In order to convert the number to decimal form, we need to look at the exponent of the number 10 multiplying the number 7.916.
The exponent is equal to -7, which means we will need to add 7 times the number 0 to the left of the number 7.916. Also, the decimal point will be moved 7 positions to the left.
So we have:
[tex]7.916\cdot10^{-7}=0.0000007916[/tex]the base of the pyramid is a square. the volume is ___ cubic cm. measurements:l = 6 cmw = 10 h = 15(unable to send pictures of question without app crashing. my apologies.)
Answer:
300 cubic meters.
Explanation:
The volume of any pyramid is obtained using the formula below:
[tex]V=\frac{1}{3}\times\text{Base Area}\times Height[/tex]Substitute the given values:
[tex]\begin{gathered} V=\frac{1}{3}\times(6\times10)\times15 \\ =\frac{1}{3}\times60\times15 \\ =300\operatorname{cm}^3 \end{gathered}[/tex]The volume of the pyramid is 300 cubic meters.
use the function f(x)=-3(x+1)2+18what is the y intercept ?does it have a max or min
hello,
First of all, we must remember that a first degree function must be in the formula f (x) = ax + b, so, lets use this form:
[tex]undefined[/tex]metro atlanta home prices are rising rapidly, and much of its a soaring demand from deep-pocketed investors,as reported in the AJC March 21st of this year. In March2022, the median sale price of a home in the Metro area was $401,500. Before the the pandemic hit, in january2020, the median sale price was $279,000 Find the rate increase of the average cost of a home in Atlanta from january2020 before the pandemic hit Atlanta to the present
We are asked to determine the rate of increase in the value of a home,
We need to have into account that at the beginning of the considered period the cost was 279000 and after two years the cost is 401500, therefore, we can use the following formula:
[tex]r=\frac{\Delta C}{\Delta t}[/tex]Where:
[tex]\begin{gathered} \Delta C=\text{ difference in cost} \\ \Delta t=\text{ difference in time} \end{gathered}[/tex]Now, we substitute the values:
[tex]r=\frac{401500-279000}{2}[/tex]Solving the operations:
[tex]r=61250[/tex]Therefore, the rate is an increase of $61250 per year.
A variable needs to be eliminated to solve the system of equations. Choose the correct first step: -3x+8y=-294x-8y=28A. Add to eliminate xB.Subtract to eliminate yC.Add to eliminate yD. Subtract to eliminate x
From the given equations, we can note that coeffcients of variable y are opposite. This means that, in order to eliminate y, we can add both equations. Then, the answer is C
Given the Exponential Equation, determine the Initial Value and Rate of Change as a Percent for each of the following.
The formula for calculating exponential growth is expressed as
y = a(1 + r)^n
where
a is the initial value
y is the final value
n is the time
r is the growth rate
The formula for calculating exponential decay is expressed as
y = a(1 - r)^n
For y = 1010(1.05)^x,
initial value = 1010
1 + r = 1.05
r = 1.05 - 1 = 0.05
Since it is positive, it is exponential growth
Growth percent = 0.05 x 100 = 5%
For y = 4932(1.26)^x,
initial value = 4932
1 + r = 1.26
r = 1.26 - 1 = 0.26
Growth percent = 0.26 x 100 = 26%
For y = 2835(1.065)^x,
initial value = 2835
1 + r = 1.065
r = 1.065 - 1 = 0.065
Since it is positive, it is exponential growth
Growth percent = 0.065 x 100 = 6.5%
For y = (0.96)^t,
initial value = 1
1 - r = 0.96
r = 1 - 0.96 = 0.04
decay percent = 0.04 x 100 = 4%
For y = 4660(0.89)^x,
initial value = 4660
1 - r = 0.89
r = 1 - 0.89 = 0.11
decay percent = 0.11 x 100 = 11%
For y = 3078(1.09)^t,
initial value =3078
1 + r = 1.09
r = 1.09 - 1 = 0.09
Growth percent = 0.09 x 100 = 9%
Michael earns a weekly salary of $365 plus a 6% commission of sales for the week. Last week, Michael's sales totaled $3200. How much did he make in commission? What was Michael's total pay?
Michael's sales are $3200, then the comission is
[tex]3200\times0.06=192,[/tex]$192 in comission.
