Answer:
In 1942 , the U.S. Mint produced 154,500,000 nickels. The scientific notation of 154,500,000 is obtained as [tex]$1.545 \times 10^{8}$[/tex].
Step-by-step explanation:
In the problem, it is given that in 1942, the U.S. Mint produced 154,500,000 nickels.It is required to write 154,500,000 in scientific notation.To solve this first, move the decimal point so that the first factor is greater than or equal to 1 also it should be less than 10.Count the number of decimal places n, and write the number as a product with a power of 10. Then check the answer.Step 1 of 2
Obtain the scientific notation.
Here the original number, 154,500,000 is greater than 1 so we will have a positive power of 10 .
Move the decimal point to get 1.545, a number between 1 and 10 . Then we get,
1.54500000
The count of the number of decimal places the point was moved is 8 .
Write as a product with a positive power of 10 .
[tex]$1.545 \times 10^{8}$[/tex]
Step 2 of 2
Check the answer.
Rewrite and simplify to check our answer.
[tex]$$\begin{gathered}1.545 \times 10^{8}=1.545 \times 100000000 \\=154500000\end{gathered}$$[/tex]
CAN SOMEONE HELP PLEASE
m4A=42°, b=10, c= 12. What is the length of a to the nearest tenth?
Answer:
a = 8.1
Step-by-step explanation:
Use the cosine rule:
[tex]a = \sqrt{b^2 + c^2 -2 bc \space\ cosA }[/tex]
Substituting the values:
[tex]a = \sqrt{10^2 + 12^2 -2(10)(12) \space\ cos 42 \textdegree\ }[/tex]
⇒ [tex]a = \sqrt{4 \space\ cos 42\textdegree\ }[/tex]
⇒ [tex]a = 8.1[/tex]
Which of the following is correct equation for the trend line in the scatter plot? A. Y= 2/5 x -2 B. Y= 5x-1 C. Y= 5x +5 D. Y= -x+5
Answer: C. Y = 5x + 5
Step-by-step explanation:
We need to write, or decide on, the equation for the blue line as this line represents the trend line for this scatter plot. We will write this in slope-intercept form. See attached for a visual.
First, we will find our slope. We will use [tex]\frac{rise}{run}[/tex] for this since we have a graph with clear points. See attached, we count up [5] and then count to the right [1] for a slope of 5.
-> Slope = 5
Now, we will find our y-intercept. This is where the line intersects the y-axis. The line hits the y-axis at point (0, 5) giving us a y-intercept of 5.
-> Y-intercept = 5
Lastly, we will write our equation and decide on an answer.
y = mx + b
y = (5)x + (5)
Y = 5x + 5
C. Y = 5x + 5
Provide the next step to derive the quadratic formula.
Step 1 : ax2+box+c=0
Step 2 : ax2+box=-c
Step 3 : x2 + b/ax=-c/a
Step 4 : ??
The next step to derive the quadratic formula is x² + (b/a)x + (b²/2a²)= -c/a + (b²/2a²)
What is an equation?An equation is an expression that shows the relationship between two or more variables and numbers.
Step 1:
ax² + bx + c = 0
Step 2:
ax² + bx = -c
Step 3:
x² + (b/a)x = -c/a
Step 4:
x² + (b/a)x + (b²/2a²)= -c/a + (b²/2a²)
The next step to derive the quadratic formula is x² + (b/a)x + (b²/2a²)= -c/a + (b²/2a²)
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Find the length of CD shown in red below. Show all work.
By definition of circumference, the length of the arc EF (radius: 6 in, central angle: 308°) shown in red is approximately equal to 32.254 inches.
How to calculate the length of an arc
The figure presents a circle, the arc of a circle (s), in inches, is equal to the product of the central angle (θ), in radians, and the radius (r), in inches. Please notice that a complete circle has a central angle of 360°.
