[/tex]
Dividing both sides by 15
[tex]\frac{15x}{15}=\frac{450}{15}\\x=30[/tex]
Putting x=30 in Eqn 1
[tex]30+y=45\\y=45-30\\y=15[/tex]
Doug have 30 quarters and 15 dimes.
Keywords: linear equation, elimination method
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Doug has 30 quarters and 15 dimes.
Let
x = number of quarters
y = number of dimes
The total number of coins is 45. Therefore,
Total number of coins:x + y = 45Total amount of the coins is $9. Therefore,
Total cost of the coins:0.25x + 0.1y = 9Therefore,
x + y = 45
0.25x + 0.1y = 9
0.1x + 0.1y = 4.5
0.25x + 0.1y = 9
0.15x = 4.5
x = 4.5 / 0.15
x = 30
y = 45 - 30
y = 15
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Substitution:
y=3x+2
-4x+2y=8
The organic garden at a restaurant is rectangular in shape and has a perimeter of 84 feet. If the length l
l
of the garden is 24 feet longer than the width w
w
of the garden, what is the area of the garden, in square feet?
Answer:
Area of the garden is [tex]306feet^2[/tex]
Step-by-step explanation:
Given:
Perimeter of the garden=84 feet
Let the width of the garden be 'W'
Length of the garden is 24 feet longer than the width of it
so, length of the garden= W+24 feet
To find the width 'W'
Perimeter of a rectangle= 2(Length+Width)
[tex]84 =2(W+24+W)\\ 84 =4W+48\\ 84-48=4W\\ 4W=36\\ W=9[/tex] feet
Width=9 feet
Length=W+24= 9+24= 34 feet
Area of the garden= Length*width
[tex]=34*9\\ =306 feet^2[/tex]
Area of the garden is 306 square feet
The possible values of x are given by x−3≥2 . What is the least possible value of 5x ?
Answer:
25
Step-by-step explanation:
Solving the inequality
x - 3 ≥ 2 ( add 3 to both sides )
x ≥ 5
Thus the least value of x is x = 5, hence
least possible value of 5x = 5(5) = 25
Final answer:
The least possible value of 5x, when x-3≥2, is 25, as x must be at least 5, and 5x equals 25 when x is 5.
Explanation:
The student's question asks to find the least possible value of 5x given the inequality x-3≥2. To solve this, we first find the smallest value of x that satisfies the inequality. We add 3 to both sides of the inequality to isolate x, obtaining x≥3+2, which simplifies to x≥5. Therefore, the smallest value of x is 5. Now, we multiply this value by 5 to find the least possible value of 5x, which is 5×5=25.
Hair Color Boys Girls
Black 4 5
Blonde 4 6
Brown 10 8
Red 2 1
The table shows the number of boys and girls that have black, blonde, brown, or red hair color.
What is the probability that a student has brown hair? (round to nearest hundredth)
A) 0.42
B) 0.45
C) 0.58
Eliminate
D) 0.82
Answer:
B) 0.45
Step-by-step explanation:
The total number of students is:
4 + 5 + 4 + 6 + 10 + 8 + 2 + 1 = 40
The number of students with brown hair is 10 + 8 = 18.
So the probability is:
P = 18/40 = 0.45
Answer: B.) 0.45
~~~~~~~~~~~~~~
Chicken costs $3.20 per pound, and beef costs $4.59 per pound. What is the exact cost of 3 pounds of beef?
Answer:
$13.77 for three pounds of beef
Answer:
THE ANSWER WOULD BE $13.77 FOR THREE LBS OF BEEF
Step-by-step explanation:
$4.59 x 3 = $13.77
PLEASE MARK BRAINLIEST IF THIS HELPED I ONLY NEED 1 MORE
write the linear equation that goes through the points (2, 20) and (-3, 8). *
Answer:
2.4x+15.2
Step-by-step explanation:
Answer:
y=-12x
Step-by-step explanation:
equation to solve with: m=y2-y1/x2-x1
m=8-20/-3-2
Then solve for m which is the slope
m=-12/-1
m=-12
equation: y=-12x
GET 20 PTS AND BE NAMED BRAINLIEST AND A THANK YOU PLEASE HELP!!!!!!!!!!!!!!!
