a)
We need to convert 1.96 x 10^-5 meters. into standard notation.
Now, on the scientific notation, the power of ten shows how many places the decimal point has been moved.
- If the exponent is positive then the decimal point has been moved to the left.
- If the exponent is negative, then the decimal point has been moved to the right.
In this case, the power is negative 5 . So, the decimal point has been moved 5 places to the right.
Hence:
1.96 x 10^-5 = 0.0000196
b)
a. Meters
First, we need to convert kilometers into meters using the rule of three:
If 1k = 1000 meters
Then 12,100k = x
Where x = (12,100k*1000m)/ 1k
x =12000000 meters
We need to convert from standard notation to scientific notation:
12000000.0 = 1.2x10^7 meters
The decimal point has been moved 7 places to the left, so the power of then is positive 7.
b) We need to convert 12,100 kilometers into scientific notation:
12,100 = 12,100.0
Converting into scientific notation
1.21x10^4 kilometers
The decimal point has been moved 4 places to the left. Hence, the power of the is positive 4.
i need these answered , i am very confused The options for them are:constant rational square root exponential growth cube root linear absolute value cubic logarithmic quadratic
Based on the question and the options provided, we have that:
[tex]7)\text{ The name of the parent function for g(x) = 3}\sqrt[]{x}\text{ is a square root}[/tex][tex]8)\text{ The name of the parent function for f(x) =}2^{x^{}}+5\text{ is exponential growth}[/tex][tex]9)\text{ The name of the parent function for f(x)=}\frac{5}{4}\sqrt[3]{x}\text{ is cube root}[/tex][tex]10)\text{ The name of the parent function for h(x) =}8x\text{ is linear}[/tex][tex]11)\text{ An example of an absolute value equation is: y = }\lvert x+5\rvert-3[/tex]Which cosine function has maximum of 2, a minimum of –2, and a period of 2pi/3 ?
Given:
maximum = 2, minimum = -2
period = 2π/3
Find: the cosine function having those attributes stated above
Solution:
Cosine equations follow the pattern below:
[tex]y=Acos(B(x-C))+D[/tex]where A = amplitude, B = 2π/period, C = horizontal shift, and D = vertical shift.
Since the only given information is the period, let's calculate for the value of B.
[tex]B=\frac{2\pi}{period}\Rightarrow B=\frac{2\pi}{\frac{2\pi}{3}}=3[/tex]Out of the choices, only y = 2cos 3θ has the value of B which is 3. Hence, y = 2cos 3θ is the cosine function that has a maximum of 2, a minimum of –2, and a period of 2pi/3. (Option 3)
Use the quadratic formula to solve for X 5x^2 +2x=2
Given:
[tex]5x^2+2x=2[/tex]To solve for x using the quadratic formula, we simplify the given equation first:
[tex]\begin{gathered} 5x^2+2x=2 \\ 5x^2+2x-2=0 \end{gathered}[/tex]Next, we use the quadratic formula of the form ax^2+bx+c=0:
[tex]x_{1,2}=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}[/tex]where:
a=5
b=2
c=-2
We plug in what we know:
[tex]\begin{gathered} x_{1,2}=\frac{-2\pm\sqrt[]{2^2^{}-4(5)(-2)}}{2(5)} \\ \text{Simplify} \\ x_{1,2}=\frac{-2\pm\sqrt[]{44}}{10} \\ x_{1,2}=\frac{-2\pm2\sqrt[]{11}}{10} \end{gathered}[/tex]We separate the solutions:
[tex]x_1=\frac{-2+2\sqrt[]{11}}{10}=\frac{-1+\sqrt[]{11}}{5}=0.46[/tex][tex]x_2=\frac{-2-2\sqrt[]{11}}{10}=-\frac{1+\sqrt[]{11}}{5}=-0.86[/tex]Therefore,
[tex]x=0.46,-0.86[/tex]The volume of a rectangular prism is 2 x cubed + 9 x squared minus 8 x minus 36 with height x + 2. Using synthetic division, what is the area of the base?