If we know that θ = 52π/180 and r = 6 inches, then the length of the arc CD is:
s = [(360π/180) - (52π/180)] · (6 in)
s ≈ 32.254 in
By definition of circumference, the length of the arc EF (radius: 6 in, central angle: 308°) shown in red is approximately equal to 32.254 inches.
RemarkThe statement has typing mistakes, correct form is shown below:
Find the length of the arc EF shown in red below. Show all the work.
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For f(x)=4x+1 and g(x) = x^2 - 5, find (f+g)(x).
Answer:
(f + g)(x) = x² + 4x - 4
Step-by-step explanation:
The statement (f + g)(x) is the same as f(x) + g(x). In other words, the question simply wants you to add the two functions together.
f(x) = 4x + 1
g(x) = x² - 5
(f + g)(x) <----- Original statement
f(x) + g(x) <----- Rewrite
(4x + 1) + (x² - 5) <----- Substitute the equations in f(x) and g(x)
4x + x² - 4 <----- Add 1 and -5
x² + 4x - 4 <----- Rearrange the terms
find the exact value
By using properties for trigonometric functions and trigonometric expressions, we find that the exact value of the sine of the angle 5π/12 radians is [tex]\frac{\sqrt{2+\sqrt{3}}}{2}[/tex].
How to find the exact value of a trigonometric expression
Trigonometric functions are trascendent functions, these are, that cannot be described algebraically. Herein we must utilize trigonometric formulae to calculate the exact value of a trigonometric function:
[tex]\sin \frac{5\pi}{12} = \sqrt{\frac{1 - \cos \frac{5\pi}{6} }{2} }[/tex]
[tex]\sin \frac{5\pi}{12} = \sqrt{\frac{1 + \cos \frac{\pi}{6} }{2} }[/tex]
[tex]\sin \frac{5\pi}{12} = \sqrt{\frac{1 + \frac{\sqrt{3}}{2} }{2} }[/tex]
[tex]\sin \frac{5\pi}{12} = \sqrt{\frac{2+\sqrt{3}}{4} }[/tex]
[tex]\sin \frac{5\pi}{12} = \frac{\sqrt{2+\sqrt{3}}}{2}[/tex]
By using properties for trigonometric functions and trigonometric expressions, we find that the exact value of the sine of the angle 5π/12 radians is [tex]\frac{\sqrt{2+\sqrt{3}}}{2}[/tex].
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The line graph on the y-axis is parallel to the x-axis, 3rd quadrant point, and an open downward parabola.
can anyone help?
Answer:
[tex](x + 5) {}^{2} = - 12(y - 1)[/tex]
Find the length of JH help pls
Answer:
19 units
Step-by-step explanation:
JM is 40 units, and it is composed of JH and HM. HM is 21 units, and so JH must be the remaining units.
40 - 21 = 19
Brainliest, please :)
Fill in the digit on the right side of each equation so that each equation has an integer solution.
A) 35x−11=107....
B)9m+34=68....
C)7965−4m=19....
20 pts
The digit on the right side of each equation so that each equation has an integer solution are 2.74, 3.78 and 1986.5 respectively.
Equation35x - 11 = 107
35x = 107 - 11
35x = 96
x = 96/35
x = 2.74
9m + 34 = 68
9m = 68 - 34
9m = 34
m = 34/9
m = 3.78
7965 - 4m = 19
-4m = 19 - 7965
-4m = -7946
m = -7946/-4
m = 1986.5
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CAN YALL PLEASE WORK IT OUTTT
$18.79 + $2.11 + ‐$1.92 + $17.28
Answer:
40.1
Step-by-step explanation:
Because the order of operations (Bodmas or Pedmas) tells you to add from left to right. So you would do 18.79 + 2.11 = 20.9, then you would do 20.90 + 1.92 (Add 0 at the end of 20.9) = 22.81. Then you will add 22.81 + 17.28 = 40.1. So your answer is 40.1. Hope this helps!
Triangles A B C and X Y Z are shown. Sides A C and Z X are congruent. Angles B A C and Z X Y are 35 degrees. Angle X Z Y is 47 degrees. Angle A B C is 98 degrees.
