Answer:
30 times
Step-by-step explanation:
There's a 50% chance that they will get heads.
60 divided by 2 is 30
50% of 60 is 30
Answer:
We expect 30 heads.
Step-by-step explanation:
There are 2 sides to a coin, heads and tails. They are equally likely. So the probably of getting a heads is 1/2
If we want to know how many times we will get heads, we multiply the number of flips by the probability of getting heads.
number of heads = 60 * 1/2
= 30
What is the name of the special point that a line has to pass through in order to be considered proportional
Solution:
In order to be considered proportional , a line must pass through Origin.
Equation of any line passing through origin is given by:
→ y = k x, k -= Slope of any line passing through origin.
[tex]\frac{y}{x}=k[/tex], Considering k as a proportionality constant.
Special Point = Origin (0,0)
If Carlos ran 3 miles in 21 minutes, how long did it take him to run 1 mile?
Answer:
7 minutes
Step-by-step explanation:
you have to set up a proportion
Determine the degree of the polynomial:
–3.1ax^4+2.5ax+2ax^4+1.1ax^4–0.5ax–2ax
The degree of the polynomial is 4.
To determine the degree of a polynomial, we look for the highest power of the variable present in any of its terms. Let's break down the given polynomial and identify the terms:
[tex]\[ -3.1ax^4 + 2.5ax + 2ax^4 + 1.1ax^4 - 0.5ax - 2ax \][/tex]
Here, we have terms with different powers of [tex]\( x \): \( x^4 \), \( x \),[/tex] and constant terms.
Combine like terms:
[tex]\[ (-3.1a + 2 + 2.1 + 1.1 - 0.5 - 2)ax^4 \][/tex]
[tex]\[ = (-3.1a + 2 + 2.1 + 1.1 - 0.5 - 2)ax^4 \][/tex]
[tex]\[ = (-0.4a)ax^4 \][/tex]
Now, let's analyze the combined term [tex]\( (-0.4a)ax^4 \)[/tex].
The highest power of ( x ) in this term is 4. So, the degree of the polynomial is 4.
Therefore, the degree of the polynomial is 4.
What equation represents the proportional relationship displayed in the table?
X: 0, 3, 8, 13
Y: 0, 18, 48, 78
Enter your answer in the box to complete the equation
y=___ x
[tex]\text{If x and y are proportional, then the quotient of x and y is constant}\\\\\dfrac{y}{x}=const.=a\to y=ax\\\\x=3,\ y=18\to\dfrac{y}{x}=\dfrac{18}{3}=6\\\\\text{therefore}\ \boxed{y=6x}\\\\\text{Check:}[/tex]
[tex]x=0\to y=6(0)=0\\\\x=3\to y=6(3)=18\\\\x=8\to y=6(8)=48\\\\x=13\to y=6(13)78\\\\\boxed{y=6x}[/tex]
what is 95 percent
of 60?
57
95% is 19/20 as a fraction. 60/20 is 3. Multiply 19 by 3 to get 57. At least that how I do it. Hopefully this helped you.
PLEASE HELP!!
What is the solution of the system? Use substitution.
y = −3x
x + y = −4
A. (-2,-6)
B. (2, −6)
C. (2, 6)
D. (−2, 6)
Answer:
x=2 ,y=-6
B (2,-6)
Step-by-step explanation:
y = -3x
x+y = -4
Substitute -3x for y in the second equation
x+y = -4
x+ (-3x) = -4
Combine like terms
-2x = -4
Divide by -2 on each side
-2x/-2 = -4/-2
x = 2
Now we still need to find y
y = -3x
Substitute x=2
y = -3(2)
y = -6
Enter an equation that passes through the point (12, 7) and forms a system of linear equations with no solution when combined with the equation y=−34x+8.
Answer:
y=-0.75x+16
Step-by-step explanation:
Answer:
y=-0.75x+16
Step-by-step explanation:
Ashley uses a cup of water and 2 cups of sugar to make a large batch of emerging bird Fugue what ratio correctly compares the amount of water she uses to the amount of sugar she uses
Answer:
1:2
Step-by-step explanation:
She uses 1 cup of water and 2 cups of sugar so
1:2 or 1/2.
Jay is running 6 miles. He had run 2/3 of the total distance. How far has he run to the nearest yard ?
Jay has run two-thirds of 6 miles, that is, 4 miles. When converted to yards, it is approximately 7040 yards.