2 x cubed + 13 x squared + 18 x
2 x cubed + 5 x squared minus 18 x
2 x squared + 13 x + 18
2 x squared + 5 x minus 18
Answer:
2 x squared + 5 x minus 18
Step-by-step explanation:
Hope this helps sorry if not right
Answer: D
Step-by-step explanation: EDGE
Convert 6 kg per inch to g per m 6 points
We can do this conversion in this way:
[tex]\frac{6\operatorname{kg}}{i}\cdot\frac{1000gr}{\operatorname{kg}}\cdot\frac{1i}{0.0254m}=23622.047g/m[/tex]Then, the answer is 23622.047g/m.
what is 2.939 radian measure to degree measure
The answer is 168.5 degrees
i do not understand what i am getting wrong for the 3rd question
ANSWER:
-4.1201
SOLUTION
[tex]\log _b\frac{1}{4}=\log _b1-\log _b4[/tex]this is also equivalent to
[tex]\log _b\frac{1\times7}{4\times7}=\log _b\frac{7}{28}=\log _b7-\log _b28=5.7833-9.9034=-4.1201[/tex]triangle OPQ is similar to triangle RST. Find the measure of side RS. Round your answer to the nearest tent if necessary
To answer this question, we have that, if two triangles are similar, they maintain the same proportion on their corresponding sides.
We have that the corresponding sides are QP and TS, OP and RS, and QO and TR, so we can write:
[tex]\frac{TS}{QP}=\frac{RS}{OP}=\frac{TR}{QO}[/tex]Then, since we have the values for QP, TS, and OP, we can find RS using the above proportion:
[tex]\frac{TS}{QP}=\frac{RS}{OP}\Rightarrow\frac{41.4}{11}=\frac{RS}{8}\Rightarrow RS=\frac{41.4\cdot8}{11}=\frac{331.2}{11}\Rightarrow RS=30.109090\ldots[/tex]Then, we have that we can round this value to 30.11 units, and if we round the answer to the nearest tenth, we finally have that RS = 30.1 units.
Answer:
x = 30.1 (round 30)
Step-by-step explanation:
being similar we can solve with a simple equation
11 : 8 = 41.4 : x
x = 8 × 41.4 : 11
x = 331,2 : 11
x = 30.1 (round 30)
circumference of the back wheel=9 feet, front wheel=7 feet. On a certain distance the front wheel gets 10 revolutions more than the back wheel. What is the distance?
The distance would be 315 feet which is a certain distance the front wheel gets 10 revolutions more than the back wheel.
What is the Circumference of a circle?The Circumference of a circle is defined as the product of the diameter of the circle and pi.
C = πd
where 'd' is the diameter of the circle
Given that the circumference of the back wheel=9 feet, the front wheel=7 feet. At a certain distance, the front wheel gets 10 revolutions more than the back wheel.
Both wheels must move at the same distance. If the number of revolutions taken by the back wheel is x, then the number of revolutions taken by the front wheel is x+10.
Because the distance traveled is the same as:
⇒ 9x = 7(x+10)
⇒ 9x = 7x+70
⇒ 9x - 7x = 70
⇒ 2x = 70
⇒ x = 35
We obtain x = 35 revolutions.
So the total distance traveled is 35×9=315 feet or 45×7=315 feet.
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I need help on this showing step by step work
Solution
Notice that we have two solid shapes and we want to find the surface area of the composite.
We have a triangular prism on a cuboid.
