Choose whether the number given in specific notation is representing a large or small number.
Answers
Given:
[tex]\begin{gathered} a)1.2\times10^3 \\ b)7.5\times10^^{-4} \end{gathered}[/tex]To find:
The number given in a specific notation is representing a large or small number.
Explanation:
a) It can be written as,
[tex]\begin{gathered} 1.2\times10^3=1.2\times1000 \\ =1200 \end{gathered}[/tex]So, it is a large number.
b) It can be written as,
[tex]\begin{gathered} 7.5\times10^{-4}=7.5\times\frac{1}{10^4} \\ =\frac{7.5}{10000} \\ =0.00075 \end{gathered}[/tex]So, it is a small number.
Final answer:
a) Large
b) Small
Related Questions
Four different stores have the same digital camera on sale. The original price and discounts offered by each store are listed below. Rank the stores from the cheapest to most expensive sale price of the camera.
Store A: price $99.99 and discount of 15%
Store B: price $95.99 and discount of 12%
Store C: price $90.99 and discount of 10%
Store D: price $89.99 and successive discounts of 5% and 5%
Answers
D<C<B<A; This is the correct ranking of the given stores in the order of cheapest to most expensive sale price of the camera as the definition of ascending order says, "Ascending order means to arrange numbers in increasing order, that is, from smallest to largest."
What is ascending order?The arrangement of numbers or other things in increasing order from smallest to largest is known as ascending order. Ascending order is demonstrated by numbers on a number line, which are listed from left to right. Usual representations include using commas or the "less-than symbol (<)" between numbers. For instance, 1, 2, 3, 4, or 5; or 1<2 <3 <4 <5.
Here,
Store A:
Price=$99.99
Discount=15%
Discount in dollar=$14.9985
Discounted price=$84.9915
Store B:
Price=$95.99
Discount=12%
Discount in dollar=$11.5188
Discounted price=$84.4712
Store C:
Price=$90.99
Discount=10%
Discount in dollar=$9.099
Discounted price=$81.891
Store D:
Price=$89.99
Discount=5% and after that 5%
net price after discount=$81.215
The price of store D is minimum that is $81.215.
According to the definition of ascending order, "Ascending order means to arrange numbers in increasing order, that is, from smallest to largest," this ranking of the given stores in order of cheapest to most expensive sale price of the camera is correct; D<C<B<A.
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which choice is equivalent to the fraction below? hint: rationalize the denominator and simplify. 6 over the square root of 2.
Answers
Answer
(6/√2) = 3√2
Explanation
We are asked to simplify
6/√2
So, we will rationalize this by multiplying numerator and denominator by √2
[tex]\frac{6}{\sqrt[]{2}}\times\frac{\sqrt[]{2}}{\sqrt[]{2}}=\frac{6\sqrt[]{2}}{\sqrt[]{2}\times\sqrt[]{2}}=\frac{6\sqrt[]{2}}{2}=3\sqrt[]{2}[/tex]Hope this Helps!!!
Hello, I'm stuck on this.Question: Calculate the slant height of this come, identified by letter X. Give your answer to the nearest whole number.
Answers
The right triangle formed is shown below
To find the slant height, x, we would apply the pythagorean theorem which is expressed as
hypotenuse^2 = one leg^2 + other leg^2
Looking at the triangle,
hypotenuse = x
one leg = 12
other leg = 7
By applying the pythagorean theorem,
x^2 = 12^2 + 7^2 = 144 + 49 = 193
x = square root of 193
x = 13.89
Rounding to the nearest whole number,
x = 14
The list price for a case of medicine is $275.49 Your pharmacy will receive a 18% trade discount. What is the amount of the discount? b) What is the net cost of the case of medicine?
Answers
The amount of the discount is $49.59, and the net cost after the discount is applied is $225.90.