Then the total pay is
[tex]365+192=557.[/tex]$567
an office administrator has an office supply budget $150. The office administrator will purchase folders, which are $2.15 each and notebooks, which are $4.60 each. which inequality represent the constrain on the number of folders f and notebook n the office administrator can purchase
If the price of each folder is $2.15, and the amount of folders is f, the total price paid for folders is the product of the unitary price by the amount bought.
[tex]\text{price}1=2.15f[/tex]Similarly, the price paid for notebooks is the unitary price of one notebook ($4.60) multiplied by the amount of notebooks (n).
[tex]\text{price}2=4.6n[/tex]Finally, the total cost of both products together is the sum of these products.
[tex]\text{cost}=\text{price}1+\text{price}2=2.15f+4.6n[/tex]The supply budget is $150, so the total cost needs to be lesser than or equal this value.
Therefore, we have that:
[tex]\begin{gathered} \text{cost}\le150 \\ 2.15f+4.6n\le150 \end{gathered}[/tex]So the correct option is B.
I’m in AP Calc AB and can’t figure this out. Any idea?
Answer::
[tex]f^{\prime}(x)=7x\sec x\tan x+7\sec x+\frac{1}{x}[/tex]Explanation:
Given f(x) defined below:
[tex]f(x)=\ln x+7x\sec x[/tex]The derivative is calculated below.
[tex]\begin{gathered} \frac{d}{dx}\lbrack f(x)\rbrack=\frac{d}{dx}\lbrack\ln x+7x\sec x\rbrack \\ =\frac{d}{dx}\lbrack\ln x\rbrack+\frac{d}{dx}\lbrack7x\sec x\rbrack \\ Take\text{ the constant 7 outside the derivative sign.} \\ =$$\textcolor{red}{\frac{d}{dx}\lbrack\ln x\rbrack}$$+7\frac{d}{dx}\lbrack x\sec x\rbrack \\ \text{The derivative of }\ln (x)=\frac{1}{x},\text{ therefore:} \\ $$\textcolor{red}{\frac{d}{dx}\lbrack\ln x\rbrack}$$+7\frac{d}{dx}\lbrack x\sec x\rbrack=$$\textcolor{red}{\frac{1}{x}}$$+7\frac{d}{dx}\lbrack x\sec x\rbrack\cdots(1) \end{gathered}[/tex]Next, we find the derivative of x sec x using the product rule.
[tex]\begin{gathered} \frac{d}{dx}\lbrack x\sec x\rbrack=x$$\textcolor{blue}{\frac{d}{dx}\lbrack\sec x\rbrack}$$+\sec x\frac{d}{dx}\lbrack x\rbrack\text{ } \\ The\text{ derivative of sec(x), }\text{\textcolor{red}{ }}\textcolor{red}{\frac{d}{dx}\lbrack\sec x\rbrack=\sec x\tan x} \\ =x$$\textcolor{blue}{\lbrack\sec x\tan x\rbrack}$$+\sec x \end{gathered}[/tex]Substitute the result into equation (1) above.
[tex]\begin{gathered} \frac{1}{x}+7\frac{d}{dx}\lbrack x\sec x\rbrack=\frac{1}{x}+7(x\sec x\tan x+\sec x) \\ =7x\sec x\tan x+7\sec x+\frac{1}{x} \end{gathered}[/tex]Therefore:
[tex]f^{\prime}(x)=7x\sec x\tan x+7\sec x+\frac{1}{x}[/tex]solve the system. given your answer as (x, y, z)-4x -y - 3z = -5-6x + y - 3z = -172x + 2y - z = - 10
Answer:
(1, -5 ,2)
Explanation:
Given the system of equations:
[tex]\begin{gathered} -4x-y-3z=-5\ldots(1) \\ -6x+y-3z=-17\ldots(2) \\ 2x+2y-z=-10\ldots(3) \end{gathered}[/tex]Make z the subject in the third equation:
[tex]z=2x+2y+10[/tex]Substitute z=2x+2y+10 into the first and second equations:
First Equation
[tex]\begin{gathered} -4x-y-3z=-5 \\ -4x-y-3(2x+2y+10)=-5 \\ -4x-y-6x-6y-30=-5 \\ -4x-6x-y-6y=-5+30 \\ -10x-7y=25\ldots(4) \end{gathered}[/tex]Second Equation
[tex]\begin{gathered} -6x+y-3z=-17 \\ -6x+y-3(2x+2y+10)=-17 \\ -6x+y-6x-6y-30=-17 \\ -6x-6x+y-6y=-17+30 \\ -12x-5y=13\ldots(5) \end{gathered}[/tex]Next, solve equations 4 and 5 simultaneously:
[tex]\begin{gathered} -10x-7y=25\ldots(4) \\ -12x-5y=13\ldots(5) \end{gathered}[/tex]Multiply equation (4) by 5 and equation (5) by 7.