Explanation:To find out how far Jay has run to the nearest yard, we first need to find out 2/3 of 6 miles since Jay has run this fraction of the distance. You can calculate two-thirds of a total by multiplying the total by 2/3. So, Jay has run 2/3 * 6 miles, which equals 4 miles.
Since we want to find out how far he has run in yards, we need to convert these miles to yards. We know that 1 mile is approximately 1760 yards. Hence, Jay has run approximately 4 * 1760 = 7040 yards.
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Stella initially put $5 into a piggy bank. Over the next few years she continued to put all of her coins in the piggy bank, such that each year the amount of money in the piggy bank doubled. Determine the equation that represents this situation and use it to decide which of the following graphs represents the amount of money, A(x), in Stella's piggy bank after x years.
Answer:
[tex]A(x)=5\cdot 2^x[/tex]
Step-by-step explanation:
The given scenario can be represented by an exponential growth function. The general form if the exponential growth function is,
[tex]y=a(1+r)^x[/tex]
where,
y = the future amount after time x,
a = initial amount,
r = rate of growth.
As here A(x) represents the amount of money after x years with initial deposit of $5 and in each year the amount doubles or duplicates itself i.e r=100% = 1, so the function would be,
[tex]A(x)=5(1+1)^x=5\cdot 2^x[/tex]
At the beginning the amount was $5, so the y intercept of the graph will be at 5.
Answer:
It’s Z Bc that’s the only one that starts at 5 and then doubles each year
Express the following as percentages. (i) 12 hours in 3 days
Answer:
16 2/3 %
Step-by-step explanation:
To put this in a percentage, they need to have the same units.
Let convert days to hours
1 day = 24 hours
Multiply by 3
3 days = 72 hours
The percentage is part over whole
12 hours / 72 hours
We can simplify by dividing top and bottom by 12
1/6
This is a fraction, change this to a decimal
.166666666
Now multiply by 100
16.666666 %
16 2/3 %
Can you help me answer 1-11?
Answer:
1. h Multiplication property for inequality
2. b Addition property for inequality.
3. i Set builder
4. f Intersection
5. k Union
6. j Subtraction property for inequalities
7. d Division property for inequality.
8. e Greater than
9. g less than
10. c compound
11. a Absolute value inequality.
Step-by-step explanation:
1/2x ≤ -5 Multiplying by 2 on both sides of the inequality
x ≤ -10
2) 8 > 4 Adding 5 on both sides of the inequality.
8 + 5 > 4+5
13 > 9
3) {h/h > 43} set builder
4) x ≥ -3 or x < -10 Intersection
5) x ≥ -4 and x < 2
6) 4x - 1 < 7 Subtract 3 on both sides
4x - 1 - 3 < 7 - 3
4x - 4 < 4
7) -3x < 9 Divide by -3 on both sides
x > -3
8) > This sign means greater than
9) < This an operation sign means less than
10) 7 > x > 1 This means that x x, 7 and x > 1.
11) /x + 6/ > 12
This means that:
(x + 6) > 12 or - (x + 6) > 12. Absolute value inequality.
1. Given the component form of vector v = (52, 12), which answer below could be the initial and terminal points for vector v?
A. initial (52, 12); terminal (0, 0)
B. initial (14, -5); terminal (66, 7)
C. initial (52, 0); terminal (0, 12)
D. initial (-12, 16); terminal (64, -4)
If we start from the origin, then the vector would be v = (52, 12) as given. But suppose we shift its initial point. Doing so would preserve its direction. For example, if we move its initial point to (1, 1), we'd have to shift its terminus by the same amount (1 unit to the right, 1 unit up) so that its terminal point would be (52 + 1, 12 + 1) = (53, 13).
Option A is not correct. If we want the vector to start at (52, 12), we have to adjust the terminus by the same distance by adding (52, 12) to the terminus. This means the resulting vector would start at (52, 12) and end at (52 + 52, 12 + 12) = (104, 24).
One important thing to observe here is that the difference between the terminal and initial points always returns v. In the first example: (53, 13) - (1, 1) = (52, 12). In checking option A: (104, 24) - (52, 12) = (52, 12). So to eliminate any other answer choices, all you need to do is subtract.
Option B is correct by this "rule". (66, 7) - (14, -5) = (52, 12).
Options C and D are not. (0, 12) - (52, 0) = (-52, 12), and (64, -4) - (-12, 16) = (76, -20).
Final answer:
The initial and terminal points that correctly represent the vector v = (52, 12) in component form are option B: initial (14, -5); terminal (66, 7), as these points give the same components when subtracted (terminal - initial).