Determine the rigid transformations that will map ΔABC to ΔXYZ.
Translate vertex B to vertex Z; reflect ΔABC across side AB.
Translate vertex X to vertex C; rotate ΔXYZ to align the sides and angles.
Reflect ΔABC across side AB; translate vertex C to vertex X.
Translate vertex X to vertex A; rotate ΔXYZ to align the sides and angles.
Translate vertex X to vertex A; rotate ΔXYZ to align the sides and angles.
We know that the sum of angles of a triangle is always. In ΔXYZ,
What is the sum angle of the triangle?
[tex]\angle A + \angle B + \angle C=180^0[/tex]
[tex]35^0+\angle Y+47^0=180^0[/tex]
[tex]\angle y=98^0[/tex]
In both triangles, it is noticed that the sides AC and XZ are equal. In given triangles [tex]\angle A=\angle X=35^0[/tex]and.[tex]\angle B = \angle Y =98^0[/tex]
By the AAS rule of congruence, ΔABC and ΔXYZ are congruent triangles, therefore we can transform ΔABC to ΔXYZ. For the transformation of ΔABC to ΔXYZ translate the vertex having the same angle and rotate the triangle to align the sides and angles.
Since vertex X and vertex A have the same angle, therefore we translate vertex X to vertex A and rotate ΔXYZ to align the sides and angles.
Hence the correct option is d.
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Answer:
D: Translate vertex X to vertex A; rotate ΔXYZ to align the sides and angles.
Step-by-step explanation:
edge 2022
The function f(x) = 5* is reflected over the y-axis. Which equations represent the reflected function? Select two
options.
f(x) = -(5)-*
0x==3(2)
Of(x) = 5(2)
f(x) = 5(5)
f(x) = 5(5)-*
Step-by-step explanation:
To reflect a function about the vertical axis, just negate the variable.
For example, if we want to reflect this function
[tex] y = log(x) [/tex]
about the y axis or vertical axis, we just make the x negative
[tex]y = log( - x) [/tex]
Another example,
[tex]y = |x| [/tex]
To reflect about y axis or vertical axis,
[tex]y = | - x| [/tex]
So here l,the answer with negative variables are function that are reflected about the y axis.
The options are the first and the fifth option.
How do I even do this...
Answer:
x = 2 ± [tex]\sqrt{15}[/tex]
Step-by-step explanation:
x² - 4x - 11 = 0 ( add 11 to both sides )
x² - 4x = 11
to complete the square
add ( half the coefficient of the x- term )² to both sides
x² + 2(- 2)x + 4 = 11 + 4
(x - 2)² = 15 ( take square root of both sides )
x - 2 = ± [tex]\sqrt{15}[/tex] ( add 2 to both sides )
x = 2 ± [tex]\sqrt{15}[/tex]
Help quick! pleaseeeeeee
A) The function ƒ(x) has a steeper slope than g(x).
B) The functions ƒ(x) and g(x) have the same slope.
C) The function g(x) has a steeper slope than ƒ(x).
D) There isn't enough information to determine which function has a steeper slope.
The slope of the function g(x) is greater than f(x) and so g(x) is steeper than f(x). The correct option is C.
What is a Straight Line Equation?A straight line equation is represented by y = mx+c, where m is the slope and c is the y-intercept.
m is given by (y₂-y₁)/(x₂-x₁)
From the graph , the y-intercept is 4 and the two points on the line are ( 0,4) and ( 1,1).
m = -3
c =4
The equation of the function g(x) is g(x) = -3x+4
The slope of the function g(x) is greater than f(x) and so g(x) is steeper than f(x).
Therefore, the correct option is C.
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Need help with Matrices!!
