A student has some 1 and 5 bills in his wallet. he has a total of 14 bills that are worth 50 how many of each type of bill does he hae
x = ones
y = fives
x+y = 14 total bills
rewrite as x = 14-y
1x +5y = 50
1(14-y) +5y = 50
14-1y +5y = 50
14 +4y = 50
4y = 36
y = 36/4 = 9
x = 14-y = 14-9 = 5
9+5 = 14
9x5 = 45 +5x1 = 50
he had 9 fives and 5 ones
Answer:
There were 5 bills of '1' and 9 bills of '5'.
Step-by-step explanation:
let the number of '1' bill be x
let the number of '5' bill be y.
Total number of bills = 14
x + y = 14 ..[1]
Worth of 14 bills = 50
So,[tex]x\times 1+y\times 5=\$50[/tex]
[tex]x+5y=50[/tex]..[2]
x + y = 14
x = 14 - y
Putting value of x in [2]:
[tex]14- y +5y=50[/tex]
[tex]y=\frac{50-14}{4}=9[/tex]
y = 9
x = 14-y = 14 - 9 = 5
There were 5 bills of '1' and 9 bills of '5'.
which description matches the transformations y=cosx undergoes to produce y= -2cos3x
A. Horizontal compression by factor 1/3, vertical stretch by factor 2, then a reflection through the x-axis
B. reflection through the y-axis, vertical shift of 2 units, horizontal shift right by 3 units
C.Horizontal shift 2 units, then vertical shift up by 3 units
D.Horizontal stretch by factor 2, reflection through the x-axis, then the vertical stretch by factor 3
Answer: A. Horizontal compression by factor 1/3, vertical stretch by factor 2, then a reflection through the x-axis
Step-by-step explanation:
Since, If there is a function, y= a cos bx
Then a shows vertical stretch while b shows horizontal compression.
Here, Given function, y= cos x
After transformation, It is giving y = -2 cos 3x
therefore here is a horizontal compression occurs with factor 1/3.
Also Negative sign shows there also did reflection through x-axis.
And, It also, stretched vertically by factor 2. ( also shown in the below graph)
Thus, Option A) is correct.
A sixteen-sided number cube has the numbers 1 through 16 on each face. each face is equally likely to show after a roll. what is the probability that you will roll an even number or an odd prime number? round to the nearest thousandth.
a. 0.063
b. 0.813
c. 0.219
d. 0.875
Answer:
B. 0.813
Step-by-step explanation:
A sixteen-sided number cube has the numbers 1 through 16 on each face.
So, [tex]|\ S\ |=16[/tex]
Let us assume that, A be the event that the number will be an even number. So,
[tex]A=\left \{ 2,4,6,8,10,12,14,16 \right \}[/tex] and [tex]|\ A\ |=8[/tex]
Then,
[tex]P(A)=\dfrac{|\ A\ |}{|\ S\ |}=\dfrac{8}{16}[/tex]
Let us assume that, B be the event that the number will be an odd prime number.
[tex]B=\left \{3,5,7,11,13 \right \}[/tex] and [tex]|\ B\ |=5[/tex]
Then,
[tex]P(B)=\dfrac{|\ B\ |}{|\ S\ |}=\dfrac{5}{16}[/tex]
So the probability that you will roll an even number or an odd prime number will be,
[tex]P(A\cup B)=P(A)+P(B)-P(A\cup B)[/tex]
[tex]=\dfrac{8}{16}+\dfrac{5}{16}-0[/tex] ( as independent events)
[tex]=\dfrac{13}{16}[/tex]
[tex]=0.813[/tex]
Choose a number. add 5. multiply by -4. subtract 3. for each starting number what is your ending number ?
The mean of a set of credit scores is u=690 and o=14. Which credit score is within z-score of 3.3?