What is the amount of the discount?If we have a original price P and we apply a discount of X, where X is a percentage, the amount of the discount is given by the formula:
D = P*(X/100%)
In this case, the original price is $275.49 and the discount is of 18%, then the amount of the discount is:
D = $275.49*(18%/100%) = $275.49*0.18 = $49.59
b) To get the net cost we need to take the difference between the original price and the amount of the discount, we will get:
net cost = $275.49 - $49.59 = $225.90
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Deon had $25 then he spent $15 on lunch. What percentage of his money did deon spend on lunch
Answers
Initial amount = $25
Amount spent on lunch = $15
The percentage of money spent on lunch
[tex]\frac{Amount\text{ spent}}{Initial\text{ amount}}\text{ x 100\%}[/tex][tex]\frac{15}{25}\text{ x 100 \%}[/tex][tex]\begin{gathered} \frac{1500}{25}^{} \\ =\text{ 60\%} \end{gathered}[/tex]how would you write this as an expression.
The quotient of 29 and the product of a number and −5.
Answers
ANSWER
[tex]\frac{29}{-5x}[/tex]EXPLANATION
Let 'x' be a number. The product of a number and -5 is: -5x
Then the quotient of 29 and something is: 29/something
Now, that something is the product -5x so, the quotient of 29 and the product of a number and -5 is:
[tex]\frac{29}{-5x}[/tex]For a given geometric sequence, the common ratio, r, is equal to 5, and the 7th term, an, is equal to -43. Find the value of the 9thterm, a9. If applicable, write your answer as a fraction.a9=
Answers
Given:
it is given that common ration of a geometric sequence is r = 5 and 7th term is - 43.
Find:
we have to find the value of 9th term.
Explanation:
we know the formula for nth term of a geometric sequence is
[tex]a_n=ar^{n-1}[/tex]since, 7the term is - 43,
Therefore, we have
[tex]\begin{gathered} a_7=-43 \\ ar^{7-1}=-43 \\ ar^6=-43 \\ a(5)^6=-43 \\ a(15625)=-43 \\ a=-\frac{43}{15625} \end{gathered}[/tex]The 9the term of the geometric sequence is
[tex]\begin{gathered} a_9=-\frac{43}{15625}\times(5)^{9-1} \\ =-\frac{43}{15625}\times(5)^8 \\ =-\frac{43}{(5)^6}\times(5)^8 \\ =-43\times25 \\ a_9=-1075 \end{gathered}[/tex]Therefore, 9th term of given geometric sequence is -1075.
High school band perform a concert on four different days bandsaw tickets each day as a fun raiser below the table shows the number of tickets sold in the amount collection of from sales slove with tablesHELPPP PLEASSEEEEEE
Answers
From the table given, Let's consider the third day
On the third day, 62 tickets were sold and $ 341 was collected
Then we can obtain the cost of a single ticket, which will be =
[tex]\frac{341}{62}[/tex]= $ 5.5
So 1 ticket cost $5.5
Then we can fill in the table
PART A
PART B
The equation that can be used to find y, the amount of money collected can be obtained since we know the cost of a single ticket which is $ 5.5
[tex]\begin{gathered} y\text{ = 5.5x} \\ \text{where x is the number of tickets sold} \end{gathered}[/tex]PART C
A dependent variable represents a quantity whose value depends on how the independent variable is manipulated.
From the equation
y = 5.5 x
y = Amount of money collected
x = Number of tickets
Since y (Amount collected) depends on x (the number of tickets sold)
y is the dependent variable
x is the independent variable
Part D
The relationship is that:
The amount of money that will be collected is dependent on the number of tickets sold.
since each ticket costs $5.5, then the amount realized is $5.5 multiplied by the number of tickets
If anyone can answer this question I will be surprised
Answers
A reflection through x-axis is the property to get a point and transform it like this:
[tex]\begin{gathered} P\rightarrow P^{\prime} \\ (x,y)\rightarrow(x,-y) \end{gathered}[/tex]If we have point P = (3,4), its reflexion through x-axis will be:
[tex]\begin{gathered} P\rightarrow P^{\prime} \\ (x,y)\rightarrow(x,-y) \\ (3,4)\rightarrow(3,-4) \end{gathered}[/tex]So our final answer will be:
[tex](3,-4)[/tex]List each real zero of f according to the behavior of the graph at the x-axis near that zero. Zero(s) where the graph crosses the x-axis:Zero(s) where the graph touches, but does not cross the x-axis:
Answers
In the graph, there are 2 zeros, one for each type.
The zero where the graph crosses the x axis is 1. When x=1, the function intercepts the x axis and crosses it.