1. Complete the table to identify habits that you have that both increase and
decrease your risk of being a victim of fraud or identity theft. Write at least three
habits in each column. (6 points)
Some habits that you can engage in that would increase your risk of being victim of fraud or identity theft are:
Using the same simple password for several online accounts. Not checking your banking and credit card statements regularly. Posting too much of your life on social media.You can be less at risk of fraud or identity theft if you:
Use multiple passwords for separate accounts. Keep an eye on your credit card and bank statement reports. Update your security and app software often.How can you avoid being a victim of fraud or identity theft?When you use the same password for various accounts, all those accounts are at risk if the password is stolen. So using multiple passwords is best.
You should also regularly monitor your credit card statements and bank reports to check for unfamiliar expenses which can be flagged immediately.
Also update your apps regularly as they come with security patches to protect your data. Avoid sharing too much information on social media as these can be used to predict your passwords.
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How to work out this linear stimultaneous equations
Step-by-step explanation:
extract the third equation from one of the given equation by making at most one variable with 1 as the coefficient the subject of the equation.[tex] x = 2 - y...........(3)[/tex]now substitute the third equation to the other equation *Not the one you extracted the new equation from*[tex]y = 2 ({2 - y})^{2} + (2 -y ) - 2[/tex]After substituting simplify[tex]y = 2(2 - y)(2 - y) + 2 - y - 2 \\ y = 2(4 - 2y - 2y + {y}^{2} ) + 2 - y - 2 \\ y = 2(4 - 4y + {y}^{2} ) - y \\ y = 8 - 8y + 2 {y }^{2} - y[/tex]Therfore group the terms in the form of a general Quadratic equation.When using BINOM.DIST to calculate a probability mass function, which argument should be set to FALSE?
The question is incomplete. Please read below to find the missing content.
D) cumulative is an argument that should be set to FALSE.
If we use cumulative =fake then we are able to get a precise probability
If we use cumulative= genuine, we will get less than or equal to possibility.
A sequence of actions wherein the effects are always unsure. I was tossing a coin, deciding on a card from a deck of playing cards, and throwing a cube. occasion. It is a single final result of a test. Getting a Head at the same time as tossing a coin is an occasion.
When using BINOM.DIST to calculate a probability mass function, which argument should be set to FALSE? Select an answer
A) number_s
B) probability_s
C) trials
D) cumulative
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=Which composition of transformations will create a pair of similar, not congruent triangles?
a rotation, then a reflection
a translation, then a rotation
a reflection, then a translation
a rotation, then a dilation
Option d) is correct, i.e. a rotation, then a dilation. Transformation will create a pair of similar but not congruent triangles.
Which composition of transformations will create a pair of similar, not congruent triangles?
In congruent geometry, the shapes that are so identical. can be superimposed to themselves.
When triangle is rotated, than position of angles will change. Aftermath the dilation of the triangle would increase the proportion of the sides, but angles remains equal, by which the triangle remain similar but not congruent.
Thus, a rotation, then a dilation transformation will create a pair of siilar but not congruent triangles.
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Answer:
D. a rotation, then a dilation
Step-by-step explanation:
got it right on edge 23
Which graph shows the solution to the system of linear inequalities?
x – 4y < 4
y < x + 1
On a coordinate plane, 2 straight lines are shown. The first solid line has a positive slope and goes through (0, negative 1) and (4, 0). Everything above the line is shaded. The second dashed line has a positive slope and goes through (negative 1, 0) and (0, 1). Everything below the line is shaded.
On a coordinate plane, 2 straight lines are shown. The first dashed line has a positive slope and goes through (negative 1, 0) and (0, 1). Everything above of the line is shaded. The second solid line has a positive slope and goes through (0, negative 1) and (4, 0). Everything above the line is shaded.
On a coordinate plane, 2 straight lines are shown. The first solid line has a positive slope and goes through (0, negative 1) and (4, 0). Everything above the line is shaded. The second solid line has a positive slope and goes through (negative 1, 0) and (0, 1). Everything below the line is shaded.
On a coordinate plane, 2 straight lines are shown. The first solid line has a positive slope and goes through (0, negative 1) and (4, 0). Everything below the line is shaded. The second dashed line has a positive slope and goes through (negative 1, 0) and (0, 1). Everything below the line is shaded.