Explanation:
The student is asking about the initial and terminal points for a vector given in component form. The vector v is (52, 12), which means it has an x-component of 52 and a y-component of 12. This can be visually represented as a directed line segment with an initial point and a terminal point. The correct initial and terminal points for vector v would result in the same component form when subtracting the coordinates of the initial point from the coordinates of the terminal point (terminal - initial).
Option B has the initial point (14, -5) and terminal point (66, 7). By calculating the difference between the terminal and initial points: (66 - 14, 7 - (-5)) = (52, 12), we can see that these points correctly represent the vector v in component form. Therefore, the answer is B.
Use what you know about the sum of the angles in a triangle together with the properties of supplementary angles to calculate the missing angles in the figure below.
Answer:
a = 35°; b = 50°; c = 85°; d = 30°
Step-by-step explanation:
a = 35° because a + 80 + 65 = 180.
b = 50° because b+ 35 + 95 = 180.
c = 85° because c + 95 = 180.
d = 30° because d + 85 + 65 = 180.
a park is 4 times as long as it is wide. if the distance around the park is 12.5 kilometers , what is the area od the park
Step by step explanation: 12.5 x 4
Answer: 50.
Consider the functions shown below.
Determine which of the following statements is true.
A.
As the value of x decreases, both the values of f(x) and g(x) will eventually be negative.
B.
At x = -1, f(x) = g(x).
C.
For x ≤ 1, g(x) < f(x).
D.
As the value of x increases, the value of g(x) will eventually exceed the value of f(x).
Answer: D
Step-by-step explanation:
A. False
f(x): x → -∞, y → -∞
g(x): x → -∞, y → 1
B. False
at x = -1, f(x) = -7
at x = -1, g(x) = 1.5
C. False
refer to A
g(x) → 1 and f(x) → -∞ so g(x) > f(x)
D. TRUE
It is hard to tell from the graph so plug in a value to check.
f(10) = 5(10) - 2
= 50 - 2
= 48
g(10) = 2¹⁰ + 1
= 1024 + 1
= 1025
g(10) > f(10)
WILL GIVE BRAINLIEST
graph f(x) = -1/2x - 5
please give me the points to put on the graph
thanks :)
Answer:
(-10, 0) and (0,-5)
Step-by-step explanation:
For the function [tex]f(x)=-\dfrac{1}{2}x-5,[/tex] find x-intercept and y-intercept:
1. when y=0, then
[tex]0=-\dfrac{1}{2}x-5,\\ \\\dfrac{1}{2}x=-5,\\ \\x=-10;[/tex]
2. when x=0, then
[tex]y=-\dfrac{1}{2}\cdot 0-5,\\ \\y=-5.[/tex]
You get two points (-10, 0) and (0,-5). Plot them on the coordinate plane and connect, obtained line is the graph of the linear function [tex]f(x)=-\dfrac{1}{2}x-5.[/tex]
Another one
Find the value
Answer:
x=8
Step-by-step explanation:
15+x = 23
Subtract 15 from each side
15-15 +x = 23-15
x = 8
Six donuts cost a total of $3.54 what is the cost for one donut? Six donuts cost a total of $3.54 what is the cost of one donut?
Answer:
Step-by-step explanation: the cost of one donut is $0.59 because when you divide 3.54 by 6, you get 0.59.
The cost for one donut will be the sixth part of $3.54 thus it will be $0.59 or 59 cents.
What is the arithmetic operator?Arithmetic operators are four basic mathematical operations in which summation, subtraction, division, and multiplication involve.,
Division = divide any two numbers or variables called division.
For example 4/8
As per the given,
Six donuts cost a total of $3.54
Cost of one donut = $3.54/6 = $0.59 = 59 cents
Hence "The cost for one donut will be the sixth part of $3.54 thus it will be $0.59 or 59 cents".
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The volume of a rectangular prism is 2x^3+9x^2-8x-36 with height x + 2. Using synthetic division, what is the area of the base?
Answer:
Area of the base = [tex]2x^2+5x-18[/tex]
Step-by-step explanation:
We know that volume of rectangular prism = (Area of base) x (Height)
or [Area of base] = [Volume]/[Height]
So basically we need to divide given area by given height to find the answer.
given height is (x+2) that means (x+2) must be factor of volume equation
or x=-2 must be root of volume equation so write down coefficients of volume equation then we divide by -2 as shown in attached picture.