[tex]\begin{gathered} -50x-35y=125 \\ -84x-35y=91 \\ \text{Subtract same sign} \\ 34x=34 \\ x=\frac{34}{34} \\ x=1 \end{gathered}[/tex]Substitute x=1 into equation (4):
[tex]\begin{gathered} -10x-7y=25\ldots(4) \\ -10(1)-7y=25 \\ -7y=25+10 \\ -7y=35 \\ y=\frac{35}{-7} \\ y=-5 \end{gathered}[/tex]Recall: z=2x+2y+10
[tex]\begin{gathered} z=2x+2y+10 \\ =2(1)+2(-5)+10 \\ =2-10+10 \\ z=2 \end{gathered}[/tex]The solution of the system is:
[tex](1,-5,2)[/tex]1 11a.) A sign in a bakery gives the following options. Find each unit price to the nearest cent, and show your reasoning. You can get 3 mini-cakes for $32. What is the cost of ONE mini-cake? * O $10.66 O $10.65 O $10.67 O $10.59
Since we can get 3 mini-cakes for $32, we can find the price of each mini-cake by taking the ratio of price to number of mini-cakes, like this:
unit price = 32/3 = 10.67
Then, the cost of ONE mini-cake is $10.67
Over the weekend, Devon baked 12 muffins. She divided them evenly among 3 plates to giveto neighbors.The letter m stands for the number of muffins on each plate. Which equation can you use tofind m?12 x 3 = m12 : 3 = m
The information given is listed below:
number of muffins (m) = 12, number of plates = 3
number of muffin on each plate = number of muffins /
Micha starts riding his bike at 12:05pm Her rides for 35 minutes What time does he stop riding his bike?
If Micha rides for 35 minutes, she'll stop riding her bike at 12:40pm
My teacher gave the answer on the right but I want know how he did it
the given number is 6^4
here is the calculation.
[tex]6^4=6\times6\times6\times6[/tex]multiply the number 6 by the times of 4
now by multiplication, the answer is
[tex]6^4=1296[/tex]so, the answer is 1296.
The directions says state if the two triangles are congruent. If they are state how you know
From the diagram, we see that the triangles have:
• equal hypotenuse,
,• equal base.
HL Theorem states that if the hypotenuse and leg of a right triangle are congruent to the hypotenuse and leg of another right triangle, then the two triangles are congruent.
We conclude that the triangles are congruent because of HL Theorem.
AnswerB) HL
twice a number decreased by 4 Is atleast 12
EXPLANATION
The appropiate relationship is:
2x - 4 = 12
Adding +4 to both sides:
2x = 12 + 4
Adding numbers:
2x = 16
Dividing both sides by 2:
x = 16/2
Simplifying:
x = 8
The solution is 8
If a = 6, which of the following is equal to a 2?1o-36O O-122
Solution:
The question given is a negative exponent.
To solve this, we apply the law of indices for negative exponents.
Negative exponent law is indicated below;
[tex]a^{-x}=\frac{1}{a^x}[/tex]Thus, applying this law to the question;
[tex]a^{-2}=\frac{1}{a^2}[/tex]Given:
a = 6
Substituting a = 6 into the expression, we have;
[tex]\frac{1}{a^2}=\frac{1}{6^2}[/tex]Therefore, the correct answer is;
[tex]\frac{1}{6^2}[/tex]The table shows x- and y-values for the equation y = 3x -1 Which number is missing in the table? 23 15 20 37
y = 3x-1
When x = 8
y = 3(8) -1
y = 24-1
y = 23
Keisha has four favorite shirts one blue, one green, one red, one yellow and two favorite pairs of pants one black and one brown she decides to randomly choose a pair of pants and a shirt to wear for the day. What is the probability that Keisha chooses and outfit that is yellow and black or red and brown round your answer to the nearest whole percent?