Given the percent bar graphs, which best represents the responses of the Economy Majors?
Very Good = 4, Good = 20, Neutral = 11
Very Good = 6, Good = 19, Neutral = 10
Very Good = 18, Good = 55, Neutral = 27
Very Good = 5, Good = 18, Neutral = 12
Answer:
The answer is C) Very good = 18 Good = 55 Neutral = 27
Step-by-step explanation:
The answer is C) Very good = 18 Good = 55 Neutral = 27
the other person was right
and i feel really bad that somebody else got their answer deleted
Solve for n: -6(n-8)=4(12-5n)+14n
Answer: use calculated
Step-by-step explanation:
Calculator
Answer:
Everything
Step-by-step explanation:
-6(n-8)=4(12-5n)+14n Given
-6n+48=48-20n+14n Distribute
-6n+48=48-6n Simplify
-6n=-6n Subtraction Property of Equality(Subtract 48 from both sides)
n=n Division Property of Equality(Divide both sides by -6)
Determind the total area of the rectangle. Give your answer in factorised form.
Answer:
2(x + 3)(4x + 1)
Step-by-step explanation:
The area (A) of the rectangle is calculated as
A = length × width
length = 2(x + 3)
width = 2x + x + 1 + x = 4x + 1
Thus
A = 2(x + 3)(4x + 1)
What is the place value of the underlined number 4,382
Answer:4 is thousands place
3 is hundredths place
8 is tens place
2 is ones place
Step-by-step explanation:
The place value of the underlined number 4,382 is,
4 is thousands place
3 is hundredths place
8 is tens place
2 is ones place.
What is place value?Place value is the basis of our entire number system. This is the system in which the position of a digit in a number determines its value.
The number 42,316 is different from 61,432 because the digits are in different positions.
here, we have,
the underlined number 4,382
so, we get the place value,
4 is thousands place
3 is hundredths place
8 is tens place
2 is ones place.
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You are selling lemonade for $1.50,a bag of kettle corn for $3, and a hot dog for $2.50 at a fair.write and simplify an expression for the amount of money you receive when p people but one of each item.
Answer:
$7
Step-by-step explanation:$1.50 + $2.50 will equal to $4. $4 added with$3 would be $7. There's your answer
Assuming she worked at a constant rate, how many rows had been completed before Elena started working?
12
14
15
19
The answer is 12 :)
The number of rows she had been completed before Elena started working is 12 rows.
How do we make graph of a function?
Suppose the considered function whose graph is to be made is
f=f(x) f(x)
The values of 'x' (also called input variable, or independent variable) are usually plotted on horizontal axis, and the output values
f=f(x) f(x)
are plotted on the vertical axis.
They are together plotted on the point
f(x)) (x,y) = (x, f(x))
This is why we usually write the functions as:
f(x) y = f(x)
We are given that;
The points= (14,19), (20,22), (30,27)
Now,
To find the number of rows completed before Elena started working, we need to find the equation of the line that passes through the given points on the graph.
Using the slope formula, we can find that the slope of the line is (27-22)/(30-20) = 0.5.
Using the point-slope form of a line, we can write the equation as y - 22 = 0.5(x - 20).
Simplifying the equation, we get y = 0.5x + 12.
To find the y-intercept, which is the number of rows completed before Elena started working, we plug in x = 0 and get y = 12.
Therefore, by the given graph the answer will be 12 rows.
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The complete question is;
Elena agrees to finish a knitting project for a friend. The graph shows the number of rows Elena completes compared to the amount of time spent knitting. The points on graph are (14,19), (20,22), (30,27).
Assuming she worked at a constant rate, how many rows had been completed before Elena started working?
12(5+2y) = 4y - (5 - 9y)
What is y?
Answer:
y=-65/9
Step-by-step explanation:
12(5+2y)=4y-(5-9y)
60+24y=4y-5+9y
60+24y=13y-5
60+24y-13y=-5
60+9y=-5
9y=-5-60
9y=-65
y=-65/9
The value of y that satisfies the equation is y = -65/11.
The equation is given as follows:
12(5+2y) = 4y - (5 - 9y)
To find the value of y that satisfies the equation, we can solve for y by simplifying the equation.