A)634
B)640
C)720
D)750
I think it is C
BMK ><
Answer:
c)720
Step-by-step explanation:
The mean of a set of credit scores is u=690 and o=14.
mean = 690 and standard deviation SD = 14
We use z- score formula
[tex]z=\frac{x-mean}{SD}[/tex]
z= 3.3 given
Plug in the values and find out x
[tex]3.3=\frac{x-690}{14}[/tex]
Multiply 14 on both sides
46.2 = x- 690
Now add 690 on both sides
x= 736.2
Credit score is 720 that comes under 736.2
So answer is 720
Tom is showing his work in simplifying (5.2 – 8.5) – 0.5 + 6.8. In which step did Tom make an error? Step 1:: (5.2 – 8.5) – 0.5 + 6.8 Step 2: 5.2 + (–8.5 – 0.5) + 6.8 (distributive property) Step 3: 5.2 – 9 + 6.8 Step 4: 5.2 + 6.8 – 9 (commutative property) Step 5: 12 – 9 = 3 Step 2; he wrote distributive instead of commutative Step 2; he wrote distributive instead of associative Step 4; he wrote commutative instead of associative Step 4; he wrote commutative instead of distributive
Answer:
B
Step-by-step explanation:
Step 2 he wrote distributive instead of associative
How do you write 5/100 in decimal form?
Jack's birthday is in 4 weeks. How many days is it until Jack's birthday? describe how you could use a number line to solve.
A vehicle travels on a highway at a rate of 65 mi/h. How long does it take the vehicle to travel 25 mi?
what are the domain and range of the following functions? write your answer using inequality symbols if possible
Create a set of numbers where the mode is equal to 10 the median is equal to 12 and the average is 12.
Please I really need help!
g(a) = 3^3a-2 . Find g(1)
A set of n = 15 pairs of X and Y scores has SSX = ...A set of n = 15 pairs of X and Y scores has SSX = 10,SSY = 40, and SP = 30. What is the slope for the regression equation for predicting Y from X?
Julio has started his very own floral business. He sells centerpieces for $19.50 each. His fixed costs are $500 per month, and each centerpiece cost $8 to produce. What is your break-even point? a. Julio must sell approximately 18 centerpieces to break even. b. Julio must sell approximately 23 centerpieces to break even. c. Julio must sell approximately 44 centerpieces to break even. d. Julio must sell approximately 55 centerpieces to break even.
500= (19.50-8.00)x
500 = 11.50x
x=500/11.50=43.48
so he needs to sell approximately 44 centerpieces to break even
The difference between the squares of two consecutive numbers is 23. what are the two numbers?
(x+1)^2-x^2=23
x^2+2x+1-x^2=23
2x+1=23
2x=22
x=11
11^2 = 121
x+1 =12
12^2=144
144-121 = 23
How to find the midpoint formula
What is the value of 3yx +2x when x=4 and y=-2
A.-28
B.-16
C.8
D.56
(HELP ASAP) Kite EFGH is inscribed in a rectangle where F and H are midpoints of parallel sides.
The area of EFGH is 35 square units. What is the value of x?
4 units
5 units
6 units
7 units
The answer is 5 units on e2020.
The absolute value function g(x) = |x + 7| − 4 is translated 5 units right and 2 units up to become g′(x). The quadratic function f(x), graphed below, is also moved 5 units right and 2 units up to become f′(x). Which of these two transformed functions has a range of y ≤ −2 and what is the vertex of this transformed function?
g′(x) has a range of y ≤ −2 and its vertex is at (−2, −2).
g′(x) has a range of y ≤ −2 and its vertex is at (2, −2).
f′(x) has a range of y ≤ −2 and its vertex is at (3, −2).
f′(x) has a range of y ≤ −2 and its vertex is at (−7, −6).
Which value of m will create a system of parallel lines with no solution?
y = mx – 6
8x – 4y = 12
Answer:
answer is D ;)
Step-by-step explanation:
William buys a basket of lemons on sale for $11 before tax. The sales tax is 15%. What is the total price William pays for the basket of lemons?
The perimeter of a rectangle is 120 feet. The ratio of the width to the length is 2:3. Find the length and width.
Solve −2x2 +3x − 9 = 0.
A basketball is thrown with an initial upward velocity of 23 feet per second from a height of 7 feet above the ground. The equation h=−16t2+23t+7h=−16t2+23t+7 models the height in feet t seconds after the basketball is thrown. After the ball passes its maximum height, it comes down and then goes into the hoop at a height of 10 feet above the ground. About how long after it was thrown does it go into the hoop? Select one: a. 1.29 seconds b. 1.44 seconds c. 1.70 seconds
Given the provided motion physics model and using the quadratic formula, it is determined that it would take approximately 3.79 seconds for the basketball to go into the hoop after it was thrown.