Last digit on the right is always remainder.
Remaining coefficients {2, 5, -18} will give the area equation: [tex]2x^2+5x-18[/tex]
Hence final answer is:
Area of the base = [tex]2x^2+5x-18[/tex]
What is the volume of a cuboid when it is 4m by 4cm by 7cm
Answer: The volume of the cuboid is: " 11 ,200 cm³ " .
_________________________________________________
Step-by-step explanation:
____________________________________________________
The formula for the volume of a "cuboid" ;
which is given in: "cubic units" ; or, "units³ " ; is:
____________________________________________________
→ Volume, "V" = length (L) * width (w) * (height) ;
____________________________________________________
→ The 3 (three given values are "4m" , "4 cm" and "7cm" .
We need the units of measurement to be equal; so we need to convert the " 4m " to "cm" :
Note that: " 1 m = 100 cm " ; {exact conversion} ;
So: 4m ( 100 cm / 1 m) = (4 * 100) cm = 400 cm.
_____________________________________________________
Now, we can plug these values and solve for the volume; in units of "cm³ " ;
_____________________________________________________
V = 400 cm * 4 cm * 7 cm ;
= 400 * 4 * 7 * cm * cm * cm ;
= 400 * 4 * 7 cm³ ;
= 1600 * 7 cm³ ;
= 11, 200 cm³
_____________________________________________________
The answer is: " 11 ,200 cm³ " .
_____________________________________________________
Given: Elmwood St. and Oak Dr. are the same distance. All intersections are perpendicular.
Prove: Peach Tree Dr. is the same distance as Sycamore Ln.
Answer:
The above result is proved with the help of Pythagoras theorem and explained below.
Step-by-step explanation:
Given figure ABCD in which AD=BC and all angles intersect at right angle. Hence, the triangle formed inside ADC and ABC are right angled triangle.
In triangle ADC,
By applying Pythagoras theorem, we get
[tex]AC^{2}=AD^{2}+DC^{2}[/tex] → (1)
In triangle ABC,
[tex]AC^{2}=AB^{2}+BC^{2}[/tex] → (2)
Now, from eq (1) and (2)
Peach Tree Dr. is the same distance as Sycamore Ln.
[tex]AD^{2}+DC^{2} = AB^{2}+BC^{2}[/tex]
⇒ [tex]DC^{2} = AB^{2}[/tex] (∵ AD=BC)
⇒ DC=AB (∵Distance can never negative)
Therefore, Peach Tree Dr. is the same distance as Sycamore Ln.
64% of the animals at an animal shelter are dogs. About what fraction of the animals at the shelter are dogs?
About 16/25 fraction of the animal shelter are dogs.
Hope helps!-Aparri
Answer:
[tex]\frac{16}{25}[/tex]
Step-by-step explanation:
64% of the animals at an animal shelter are dogs.
This can also be expressed as: [tex]\frac{64}{100}[/tex] of the animals are dogs
Simplifying gives a fraction: [tex]\frac{16}{25}[/tex] of the animals are dogs.
Explain why |-3| + |9| represents the distance between the points (-3,-5) and (9,-5)
Answer:Sample Response: The points are on a horizontal line, parallel to the x-axis. The absolute value of −3 represents the distance from (−3, −5) to the y-axis, and the absolute value of 9 represents the distance from the y-axis to (9, −5).
Step-by-step explanation:
|-3| + |9| represents the distance between the points (-3,-5) and (9,-5) because the two points form a horizontal line
Distance of a lineThe line passes through the points (-3,-5) and (9,-5)
That is, [tex]x_1=-3, y_1=-5, x_2=9, y_2=-5[/tex]
Since [tex]y_1=y_2=-5[/tex], the line is a horizontal line
Horizontal line distanceFor a horizontal line passing though the points [tex](x_1, y_1)[/tex] and [tex](x_2, y_1)[/tex], the distance(D) between the two points is given as:
[tex]D=|x_1|+|x_2|\\\\ D=|-3|+|9|[/tex]
Therefore, |-3| + |9| represents the distance between the points (-3,-5) and (9,-5) because the two points form a horizontal line
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Which letter represents where the number 29 lies?
chapman’s brickyard sells brick and blocks. a brick costs .38 dollars and a block cost 1.56 dollars. the brickyard filled with a 24.80 dollars order, which contained 28 items
Answer:
The number of bricks is 16 and the number of blocks is 12
Step-by-step explanation:
Let the number of bricks be x and blocks be y.