The zero where the graph touches but does not cross the x axis is -1. When x=-1, the function touches x axis but goes back to the quadrant.
Question 1.) d.) how to find instantaneous rate of change if x= 2pi
Answers
Explanation
We are given the following function:
[tex]f(x)=3\cos2x[/tex]We are required to determine the instantaneous rate of change at x = 2π.
This is achieved thus:
[tex]\begin{gathered} f(x)=3\cos2x \\ \frac{\triangle f(x)}{\triangle x}=3\cdot-2\sin2x \\ \frac{\operatorname{\triangle}f(x)}{\operatorname{\triangle}x}=-6\sin2x \\ \text{ At the point }x=2\pi \\ \frac{\operatorname{\triangle}f(x)}{\operatorname{\triangle}x}=0 \end{gathered}[/tex]Hence, the answer is:
[tex]\frac{\operatorname{\triangle}f(x)}{\operatorname{\triangle}x}=0[/tex]Use the data in the following table, which shows the results of a survey of 2000 gamers concerning their favorite home video game systems, organized by age group. If a survey participant is selected at random, determine the probability of the following. Round to the nearest hundredth.The participant prefers the Nintendo Wii U system.
Answers
0.30
Explanations:What is probability?Probability is the likelihood or chance that an event will occur. Mathematically:
[tex]Probability=\frac{n(E)}{n(S)}[/tex]where:
• n(E) is the ,expected outcome
,• n(S) is the ,total outcome
Since the results shows a total survey of 2000 gamers, hence the total outcome is 2000.
Determine the total participant that prefers Nintendo Wii U system
Total participant that refers Nintendo Wii U system = 64 + 103 + 246 + 193
Total participant that refers Nintendo Wii U system n(E) = 606
Determine the required probability
[tex]\begin{gathered} Pr(participant\text{ prefers the Nintendo})=\frac{606}{2000} \\ Pr(participant\text{ prefers the Nintendo})=0.303 \\ Pr(participant\text{ prefers the Nintendo})\approx0.30 \end{gathered}[/tex]Hence the probability the participant prefers the Nintendo Wii U system is 0.30
Area of Triangles What is the area of this triangle? bh A 0 24 in? 8 in O 30 in 48 in 96 in
Answers
Given the triangle:
We're going to find its area.
To do this, we just multiply the base of the triangle by its height and then divide this result by 2:
[tex]A=\frac{6in\cdot8in}{2}=24in^2[/tex]Therefore, the area equals 24 in2.
The equation y = 5x represents a proportional relationship. What is the constant of proportionality?A. xB. 1/5C. 0D. 5
Answers
ANSWER
D. 5
EXPLANATION
We have to find the constant of proportionality in the equation:
[tex]y=5x[/tex]The general form of a proportional relationship is:
[tex]y=kx[/tex]where k = constant of proportionality
Therefore, comparing the given equation with the general equation, the constant of proportionality is 5.
Can you please help me with number 34. Determine the number of ways that each can occur
Answers
You need to determine the number of possible combinations when you choose 4 appetizers out of 11 options in the dinner menu. Assuming that you are not going to repeat appetizers, to determine this number you have to apply combinations, using the formula:
[tex]C(n,r)=\frac{n!}{r!(n-r)!}[/tex]Where
n is the number of options available
r is the number of options you have to choose, with no repetition, and the order doesn't matter.
For this exercise:
n=11
r=4
The combination can be determined as follows:
[tex]\begin{gathered} C(11,4)=\frac{11!}{4!(11-4)!} \\ C(11,4)=\frac{11!}{4!\cdot7!} \\ C(11,4)=\frac{39916800}{24\cdot5040} \\ C(11,4)=330 \end{gathered}[/tex]There are 330 combinations possible to choose 4 out of 11 appetizers from the menu.
Robert moved 4 cards that are worth -10 points each. How did thier score change.
Answers
We have the following:
Since there are 4 cards and each one has a value of -10 points, we have
[tex]4\cdot-10=-40[/tex]Which means that the score changed by -40 points
Entrance Ticket on Translations Sarah graphed a triangle with vertices X (3,3) Y (4,1) Z (1,1). She asked her classmate Paul to translate the triangle (x-4) (y+2). Paul stated that the triangle will move down by 4 and right by 2 putting the triangle in the 4th quadrant. Graph the translation to see if Paul is correct? Explain your reasoning. Your explanation should include: • What is a translation? • Is Paul correct? Why or why not • Which direction should you move the triangle? • Which quadrant is the translation located?