The expression square root of 25/49 can be given as 5/7
What is an equation?An equation is an expression that shows the relationship between two or more variables and numbers.
Inequality is the non equal comparison of two or more numbers and variables.
The solution to the system of inequalities x – 4y < 4 and y < x + 1 is shown in the graph.
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Answer:
its c
Step-by-step explanation:
cos(x)=2cos^2(x)-1 0≤x≤2π
Answer:
[tex]x=0,~x=\frac{2\pi }{3},\:x=\frac{4\pi }{3},~x=2\pi[/tex]
Step-by-step explanation:
The given equation:
[tex]\cos(x)=2\cos^2(x)-1[/tex]
Let [tex]\cos(x)[/tex] be [tex]y[/tex]:
[tex]y=2y^2-1[/tex]
Rewrite as:
[tex]2y^2-y-1=0[/tex]
After solving quadratic equation, the solutions are:
[tex]y=1~~~~y=-\frac{1}{2}[/tex]
Substitute back [tex]\cos(x)[/tex], it follows:
[tex]\cos(x)=1~~~~\cos(x)=-\frac12[/tex]
For the first equation, the solution is [tex]x=0[/tex] and [tex]x=2\pi[/tex].
For the second equation, general solution is:
[tex]x=\frac{2\pi }{3}+2\pi n,\:x=\frac{4\pi }{3}+2\pi n[/tex]
But for the given interval, we must substitute n=0 into the equations so that the values of x must be within interval. Therefore:
[tex]x=\frac{2\pi }{3},\:x=\frac{4\pi }{3}[/tex]
So, the answers are:
[tex]x=0,~x=\frac{2\pi }{3},\:x=\frac{4\pi }{3},~x=2\pi[/tex]
what is the gradient?
please help
The gradient of line A is -2. 67
How to determine the gradient
Gradient = slope = Δy/ Δx
We have,
y2 = 3
y1 = -5
x2 = -3
x1 = 0
Substitute the values
Gradient = [tex]\frac{3 - (-5)}{-3 -0}[/tex]
Gradient = [tex]\frac{3 + 5}{-3}[/tex]
Gradient = [tex]\frac{8}{-3}[/tex]
Gradient = -2. 67
Thus, the gradient of line A is -2. 67
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To prove part of the triangle midsegment theorem using the diagram, which statement must be shown?
The length of JK equals the length of JL.
The length of GH is half the length of KL.
The slope of JK equals the slope of JL.
The slope of GH is half the slope of KL.
The statement which the diagram shows is that the length of GH is half of the length of KL . Option B
What is the midsegment theorem?
The midsegment theorem holds that any segment that forms the joining midpoints of two sides of a triangle is parallel to half the length of the third side.
It can be seen that the length of GH is half of the length of KL as deduced from the diagram
Therefore, the statement which the diagram shows is that the length of GH is half of the length of KL . Option B
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please help its confusing me
Answer:
x=−9 and y=8
Step-by-step explanation:
Let's solve your system by elimination.
2x+3y=6;4x−y=−44
Multiply the first equation by -2,and multiply the second equation by 1.
−2(2x+3y=6)
1(4x−y=−44)
Becomes:
−4x−6y=−12
4x−y=−44
Add these equations to eliminate x:
−7y=−56
Then solve−7y=−56for y:
−7y=−56
-7y/-7 = = -56/-7
(Divide both sides by -7)
y=8
Now that we've found y let's plug it back in to solve for x.