Cost of each brick = $0.38
Total cost of x bricks = 0.38*x
Cost of each block = $1.56
Total cost of y blocks = 1.56*y
Total amount spent for the brickyard = $24.80
So,
Total cost of x bricks + Total cost of y blocks = Total amount spent for the brickyard
=> 0.38x + 1.56y = 24.80 ____equation (1)
Total number of items (bricks+blocks) = 28
So,
Number of bricks + Number of blocks = Total number of items
=> x + y= 28 ____equation (2)
We will solve the two equations by the method of elimination.
Let's multiply equation 2 by -0.38
(-0.38)*x + (- 0.38)*y = (-0.38)*(28)
=> -0.38x - 0.38y = -10.64 ____equation (3)
Adding equation 1 to the equation 3, we get
-0.38x - 0.38y + 0.38x + 1.56y = -10.64 + 24.80
Cancelling out -0.38x and +0.38x on the left side, we get
1.56y - 0.38y = 24.80-10.64
=> 1.18y = 14.16
Dividing both sides by 1.18, we get
[tex]\frac{1.18y}{1.18}[/tex] =[tex]\frac{14.16}{1.18}[/tex]
=> y = 12
Plugging in y=12 in the equation 2, we get
x + y= 28
=> x + 12 =28
Subtracting 12 from both sides, we get
x+ 12 -12 = 28- 12
Cancelling out the +12 and -12 from the left side, we have
x = 16
So, the number of bricks is 16 and the number of blocks is 12.
The ratio rock music to total CDs that Ella Owens is 15/40. Paolo has 50 rock music CDs the ratio of rock music to total CDs in his collection is equivalent to the ratio of rock music to total CDs in ours collection how many CDs do they own ? Explain ?
Answer: There are 184 total number of CDs they own.
Step-by-step explanation:
Since we have given that
Ratio of rock music to total CDs that Ella Owens is
[tex]15:40\\\\=3:8[/tex]
Now, Number of rock music CDs Paolo has = 50
According to question, the ratio of rock music to total CDs in his collection is equivalent to the ratio of rock music to total music to total CDs in ours collection,
[tex]15:40=3:8[/tex]
Let the total number of CDs be x
So, our equation becomes,
[tex]\frac{3}{11}\times x=50\\\\x=\frac{50\times 11}{3}\\\\x=\frac{550}{3}\\\\x=183.34[/tex]
Hence, there are 184 total number of CDs they own.
If 2 cm represents 9 cm on a scale drawing, how many meters do 15 cm represent
Answer: 22 cm
Step-by-step explanation:
can sombody explain how to solve this and give me the answer please
Answer: 12 texts per dollar.
The slope of the line is 1/5
Step-by-step explanation: If Ruby can send 48 text messages for $4, we divide 48 by 4 to get amount of texts per dollar: 12. Ruby can send 12 text messages for $1.
To figure out the slope of a line, use the formula y2 - y1 / x2 - x1.
-4 - (-9) / 22 - (-3) = 5 / 25 (rise over run)
Simplify to 1/5
two trains,Old Steamy and Chug-a-Lug,are 290 miles apart from each other and headed for the same station. They started toward the station at 8:00 a.m. If they are both set to arrive at 10:30 a.m. and Old Steamy is going 6.14 mph, how fast must Chug-a-Lug be going? How far does Chug-a-Lug have to travel?
8 am to 10:30 am is 2.50 hours.
Old Steamy is going 6.14 mph for 2.5 hours so travels : 6.14 * 2.5 = 15.35 miles.
This means Chug a lug has to travel 290 - 15.35 = 274.65 miles in 2.5 hours.
The speed would be 274.65 / 2.5 = 109.86 miles per hour.
Answer:
The speed of Old Steamy train = 6.14 mph
Train started at 8 a.m. and arrived at 10.30 a.m, this becomes 2.5 hours.
So, distance traveled by Old Steamy train = [tex]Speed\times time[/tex]
=> [tex]6.14\times2.5=15.35[/tex] miles
Now we get that Chug-a-Lug was 290 miles behind the Old steamy.
To know the distance traveled by Chug-a-Lug, we will add distance traveled by Old Steamy to the station plus the distance between the trains.
So, distance traveled by Chug-a-Lug = [tex]15.35+290=305.35[/tex] miles
The speed of Chug-a-Lug =[tex]\frac{Distance}{Time}[/tex]
= [tex]\frac{305.35}{2.5}=122.14[/tex] mph