Answers
The coordinates of the triangle XYZ are:
X(3,3)
Y(4,1)
Z(1,1)
The translation to perform is (x-4) and (y+2)
Translations are rigid transformations of a figure, this means that the triangle will move but won't change its shape or size.
A translation over the x axis results in a horizontal movement.
If you subtract a factor k x-coordinate, the movement will be to the left.
If you add the factor k x-coordinate, the movement will be to the rigth.
In this example the translation over the x-coordinate is (x-4) → 4 unit are being subtracted to the x-coordinate of each point, this results in a horizontal movement 4 units to the left
A translation over the y axis results in a vertical movement.
If you subtract a factor m from the y-coordinate, the movement will be downwards.
If you add the factor m from the y-coordinate, the movement will be upwards
In this example the translation over the y-coordinate is (y+2)→ 2 units were added to the y-coordinate, this results in a vertical movement 2 units up.
Paul moved the triangle 4 units down and 2 units right, he performed the wrong translation.
THe triangle was moved "left" and "up", the translation will be located in the second quadrant
apple trees need to be planted in an orchard this process takes two hours per tree
Answers
the fact that we can not plant the half of tree imples that there is no line between the points of the graph. So the answer is letter B
write the er exponent expression forty-one to the seventh power
Answers
Write the exponential expression, forty one to the seventh power;
[tex]41^7[/tex]Whats the other side?
Image attached
please show work
Answers
The perimeter of the rectangle is 129.2×10⁵ if the area and one side of the rectangle is given.
What is the area of the rectangle?It is defined as the area occupied by the rectangle in two-dimensional planner geometry.
The area of a rectangle can be calculated using the following formula:
Rectangle area = length x width
It is defined as the two-dimensional geometry in which the angle between the adjacent sides are 90 degree. It is a type of quadrilateral.
It is given that:
The area of the rectangle = 2.76×10¹² square cm
The length of the rectangle = 4.6×10⁵ cm
The other side measure = 2.76×10¹²/4.6×10⁵ = 0.6×10⁷ = 60×10⁵ cm
The perimeter of the rectangle = 2(4.6×10⁵ + 60×10⁵)
The perimeter of the rectangle = 129.2×10⁵
Thus, the perimeter of the rectangle is 129.2×10⁵ if the area and one side of the rectangle is given.
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What is the total paymentrequired to pay off a promissorynote issued for $700.00 at 12%ordinary interest and a 180-dayterm?A. $760.00B. $742.00C. $712.00D. $721.60
Answers
Given:
Promissory note issued for $700 at 12%.
[tex]P\text{ayment of 12\% for 700=}\frac{700\times\frac{6}{12}\times12}{100}[/tex][tex]\text{Payment for 12\% for 700= \$}42[/tex][tex]\text{Total payment required to pay off=}700+42[/tex][tex]\text{Total payment required to pay off= \$742}[/tex]Therefore, Option B is the correct answer.
AC=AB=16cm.BC=20cm. How do i find the height of the triangle?
Answers
Given that
[tex]\begin{gathered} AB=AC=16\operatorname{cm} \\ BC=20\operatorname{cm} \\ BD=\frac{BC}{2}=\frac{20\operatorname{cm}}{2}=10\operatorname{cm} \\ CD=\frac{BC}{2}=\frac{20\operatorname{cm}}{2}=10\operatorname{cm} \\ AD=h \end{gathered}[/tex]To calculate the height of the triangle, we will use the Pythagoras theorem
With the Pythagorean theorem, we will have
[tex]\begin{gathered} \text{hypotenus}^2=\text{opposite}^2+\text{adjacent}^2 \\ \text{where,} \\ \text{HYPOTENUS}=AC=16\operatorname{cm} \\ \text{opposite}=DC=10\operatorname{cm} \\ \text{adjacent}=AD=h \end{gathered}[/tex]By substituting the values, we will have
[tex]\begin{gathered} \text{hypotenus}^2=\text{opposite}^2+\text{adjacent}^2 \\ 16^2=10^2+h^2 \\ 256=100+h^2 \\ \text{substract 100 from both sides} \\ 256-100=100-100+h^2 \\ 156=h^2 \\ \text{square root both sides} \\ \sqrt[]{h^2}=\sqrt[]{156} \\ h=\sqrt[]{4}\times\sqrt[]{39} \\ h=2\sqrt[]{39} \\ or\text{ } \\ h=12.39\operatorname{cm}\approx to\text{ 1 d.p=} \\ h=12.5\operatorname{cm} \end{gathered}[/tex]Therefore,
The height of the triangle is = 12.5 cm
i need help with question 2
Answers
To find the vertex (h,k), we have to find h using the following formula
[tex]h=-\frac{b}{2a}[/tex]Where a = 1 and b = -10.