Answer:
25%
Explanation:
First, let's calculated the total number of outfits that Keisha can choose. So, we will use the rule of multiplication as:
4 * 2 = 8
Shirts Pants
Because she has 4 options for shirts and 2 options for pants. So, there 8 possible outfits.
Then, from those outfits, there is 1 that is yellow and black, and 1 that is red and brown. So, the probability that Keisha chooses an outfit that is yellow and black or red and brown is:
[tex]P=\frac{1+1}{8}=\frac{2}{8}=0.25=25\text{ \%}[/tex]Therefore, the answer is 25%
ylinders, cone Justin uses the mold picture cement column posts to use a height of the Cylinder = 18 in To make a post, Justin completel wet cement How much wet cement, in cubic inche make 4 posts? dus 3 in Formula Sheet
question is in image
The function f(x) is given by,
[tex]f(x)=x^2[/tex]The function g(x) is given by,
[tex]g(x)=\frac{-2}{3}x^2[/tex]If f(x) becomes -kf(x), where 0Comparing the above functions, we get
[tex]g(x)=-\frac{2}{3}f(x)[/tex]So, k=2/3. Hence, 0 < 2/3 < 1.
Therefore, the graph of g(x) is the graph of f(x) compressed vertically and reflected across the x axis.
Hence, option D is correct.
How do I find the sum of this equation and express it in simplest form [tex]( {n}^{3} - 5n - 2) + (4 {n}^{3} + n - 4)[/tex]
The table below shows the average amount of time spent per person on entertainment per year from 2000 to 2005.Year Hours2000 34922001 35402002 36062003 36632004 37572005 3809(a) Use a graphing calculator or spreadsheet program to find a quadratic model that best fits this data. Let t represent the year, with t=0 in 2000. Round each coefficient to two decimal places.Pt =(b) Based on this model, how many hours would you expect the average person to spend on entertainment in 2012? Round your answer to the nearest whole number.hours(c) When would you expect the average amount of entertainment time to reach 4000? Give your answer as a calendar year (ex: 1997).During the year
EXPLANATION
Given the table,
Year Hours
2000 3492
2001 3540
2002 3606
2003 3663
2004 3757
2005 3809
Plugging in the data into a graphing calculator with a quadratic regression model AX^2+BX+C:
The function is:
P(t) = 2.35714 X^2 -9376.16 X +9325921.701
B)
When the time is 2012 substituting on the function:
P(t) = 2.357*(2012)^2 - 9,374.84*(2012) + 9.3246X10^6 = 3897.32
Hence, the number of hours spent in 2012 would be 3897 hours.
C) By using the graph, we can expect that the average amount of entertainment time to reach 4000 would be 9,540,465 hours.
Express the given Hindu-Arabic numeral in expanded form 26
Given:
The numeral is 26.
To find: The expanded form
Explanation:
As we know,
Expanded form or expanded notation is a way of writing numbers to see the math value of individual digits.
Separating the numbers into the individual place values, we get
[tex]26=(2\times10)+(6\times1)[/tex]Final answer: The expanded form of 26 is,
[tex](2\times10)+(6\times1)[/tex]Samson buys a newcomputer for class. Thecomputer costs $550, aswell as an additional tax of10.2%.How much does he pay forthe computer?
The cost of the computer is: $550
The additional tax is: 10.2%
To find the final cost of the computer, first, we need to find how much is the tax of 10.2%.
Step 1. Calculate how much is 10.2% of $550.
In general, to calculate a percentage we divide the quantity by 100 and then multiply by the percentage we need. In this case:
[tex]\frac{550}{100}\times10.2[/tex]Solving the operations:
[tex]5.5\times10.2[/tex][tex]=56.1[/tex]The tax is $56.1
Step 2. Add the cost of the computer and the tax to find how much he paid for the computer:
[tex]550+56.1=606.1[/tex]Answer: $606.1
-Convert the following into given base units of measurement. (Refer to slide 21 &27 on uploaded ppt).