Note: Formula For Finding the Surface Area Of A Cuboid
[tex]Surface\text{ }Area=2(lw+lh+wh)[/tex]From the question, we have that
[tex]\begin{gathered} Length(l)=12cm \\ Width(w)=4cm \\ Height(h)=14cm \end{gathered}[/tex]The area will be
[tex]\begin{gathered} Surface\text{ A}rea=2(lw+lh+wh) \\ \\ Surface\text{ A}rea=2(12(4)+12(14)+4(14)) \\ \\ Surface\text{ A}rea=2(48+168+56) \\ \\ Surface\text{ A}rea=2(272) \\ \\ Surface\text{ A}rea=544cm^2 \end{gathered}[/tex]Now, we find the Area of the Triangular Prism
Note: Formula To Use
From the question, we have
[tex]\begin{gathered} b=4cm \\ h=2\sqrt{3}\text{ \lparen since the triangle is an equilateral triangle\rparen} \\ L=12cm \\ S_1=S_2=S_3=4cm \end{gathered}[/tex]Substituting we have
[tex]\begin{gathered} Surface\text{ }Area=bh+L(S_1+S_2+S_3) \\ \\ Surface\text{ }Area=4(2\sqrt{3})+12(4+4+4) \\ \\ Surface\text{ }Area=(8\sqrt{3}+144)cm^2 \end{gathered}[/tex]Therefore, the total surface area of the composite is
[tex]\begin{gathered} Surface\text{ }Area=544+8\sqrt{3}+144 \\ \\ Surface\text{ }Area=(688+8\sqrt{3})cm^2 \\ or\text{ if we want to write the answer in decimal point, we have} \\ Surface\text{ }Area=701.8564065cm^2 \end{gathered}[/tex]Martin finds an apartment to rent for $420 per month. He must pay a security deposit equal to one and a half months' rent. How much is the security deposit? Alexis earns $31,350 per year. According to the banker's rule, how much money can she afford to borrow for a house?
if one month is $420
and the security deposit is one and a half month= 1.5*$420
1.5*420=630
So the answer is: 630
OA.y> -22² +10z - 8OB. y<-2x² +102-8OC. y2-22² +10r - 8OD. y ≤-22² +10z - 8
Solution:
Using a graph plotter,
The correct answer that satisfies the graph is OPTION C.
Americans who are 65 years of age or older make up 13.2% of the total population. If there at 30.3 million american in this age group, find the total u.s. population
Given:
Americans who are 65 years of age or older make up 13.2% of the total population.
Required:
The total u.s. population
Explanation:
Let the total population of u.s be x.
According to the given condition.
[tex]13.2\text{ \% of x = 30.3 billion}[/tex]Therefore,
[tex]\begin{gathered} \frac{13.2}{100}\text{ }\times\text{ x = 30.3} \\ x\text{ = }\frac{30.3\text{ }\times\text{ 100}}{13.2} \\ x\text{ = 229.55 billion} \end{gathered}[/tex]Answer:
Thus the total population of u.s is 229.55 billion.
You are offered two different furniture sales jobs. The Furniture Barn offers you a job that pays straight commission of 6% of the sales. The Furniture Warehouse offers you a job that pays a salary of $350 per week plus 1% of the sales. How much would you have to sell in a week in order for the job at The Furniture Barn to pay as well as the job at The Furniture Warehouse? Round the answer to the nearest cent.
The Furniture Barn pays the same as The Furniture Warehouse if my sales are $
The amount to be sold in a week in order for the job at The Furniture Barn to pay as well as the job at The Furniture Warehouse is $7000.
How to calculate the value?Lat the amount of sales be represented as x.
Since the Furniture Barn offers you a job that pays straight commission of 6% of the sales. This will be:
= 6% × x = 0.06x
Also, the Furniture Warehouse offers you a job that pays a salary of $350 per week plus 1% of the sales. This will be:
= 350 + (1% × x)
= 350 + 0.01x
The equation will be expressed as:
0.06x = 350 + 0.01x
Collect like terms
0.06x - 0.01x = 350
0.05x = 350
Divide
x = 350 / 0.05
x = 7000
The sale is $7000.
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Find the area of the yellow region. Round to the nearest tenth. 7.53cm
The figure shows a square inscribed in a circle of radius r = 7.53 cm.
The yellow region corresponds to the area of the circle minus the area of the square.