Given equation:
12(5 + 2y) = 4y - (5 - 9y)
First, let's simplify both sides of the equation:
60 + 24y = 4y - 5 + 9y
Next, let's combine like terms:
24y - 4y - 9y = -5 - 60
Simplifying further:
11y = -65
Finally, divide both sides of the equation by 11 to solve for y:
y = -65/11
Therefore, the value of y that satisfies the equation is y = -65/11.
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Pleeease help, I've been stuck on this for weeks!!
Answers:
complementary Angles
Supplementary Angles
definition of complementary angles
definition of supplementary angles
distributive property
substitutive property
Answer:
It is given that [tex]\angle ABC[/tex] and [tex]\angle CBD[/tex] are complimentary angles.
[tex]m\angle ABC + m\angle CBD = 90 \textdegree[/tex] using the definition of complementary angles.
given that [tex]m\angle ABC = 35 \textdegree .[/tex] Using the substitutive property
[tex]35 \textdegree + m \angle CBD = 90\textdegree[/tex]
Therefore, using subtraction property of equality [tex]m \angle CBD = 55 \textdegree[/tex]
Step-by-step explanation:
It is given that [tex]\angle ABC[/tex] and [tex]\angle CBD[/tex] are complimentary angles.
[tex]m\angle ABC + m\angle CBD = 90 \textdegree[/tex] using the definition of complementary angles.
given that [tex]m\angle ABC = 35 \textdegree .[/tex] Using the substitutive property
[tex]35 \textdegree + m \angle CBD = 90\textdegree[/tex]. Therefore, using subtraction property of equality [tex]m \angle CBD = 55 \textdegree[/tex]
find an obtuse angle whose sine is
a) 0.25
b) 0.75
c) 0.875
d) 0.3465
Answer:
a) 165.52 degrees.
b) 131.41 degrees.
c) 118.96 degrees.
d) 159.73 degrees.
Step-by-step explanation:
The sine of an obtuse angle is positive as it is in the second quadrant.
a) Using a calculate the angle whose sine ( arcsin) is 0.25 = 14.478 degrees
so the obtuse angle = 180 - 14.478 = 165.52 degrees to nearest hundredth
b) c) and d) are calculated in the same way.
Melanie read 45 pages of a hundred page book her younger sister read half of a 10 page book who read a greater fraction of her book Melanie or her sister
Solve the system is of linear equations by substitution.What is the solution to x=2y+7 and 3x+2y=3?
Answer:
(5/2, -9/4)
Step-by-step explanation:
What is the value of 7 in the number 82.76? Give your answer as a fraction
Answer:
it would be 7/10
The required value of the 7 in the number is 1/10th of the given number.
Given that,
The value of 7 in the number 82.76, is to be determined.
A number system is described as a technique of composing to represent digits. It is the mathematical inscription for describing numbers of a given set by using numbers or other characters in a uniform method. It delivers a special presentation of every digit and describes the arithmetic structure.
Here,
The number 82.76 = 8 × 10 + 2 × 1 + 1/10×7 + 1/100×6
So the position of the value 7 in the given number from the above expression is given as 1/10th.
Thus, the required value of the 7 in the number is 1/10th of the given number.
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a coin is tossed, then a letter in the word accomplishment is chosen at random. find the probability of heads, then a vowel
Answer:
1/7
Step-by-step explanation:
Heads: 1/2
Accomplished: 14 letters
Accomplished: 4 vowels
P(vowel) = 4/14 = 2/7
P(H and vowel) = 1/2 * 2/7 = 1/7
Final answer:
The probability of tossing a head and then selecting a vowel from the word 'accomplishment' is 3/28 or approximately 0.107.
Explanation:
The question asks us to find the probability of getting a head on a coin toss and then picking a vowel from the word 'accomplishment'. First, we determine each probability separately. The probability of getting a head when tossing a fair coin is 1/2, as there are two outcomes (head or tail), and getting a head is one of them.
The word 'accomplishment' has 14 letters, of which 3 are vowels (a, o, i). Therefore, the probability of picking a vowel at random from 'accomplishment' is 3/14. To find the combined probability of both events happening in sequence (tossing a head then picking a vowel), we multiply the probabilities of the individual events: (1/2) * (3/14) = 3/28 or approximately 0.107.