1. 3.65 mg =______ dg
2. 9.987 g =______ hg
3. 12.203 km =______ mm
The conversion of the given base units of measurements are
Part 1
3.65 mg = 0.0365 dg
Part 2
9.987 g = 0.09987 hg
Part 3
12.203 km = 12203072.2 mm
Part 1
The given quantity is 3.65 mg
mg is the milligram and dg is the decigram
We know
1 mg = 0.01 dg
Then,
3.65 mg = 3.65×0.01
Multiply the terms
3.65 mg = 0.0365 dg
Part 2
The given quantity is 9.987 g
g is the gram and hg is the hectogram
1 g = 0.01 hg
Then,
9.987 g = 0.09987 hg
Part 3
The given quantity is 12.203 km
km is the kilometer and mm is the millimeter
1 km = 1000000 mm
12.203 km = 12203072.2 mm
Hence, the conversion of the given base units of measurements are
Part 1
3.65 mg = 0.0365 dg
Part 2
9.987 g = 0.09987 hg
Part 3
12.203 km = 12203072.2 mm
Learn more about conversion here
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A metal plate has the form of a quarter circle with a radius of R = 106cm . Two 3 cm holes are to be drilled in the plater r = 95cm from the corner at 30 degrees and 60as shown above. To use a computer controlled milling machine you must know the Cartesian coordinates of the holes. Assuming the origin is at the corner what are the coordinates of the holes (x_{1}, y_{1}) and (x_{2}, y_{2}) ? Round your answer to 3 decimal places
1) Considering that this quarter circle is one sector of the unit circle and that
[tex]30^{\circ}=\frac{\pi}{6}[/tex]2) Let's sketch this out to better grasp the idea:
Note that the first coordinate will be given by its cos(theta), and the second one by its sine(theta)
3) Based on that principle, we can tell the following:
[tex]\begin{gathered} (x_1,y_1)--->(cos(30^{\circ}),\sin(30^{\circ}))=(\frac{\sqrt{3}}{2},\frac{1}{2}) \\ \\ (x_{2,}y_2)-->(\cos(60),\sin(60))=(\frac{1}{2},\frac{\sqrt{3}}{2}) \\ \end{gathered}[/tex]As the holes need to be drilled by the machine, so we need to find approximations to those coordinates:
[tex]\begin{gathered} (x_1,\:y_1)-->(0.866,0.500) \\ (x_2,y_2)-->(0.500,0.866) \end{gathered}[/tex]Thus, these are the coordinates to be put into the computer.
In ABC, A = 68°, a = 14 and c = 17. Which of these statements best describes the triangle?
Given for the triangle ABC:
[tex]\begin{gathered} \angle A=68\degree \\ a=14,c=17 \end{gathered}[/tex]Using the sine rule, we will solve the triangle by finding the missing angles
So,
[tex]\frac{a}{\sin A}=\frac{c}{\sin C}[/tex]substitute with the given data:
[tex]\begin{gathered} \frac{14}{\sin68}=\frac{17}{\sin C} \\ \\ \sin C=\frac{17}{14}\cdot\sin 68=1.125866 \end{gathered}[/tex]The value of (sin C) must be 1 or less than 1
So, the triangle ABC cannot be constructed
The answer will be the last option
taliyah 1. If Mrs. Wozniak runs 8 miles a day. How many miles will she run in 4 weeks? Your answer 2. Fach fourth trade class at a local elementan answered 1 209 multiplication fact problems last
Use the given rate to find how many miles will Mrs. Wozniak run in 4 weeks. Remember that 1 week is equal to 7 days, then 4 weeks is 28 days.
[tex]28days\cdot\frac{8miles}{1day}=224miles[/tex]She will run 224 miles in 4 weeks.
the total amount of flour in a bakery after receiving new stock equal to 3/10 of its current stock (x)Find the expression that represents the scenario
Answer:
(3/10)x
Explanation:
The expression that represents the scenario is an expression that we can use to calculate the total amount of flour, so the correct expression is:
[tex]\frac{3}{10}x[/tex]Because the amount of flour is 3/10 of x ( the current stock)
The number of compounding periods is equal to what: what is the formuls
Answer
When compound interest is discussed, the time rate for the compound interest is usually mentioned. For example, they would say that
- a certain amount of money has its interest compounded at 5% annually,
- a certain amount of money has its interest compounded at 7% every 3 months,
- a certain amount of money has its interest compounded at 2% every 6 months,
In each of the examples given above, the compounding period is 1 year, 3 months and 6 months respectively.
If one is now asked to calculate the compound interst on a particular amount of money after time, T, we usually express this time T in terms of the number of time periods, t, that exist inside the given time T.
Hence, the time T is expressed in terms of time period t, as
T = nt
Such that the number of compounding periods in T is given as
n = (T/t)
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