The area of a circle of radius r is:
[tex]A_c=\pi r^2[/tex]Calculating:
[tex]A_c=\pi(7.53\text{ cm})^2=178.13\text{ }cm^2[/tex]The radius of the circle is half the diagonal of the square. The diagonal of the square is:
d = 2 x 7.53 cm = 15.06 cm
The area of a square, given the diagonal d, is calculated as follows:
[tex]A_s=\frac{d^2}{2}[/tex]Calculating:
[tex]\begin{gathered} A_s=\frac{(15.06\text{ cm})^2}{2} \\ \\ A_s=113.40\text{ }cm^2 \end{gathered}[/tex]The required area is:
A = 178.13 - 113.40 = 64.73 square cm
Suppose A and B are points on the number line. If AB=10 and B lies at -6, where could A be located?
Answer: 16 or 4
Step-by-step explanation:
-6-10=-16
10-6=4
Question : Suppose A and B are points on the number line. If AB=10 and B lies at -6, where could A be located?
Answer: 16
ABCD is a rectangle. Find the length of AC and the measures of a and f.
SOLUTION
Consider the diagram
We need to obtain the value of length AC
Using the pythagoras rule, we have
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help in this question pls
what is the substitution for f7=3(x)^2+2(x)-9
Given a function f(x), whenever you want to evaluate the function, you simply change the variable for the value you where you want to evaluate the function at, and then perform the mathematical operations the function tells you to do.
In our case f(x) = 3x^2 + 2x -9
If we evaluate f(x) at x=7, then
[tex]f(7)=3(7)^2+2(7)\text{ -9 = 3 }\cdot\text{ 49 + 2}\cdot\text{ 7 - 9 = 152}[/tex]So f(7) = 152.
Let w be defined as 2 more than the number of digits in the integer w. For example, 15* = 4 (2 digits in 15 + 2). If whas 7000 digits, then what is the value of (w)*?
The number of digits in 7000 is 4
The number of digits in w=7000
[tex](w)^{\cdot}=\text{ the number of digits in w+2}[/tex][tex](w)^{\cdot}=\text{7000+2}[/tex][tex](w)^{\cdot}=7002[/tex]Hence the required value is 7002.
passes through (1,3) and parallel to y=-x
The equation of a line parallel to y=-x and passes through (1,3) is x+y=4
What is the relationship between coordinates and the equation of a line?The coordinates of a line pass through the equation of a line.
What is the relationship between two parallel lines?Two parallel lines make the same angle with respect to the x-axis ie. make the same slope.
We have been given that the line is parallel to y=-x or x+y=0
Thus, they will be having the same slope which is -1.
Since, in the equation Ax+By+C=0, the slope is equal to -A/B
So putting the values in the equation y=mx+c where m is the slope and c is the constant
y=-x+c
Now we know that the equation passes through (1,3)
So, putting values 1=-3+c which gives c=4
Therefore, the equation of the line is y=-x+4 or x+y=4.
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what is the slope formula of (4,2) and (7, 6.5)
Suppose the given coordinates are represented as,
[tex]\begin{gathered} (x_1,y_1)=(4,2) \\ (x_2,y_2)=(7,6.5) \end{gathered}[/tex]Then, the formula for slope can be expressed as,
[tex]\begin{gathered} m=\frac{y_2-y_1}{x_2-x_1} \\ m=\frac{6.5-2}{7-4} \end{gathered}[/tex]Solving it,
[tex]m=\frac{4.5}{3}=1.5[/tex]The slope is 1.5.
The formula of (10, 8) anjd (-5,8) is
[tex]m=\frac{8-8}{-5-10}[/tex]an environmental scientists is conducting research on a particular type of air pollutant. She collects air samples over time and determines the average number of micrograms (ug) of the pollutant in a cubic meter (m^3). Her data are shown in the table below.Which Function models the scientists data?A. F(×)=1.12t +50B. F(×)=50 · 1.12tC. F(×)=50 - 6tD. F(×)=50 · 0.88^t
If we graph the points of the table in a coordinate system we'll see that they line up like a line function, so option D is not possible.
If we also add the graphs for the other 3 options, we get:
The points don't line up perfectly but they are much closer to the line in blue than the red or black lines.