[tex]h=-\frac{-10}{2\cdot1}=5[/tex]Then, we find k by evaluating the function when x = 5.
[tex]y=5^2-10\cdot5+9=25-50+9=-16[/tex]Hence, the vertex is (5,-16).The axis of symmetry is given by the h coordinate of the vertex.
Hence, the axis of symmetry is x = 5.The y-intercept is found when x = 0.
[tex]y=0^2-10\cdot0+9=9[/tex]The y-intercept is (0,9).The x-intercepts are found when y = 0.
[tex]x^2-10x+9=0[/tex]To solve this expression, we have to look for two numbers which product is 9, and which addition is 10. Those numbers are 9 and 1.
[tex](x-9)(x-1)=0[/tex]Then, we use the zero product property to express both solutions
[tex]\begin{gathered} x-9=0\rightarrow x=9 \\ x-1=0\rightarrow x=1 \end{gathered}[/tex]Hence, the x-intercepts are (9,0) and (1,0).The minimum value is defined by the k coordinate of the vertex.
Therefore, the minimum value of the function is -16.The domain of the function would be all real numbers because quadratic functions don't have any domain restrictions.
[tex]D=(-\infty,\infty)[/tex]The range of the function is determined by the vertex, given that the parabola opens upwards, then the range is
[tex]R\colon\lbrack-16,\infty\rbrack[/tex]a tank in the shape of a sphere is filled with water and has a diameter of 15ft. if water weighs 62.4 pounds per cubic foot what is the total weight of the water in a full tank to the nearest pound
Answers
Answer:
110,270 pounds.
Explanation:
Diameter of the Spherical Tank = 15 ft
• Radius = 15 ÷ 2 = 7.5 ft
For any sphere with radius, r:
[tex]\text{Volume}=\frac{4}{3}\pi r^3[/tex]Therefore, the volume of water that will fill the tank:
[tex]\begin{gathered} V=\frac{4}{3}\times\pi\times7.5^3 \\ =1767.15\; ft^3 \end{gathered}[/tex]If water weighs 62.4 pounds per cubic foot:
[tex]\begin{gathered} \text{Density}=\frac{\text{Weight}}{\text{Volume}} \\ 62.4=\frac{\text{Weight}}{1767.15} \\ \text{Weight}=62.4\times1767.15 \\ \text{Weight}=110,270.16\text{ pounds} \\ \text{Weight=}110,270\text{ pounds} \end{gathered}[/tex]The total weight of the water in a full tank is 110,270 pounds. (correct to the nearest pound).
48. Mrs. Dalton is selling pieces of cake at the school carnival. She baked 8 cakes and cut them
each into 12 pieces. If she sold 81 slices of cake, how many total cakes does she have left?
Circle the correct option.
Answers
Total number of cakes left is 1.25 i.e. 1 and quarter.
Given,
Number of cakes = 8
Number of pieces of each cake =12
Number of slices sold = 81
Then,
Total number of slices of cake = [tex]12*8=96[/tex]
Now,
number of remaining slices =[tex]96-81=15[/tex]
To find number of remaining cake left, divide number of remaining slices to the pieces of each cake.
Number of remaining cake = [tex]\frac{15}{12} =1.25[/tex]
Thus, total number of cakes left is 1.25 i.e. 1 and quarter.