Please solve for x. (-:
Also please show me a step-by-step, thanks! uwu
Answer:
[tex]x=27[/tex]
Step-by-step explanation:
we know that
[tex](3x+9)^o+90^o=180^o[/tex] ----> by supplementary angles (form a linear pair)
Solve for x
Combine like terms
[tex](3x+99)^o=180^o[/tex]
subtract 99 both sides
[tex]3x=180-99\\3x=81[/tex]
Divide by 3 both sides
[tex]x=27[/tex]
Help ASAP!!! Which expression gives the length of the transverse axis of the hyperbola
shown below?
The expression which gives the length of the transverse axis of the hyperbola is; Choice D; a-b.
Which expression gives the length of the transverse axis of the hyperbola?The transverse axis is by definition, a line segment that passes through the center of the hyperbola and has vertices as its endpoints. The foci therefore lies on the line that contains the transverse axis. Hence, it follows that the correct answer choice is; a-b.
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martin throws a ball straight up in the air. the equation h(t) = -16t^2 + 40t + 5 gives the height of the ball, in feet, t seconds after martin releases it.
how many seconds before the ball martin threw hits the ground?
show your work.
(pls answer asap!!)
Answer:
2.62 seconds
Step-by-step explanation:
Let
t ----> the time in seconds
h(t) ----> he height of the ball, in feet
we have
[tex]h(t)=-16t^2+40t+5[/tex]
we know that
When the ball hits the ground, the height is equal to zero
so
[tex]-16t^2+40t+5=0[/tex]
The formula to solve a quadratic equation of the form
[tex]at^{2} +bt+c=0[/tex]
is equal to
[tex]t=\frac{-b\pm\sqrt{b^{2}-4ac}} {2a}[/tex]
in this problem we have
[tex]-16t^2+40t+5=0[/tex]
so
[tex]a=-16\\b=40\\c=5[/tex]
substitute in the formula
[tex]t=\frac{-40\pm\sqrt{40^{2}-4(-16)(5)}} {2(-16)}[/tex]
[tex]t=\frac{-40\pm\sqrt{1,920}} {-32}[/tex]
[tex]t=\frac{-40+\sqrt{1,920}} {-32}=-0.12\ sec[/tex]
[tex]t=\frac{-40-\sqrt{1,920}} {-32}=2.62\ sec[/tex]
therefore
The solution is t=2.62 seconds
help hurry plzzzzzzzzzz
Answer:
The percentage of Guanine will be 17%
Step-by-step explanation:
As we know from Chargaff's rule, DNA from any organism will contain 1:1 purine and pyrimidine ratio.
so, The adenine (Purine) ratio is 33% because the Thymine is 33%(Pyrimidine)
Then Guanine (Purine) will be 17% because the Cytosine (Pyrimidine) is 17%
What is the volume of this cylinder?
Use π ≈3.14 and round your answer to the nearest hundredth.
Answer:
301.59 or estimated value is 301.60
first you have to find the circumference and then multiply the height by the circumference.
hope it helps
What is the quotient?
212,960 - 1000
o
2.1296
21.296
212.96
0
2129.6
The quotient is 212.96.
Solution:
Given expression is [tex]\frac{212,960}{1000}[/tex].
Divide the given expression to find the quotient.
Decimal rule when numerator is divided by 10, 100, 1000, 10000 etc..
If you have one zero in the divisor (10), then the decimal point will move 1 place to the left of the last digit.If you have two zeros in the divisor (100), then the decimal point will move 2 place to the left of the last digit.If you have three zeros in the divisor (1000), then the decimal point will move 3 place to the left of the last digit.[tex]$212960\div1000=\frac{212960}{1000}[/tex]
Here, we have 3 zeros in the denominator.
So, the decimal point is move 3 digit to the left of the last digit.
[tex]$212960\div1000=212.96[/tex]
So, option C is the right answer.
Hence the quotient is 212.96.
Answer:212.96
Step-by-step explanation:
Which expressions are equivalent to 5 (one-third x + 7) minus 3 (one-half x minus 4)? Select three options.