Explanation:The subject in consideration here is a problem related to quadratic equations in motion physics. The equation given in the question signifies a model of the height of the basketball as a function of time in the format of a quadratic equation. The equation is h = -16t² + 23t + 7.
With this equation, we can apply the quadratic formula to find the amount of time it takes for the ball to reach the hoop.
Upon using the quadratic formula, two solutions come up, t = 3.79 s and t = 0.54 s. The ball is at a height of 10 m at two times during its trajectory—once on the way up (as it rises) and once on the way down (as it falls). Since the question is about the time the ball goes into the hoop after reaching its maximum height and coming down, the larger value of t (3.79s) is considered as the valid solution.
Therefore, the time it takes for the basketball to go into the hoop after it was thrown is approximately 3.79 seconds which is not an offered option.
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All right triangles with the same acute angle θ are
give and example of a line that is parrallel to 9x+6y= -6
How can 3.7=x+(-5) be solved for x in one step?Add 3.7 to both sides .Add 5 to both sides. Subtract 3.7 from both sides Subtract 5 from both sides
The first step to solve for x in the given algebra using properties of equality is; Add 5 to both sides.
How to Simplify Algebra?We want to simplify the algebraic expression;
3.7 = x + (-5)
When dealing with algebra like this, what we have to first do is to balance both sides of the equation.
To solve this particular algebra problem, we will use additional property of equality by adding 5 to both sides to get;
3.7 + 5 = x + (-5) + 5
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The first step to solving the expression 3.7 = x + (- 5) is,
''Add 5 to both sides''
The process of combining two or more numbers is called the Addition. The 4 main properties of addition are commutative, associative, distributive, and additive identity.
We have to give that,
An algebraic expression to simplify,
⇒ 3.7 = x + (- 5)
Now, Simplify the expression by combining like terms as,
⇒ 3.7 = x + (- 5)
⇒ 3.7 = x - 5
Use the additional property of equality by adding 5 to both sides to get;
3.7 + 5 = x + (-5) + 5
8.7 = x
x = 8.7
So, the first step is, ''Add 5 to both sides''.
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what is the solution to 2sin^(2)x+sinx+1=0
a. 30 deg
b.150 deg
c.240 deg
d. 270 deg
e. 330 deg
A tree casts a shadow of 26 meters when the angle of elevation of the sun is 24°. find the height of the tree to the nearest meter.
Using the trigonometric tangential function, the height of the tree casting a 26-meter shadow at an angle of elevation of 24° is approximately 11 meters.
Explanation:The given problem can be solved by applying trigonometric principles, specifically the tangent function. In this case, we know the shadow length (26m) and the angle of elevation of the sun (24°). The height of the tree is the side opposite the angle, and the shadow is the adjacent side. Thus, we can use the tangent equation (Tan θ = Opposite/Adjacent). So, Tan 24° = Height of the tree / 26m. By cross multiplying and evaluating Tan 24°, we get the height of the tree to be approximately 11 meters.
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A cylindrical tank standing upright (with one circular base on the ground) has a radius of 1212 cm for the base. how fast does the water level in the tank drop when the water is being drained at 2323 cm33/sec? note that the volume of a cylinder is v=πr2hv=πr2h where rr is the radius of the base and hh is the height of the cylinder.
To find the rate of change of height with respect to time, we use the formula dh/dt = dV/dt / (πr²) and substitute the given values for the rate of volume change and the radius.
We have the rate of volume change as 23 cm³/sec and the cylinder has a radius of 12 cm. Note that the typo '2323 cm³/sec' and '1212 cm' should be read as '23 cm³/sec' and '12 cm,' respectively.
The volume of a cylinder is given by the formula V = πr²h, where V is the volume, r is the radius, and h is the height. To find the rate at which the height h changes over time, we can take the derivative of the volume with respect to time, which gives us dV/dt = πr² dh/dt. We can solve this equation for dh/dt (the rate of change of height with respect to time) by dividing both sides by πr² and substituting the given values. Therefore, dh/dt = dV/dt / (πr²).
Substituting the values, we get:
dh/dt = 23 cm³/sec / (π * (12 cm)²)
Upon simplifying, we will obtain the rate at which the height of the water is decreasing in cm/sec.