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Use the fermi process to estimate the number of bricks needed to fill an empty bathtub assume a typical brick has the length of 4 inches a width of 2 inches and a height of 8 inches a typical bathtub has a length of 60 inches a height of 30 inches and a width of 18 inches
Answers
Solution
A brick has the dimension 4in by 2in by 8 in
The bathtub has dimension 60in by 30in by 18in
[tex]\begin{gathered} Volume\text{ of a brick = 4in x 2in x 8in = 64in}^3 \\ Volume\text{ of the bathtub = 60in x 30in x 18in = 32400in}^3 \end{gathered}[/tex]Number of bricks needed to fill an empty bathtub =
[tex]\begin{gathered} \frac{32400in^3}{64in^3}=506.25\text{ bricks} \\ =506\text{ bricks \lparen to nearest whole number\rparen} \end{gathered}[/tex]To
Write the following ratio as a fraction in lowest terms. 36 to 38
Answers
Given:
Write the following ratio as a fraction in the lowest terms.
36 to 38
the ratio will be as follows:
[tex]36\text{ }to\text{ }38=\frac{36}{38}=\frac{2*18}{2*19}=\frac{18}{19}[/tex]So, the answer will be: 18/19
14. Log(x)=2meansa. x=10b. x=2^10c. x=10^2d. x=0e. none of the above
Answers
Without graphing, identify the vertex, axis of symmetry, and transformations from the parent function f(x)= |x|y = |x-5|-1
Answers
Answer:
• Vertex: (5, –1)
,• No symmetry
,• Transformations: 5 units to the right, and 1 unit down.
Explanation
We are given the parent function f(x)= |x| and the transformed function:
[tex]y=|x-5|-1[/tex]Thus, we can get the vertex considering that a function in the form:
[tex]y=|x\pm a|\pm b[/tex]has a vertex at (+a, ±b).
Therefore, our vertex is at (5, –1). Additionally, as an absolute function has the form of a 'v', and as the vertex is at (5, –1) then it has no symmetry about the x-axis, nor y-axis, and nor about the origin, meaning it has no symmetry.
Finally, the transformation from the parent function is a shift 5 units to the right and one unit down.
Answer:
Answer:
• Vertex: (5, –1)
,
• No symmetry
,
• Transformations: 5 units to the right and 1 unit down.
Explanation
We are given the parent function f(x)= |x| and the transformed function:
Thus, we can get the vertex considering that a function in the form:
Has a vertex at (+a, ±b).
Therefore, our vertex is at (5, –1). Additionally, as an absolute function has the form of a 'v', and as the vertex is at (5, –1) then it has no symmetry about the x-axis, nor y-axis, nor about the origin, meaning it has no symmetry.
Finally, the transformation from the parent function shifts 5 units to the right and one unit down.
Step-by-step explanation:
Can you help me with this, I’ve already completed the assignment but trying to go back and figure out what I missed and what I did wrong
Answers
OK
the base in this case is an hexagone
we can find the area of the base with the following formula
[tex]A=\frac{3\sqrt{3}S^2}{2}[/tex]where S represent the side of the hexagone
s=20
[tex]A=\frac{3\sqrt{3}*20^2}{2}[/tex][tex]A=600\sqrt{3}=1039.23[/tex]Perimiter is given by 6*S
P=6*20=120
h=22
Given the following formula for the hexagone
[tex]A=\frac{p*a}{2}[/tex][tex]600\sqrt{3}=\frac{120*a}{2}[/tex]solving for a
[tex]a=\frac{2*600\sqrt{3}}{120}=10\sqrt{3}=17.32[/tex]applying pythagoras theorem
[tex]l^2=a^2+h^2[/tex][tex]l^2=(10\sqrt{3})^2+22^2[/tex][tex]l=\sqrt{784}=28[/tex]Lateral surface
[tex]LS=\frac{p*l}{2}[/tex][tex]LS=\frac{120*28}{2}=1680[/tex]Total surface
[tex]TS=LS+A[/tex][tex]TS=1680+600\sqrt{3}[/tex][tex]TS=2719.23048[/tex]Volume
[tex]V=\frac{1}{3}A*h[/tex][tex]V=\frac{1}{3}600\sqrt{3}*22[/tex][tex]V=4400\sqrt{3}=7621.02[/tex]