5 and one-third x minus 3 and one-half x + 35 minus 12
One-sixth x + 47
1 and two-thirds x + 35 minus 1 and one-half x + 12
5 (one-third x) + (5) (7) minus (3) (one-half x) + (3) (4)
1 and one-third x + 35 minus 1 and one-half x minus 12
Answer:
One-sixth x + 47
1 and two-thirds x + 35 minus 1 and one-half x + 12
1 and one-third x + 35 minus 1 and one-half x minus 12
Step-by-step explanation:
The original expression in this problem is
[tex]5(\frac{1}{3}x+7)-3(\frac{1}{2}x-4)[/tex]
We start by applying the distributive property and multiplying each factor outside the brackets by each factor inside:
[tex]5\cdot \frac{1}{3}x+5\cdot 7 -3\cdot \frac{1}{2}x+3\cdot 4[/tex]
So we get:
[tex]\frac{5}{3}x+35-\frac{3}{2}x+12[/tex]
Now we can rewrite this using mixed fractions:
[tex]1\frac{2}{3}x+35-1\frac{1}{2}x+12[/tex] (1)
Which can be also written as
[tex]1\frac{2}{3}x+35-(1\frac{1}{2}x-12)[/tex] (2)
And finally, by solving it, we find
[tex]\frac{1}{6}x+47[/tex] (3)
So the three correct options are
One-sixth x + 47
1 and two-thirds x + 35 minus 1 and one-half x + 12
1 and one-third x + 35 minus 1 and one-half x minus 12
Explain how you find a solution to a system of linear inequalities.
The solution of a linear inequality is the ordered pair that is a solution to all inequalities in the system and the graph of the linear inequality is the graph of all solutions of the system.
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
When two expressions are connected by a sign like "not equal to," "greater than," or "less than," it is said to be inequitable. The inequality shows the greater than and less than relationship between variables and the numbers.
Graph one line at a time in the same coordinate plane and shade the half-plane that satisfies the inequality.
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plz help asap......................................
Option B:
Law of cosine, two sides and the included angle are known.
Solution:
Let us first know the law of cosines and law of sines.
Law of cosine:
If we know the sides a, b and the included angle θ, then we can find the third side c. This is known as the law of cosine.
[tex]c^2=a^2+b^2-2abcos\theta[/tex]
Law of sine:
The sides of a triangle are to one another in the same ratio as the sines of their opposite angles.
[tex]$\frac{a}{sinA} =\frac{b}{sinB} =\frac{c}{sinC}[/tex]
Given ∠P and the sides r, q are known.
To find the value of p:
Option A: Law of cosines, all sides are known.
It is false by the above definition of law of cosine.
Option B: Law of cosine, two sides and the included angle are known.
It is true by the above definition of law of cosine.
Option C: Law of sines, all sides are known.
It is false, because one angle is given in question.
Option D: Law of sines, two angles and the included side are known.
It is false, because two angles are not given.
Option B is the correct answer.
Hence the answer is "Law of cosine, two sides and the included angle are known".
april bought some sports drinks and slices of pizza for her friends. She bought 3 more sports drinks than slices of pizza. If her total order was 21.25, how many sports drinks did she purchase? one slice of pizza cost 2.25 and one sport drink cost 1.25
Answer: She purchased 8 sports drinks,
Step-by-step explanation:
Let be "d" the number of sports drinks that April purchased and "p" the number of slices of pizza that April purchased.
Set up a System of equations:
[tex]\left \{ {{d=p+3} \atop {2.25p+1.25d=21.25}} \right.[/tex]
In order to solve the System of equations you can use the Substitution Method:
1. Solve for "p" from the first equation:
[tex]d=p+3\\\\p=d-3[/tex]
2. Substitute it into the second equation:
[tex]2.25(d-3)+1.25d=21.25[/tex]
3. Finally, you must solve for "d" in order to find its value. You get that this is:
[tex]2.25(d-3)+1.25d=21.25\\\\2.25d-6.75+1.25d=21.25\\\\3.5d=21.25+6.75\\\\d=\frac{28}{3.5} \\\\d=8[/tex]
Answer:
Step-by-step explanation:
8 sport drinks
In 20 days Ken drove 334.9 miles. How many miles did Ken drive each day?