Therefore answer is option C f(t) = 50 - 6t
Hey need your help it’s the one about the %
Answer:
[tex]\text{\$}$219.27$[/tex]Explanation:
We were given that:
Pamela bought an electric drill at 85% off the original price (she bought it at 15% of the original price)
She paid $32.89 for the drill
The regular price is calculated using simple proportion as shown below:
[tex]\begin{gathered} 15\text{\%}=\text{\$}32.89 \\ 100\text{\%}=\text{\$}x \\ \text{Cross multiply, we have:} \\ x\cdot15\text{\%}=\text{\$}32.89\cdot100\text{\%} \\ x=\frac{\text{\$}32.89\cdot100\text{\%}}{15\text{\%}} \\ x=\text{\$}219.27 \\ \\ \therefore x=\text{\$}219.27 \end{gathered}[/tex]Therefore, the regular price was $219.27
I just want to go to sleep but I need the answer to this question
The average rate of change of a function f(x) from x1 to x2 is given by:
[tex]\frac{f(x_2)-f(x_1)}{x_2-x_1}[/tex]In this case we need the first three seconds so x1=0 and x2=3.
Calculate the values of the function at x=0 and x=3 to get:
f(0)=150 and f(3)=0.
Substitute these values into the formula for average rate of change:
[tex]\begin{gathered} \frac{f(3)-f(0)}{3-0} \\ =\frac{0-150}{3} \\ =\frac{-150}{3} \\ =-50 \end{gathered}[/tex]Hence the avearage rate of change of the function for the first three seconds is -50.
Note that the negative sign shows that the function is decreasing in the time interval (first three seconds).
Calculate the determinant of this 2x2 matrix. Provide the numerical answer. |2 -1 | |4 -5|
Given the matrix
[tex]\begin{bmatrix}{a} & {b} & {} \\ {c} & {d} & {}{}\end{bmatrix}[/tex]its determinant is computed as follows:
ad - cb
In this case, the matrix is
[tex]\begin{bmatrix}{2} & {-1} & \\ {4} & -5 & {}\end{bmatrix}[/tex]and its determinant is
2(-5) - 4(-1) = -10 - (-4) = -10 + 4 = -6
Find d the side length of a square given the area of the square
Area of a square = side length ^2
Given: A= 20.25
Replacing:
20.25 = s^2
√20.25 = s
s = 4.5 m
Find the real part and the imaginary part of the following complex number. (sqrt(6) - sqrt(6i))/4
In this case, we'll have to carry out several steps to find the solution.
Step 01:
data:
(√6 - √6i) / 4
Step 02:
complex numbers:
[tex]\frac{\sqrt{6}-\sqrt{6}i}{4}=\frac{\sqrt{6}}{4}-\frac{\sqrt{6}i}{4}[/tex]real part:
√6 / 4
imaginary part:
- √6i / 4
That is the full solution.
{x|x ≤ - 6}
Write written interval motion and graph the interval
The inequality to interval notation. (−∞,−6) ( - ∞ , - 6 ).
What exactly is interval notation?
The number line's left to right location in the solution is indicated using interval notation (i.e., which part of the number line is shaded). Endpoints that are part of the solution are denoted by parentheses, while those that are not are denoted by brackets.For instance, the expressions -3x2, [-3,2], and xR|-3x2 denote that x is between -3 and 2 and might be either endpoint.Interval Notation x<-6. x<−6 x < - 6.
Convert the inequality to interval notation. (−∞,−6) ( - ∞ , - 6 ).
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In the similaritytransformation of AABCto ADFE, AABC was dilated bya scale factor of 1/2, reflected4 across the x-axis, and movedthrough the translation [? ].
We have to identify the translation.
We can see that the green triangle represents the transformation of triangle ABC after a dilation with a scale factor of 1/2 and a reflection across the x-axis.
We can then find the translation in each axis from the image as:
Triangle is DEF is translated 3 units to the left (and none in the vertical axis).
We can express this translation as this rule:
[tex](x+3,y+0)[/tex]Answer: (x+3, y+0)