Write down an original equation:
2x+3y=6
Substitute8 for y in 2x+3y=6:
2x+(3)(8)=6
2x+24=6(Simplify both sides of the equation)
2x+24+−24=6+−24(Add -24 to both sides)
2x=−18
2x/2 = -18/2 (Divide both sides by 2)
x=−9
Answer:
x=−9 and y=8
Answer:
x = -9
y = 8
Step-by-step explanation:
(using substitution)
4x-y = -44
4x + 44 = y
substitute (4x+44) as y in the other equation
2x + 3(4x+44) = 6
2x+12x+132 = 6
14x = -126
x = -9
then plug -9 as x into one of the equations to find y
4(-9) - y = -44
-36-y=-44
-y=-8
y=8
then check the answer by plugging in the values of x and y (-9 and 8) for x and y in one of the equations
4(-9) - (8) = -44
you get: -44 = -44, which is true, so the x and y values are correct
Write the equation of an ellipse with center (-2,-3), vertical major axis of length 14, and minor axis of
length 8.
Step-by-step explanation:
Since we have a vertical major axis, our ellipse is vertical.
The equation of a vertical ellipse is
[tex] \frac{(y - k) {}^{2} }{ {a}^{2} } + \frac{(x - h) {}^{2} }{ {b}^{2} } = 1[/tex]
where
(h,k) is the center
a is the semi major axis,
b is the semi minor axis
First, let plug in our center
[tex] \frac{(y + 3) {}^{2} }{ {a}^{2} } + \frac{(x + 2) {}^{2} }{ {b}^{2} } = 1[/tex]
Semi means half, so
a is half of 14 which is 7
B is half of 8, which is 4.
[tex] \frac{(y + 3) {}^{2} }{49} + \frac{(x + 2) {}^{2} }{16} = 1[/tex]
I’m confused on this
Answer:
x = 25
Step-by-step explanation:
The mistake here is the squaring. When you square one side, you have to do the same on the other side:
[tex]\sqrt{3x+6}[/tex] = 9
[tex](\sqrt{3x+6}) ^{2}[/tex] = [tex]9^{2}[/tex]
3x + 6 = 81
3x = 75
x = 25
[tex]\huge\boxed{x=25}[/tex]
The mistake is in Step 1. The solver should have also squared [tex]9[/tex] when squaring the other side of the equation.
Correctly solving[tex]\begin{aligned}\sqrt{3x+6}&=9\\(\sqrt{3x+6})^2&=9^2\\3x+6&=81\\3x+6-6&=81-6\\3x&=75\\\frac{3x}{3}&=\frac{75}{3}\\x&=25\end{aligned}[/tex]
HELP QUICKLY PLEASE!!!!!!!!
Answer: 20
Step-by-step explanation:
We will set up a proportion to solve.
[tex]\displaystyle \frac{?}{16}=\frac{15}{12}[/tex]
Now, we will cross-multiply.
12 * ? = 16 * 15
12? = 240
? = 20
Drag each ratio to the correct location on the image. Not all ratios will be used.
Match each ratio of the volumes of two solids to the pair of solids it represents.
3:1
2r: 3h
h: 4r
4r: h
4r: 3h
4:1
Answer:
cylinder to cone = 3:1
sphere to cylinder = 4r:3h
cone to sphere = h:4r
hemisphere to cylinder = 2r:3h
Step-by-step explanation:
if a cake was sold GH 200 cedis. However, there is a reduction sale of 10% on each cake if you buy 4. Amanda decides to buy 8 cakes, how much would she pay
Amanda needs to pay 1440 cedis for purchasing 8 cakes on discounted price.
What is Cost Price?
Cost price is the amount we pay to buy an item at which it is available.
Here,
Selling price of a cake = 200 cedis
Discount because of sale = 10% on each unit.
(Only if 4 cakes purchased at a time)
Amanda purchased 8 cakes
So, Amanda need to pay only 90 percent of the total amount.
Total cost price of 8 cakes for Amanda = (200 X 90%) X 8
= 180 X 8
= 1440
Thus, Amanda needs to pay 1440 cedis for purchasing 8 cakes on discounted price.
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How many heartbeats is 4800 in a day? Put your answer in scientific notation
Answer:
Step-by-step explanation:
4.8 x 10^3 heartbeats/day
Answer: A humans heart average per minute is 80 then you got one hour 60 x 80 equals 4800
which would be 4.8x 10 over 3 which is your answer
Step-by-step explanation: