Answer:
The nearest 10,000 is;
[tex]20,000[/tex]Explanation:
We want to round off the given number to the nearest 10,000.
[tex]18,600[/tex]We will find the closest ten thousand to the given number;
[tex]18,600\rightarrow20,000[/tex]Therefore, the nearest 10,000 is;
[tex]20,000[/tex]
A construction crew built 1/2 miles of road in 1/6 days. What is the unit rate in simplest form.
For this problem, we are given the distance a construction crew built a road and the time in days it took to build it. We need to determine the unit rate for this problem, which is achieved by dividing the distance and time. We have:
[tex]\text{ unit rate}=\frac{\frac{1}{2}}{\frac{1}{6}}=\frac{1}{2}\cdot\frac{6}{1}=\frac{6}{2}=3\text{ miles per day}[/tex]The unit rate is 3 miles per day.
Consider the equation 14 x 10^0.5w= 100.Solve the equation for w. Express the solution as a logarithm in base-10.W = _____ Approximate the value of w. Round your answer to the nearest thousandth.w ≈ _____
Solution:
Given;
[tex]14\cdot10^{0.5w}=100[/tex]Divide both sides by 14, we have;
[tex]\begin{gathered} \frac{14\cdot10^{0.5w}}{14}=\frac{100}{14} \\ \\ 10^{0.5w}=\frac{50}{7} \end{gathered}[/tex]Take the logarithm of both sides; we have;
[tex]\log_{10}(10)^{0.5w}=\log_{10}(\frac{50}{7})[/tex]Applying logarithmic laws;
[tex]0.5w=\log_{10}(\frac{50}{7})[/tex]Divide both sides by 0.5;
[tex]\begin{gathered} \frac{0.5w}{0.5}=\frac{\log_{10}(\frac{50}{7})}{0.5} \\ \\ w=\frac{\operatorname{\log}_{10}(\frac{50}{7})}{0.5} \end{gathered}[/tex](b)
[tex]\begin{gathered} w=\frac{\operatorname{\log}_{10}(\frac{50}{7})}{0.5} \\ \\ w\approx1.708 \end{gathered}[/tex]The function f(x) = -x2 - 4x + 5 is shown on the graph. What is the domain and range of this function?
Step 1
The domain includes all the x-values that fall within the function
Hence, the domain of this function is [ All real values of x]
Step 2
Find the range
The range includes all values of y that fall within the function
Hence the range of the function is [-∞, 9]
If triangle ABC is reflected across the y-axis, what are the coordinates of C?O A. (5,-3)O B. (-5, 3)O C. (3,-5)O D. (-3, -5)
B) (-5,3)
1) We need to locate the vertex location since the point here is to find the coordinates of C'. So, let's do it before applying the required transformation.
C(5,3)
2) Since we want to know the coordinates of C', and there was a reflection across the y-axis, we can write the following:
C(5,3) Rule (x,y) --> (-x,y) C'(-5,3)
3) Thus, the answer is (-5,3)
what type from f x to g x on the graph ?
When looking at the graph, we can discard two of the options, rotation (as they don't have any intersection, there are no possibilities of having a rotation axis) and reflection. It occured a translation. To know which of the options is correct, we can see the y intercepts of both lines. The y intercept of f(x) is 0 and the y intercept of g(x) is -4, which means that the line was translated down 4 units.
It means the right answer is D. Vertical Translation down 4 units.
the product of 8 and a number increased by 17
You have the following stament:
The product of 8 and a number increased by 17
In order to write the previous statment in an algebraic way, you take into account that "the product of 8 and a number" means the multiplication of 8 and a variable, which is "increased" by 17. That is, number 8 is multiplying the sum of a variable and 17.
Thus, you have:
The product of 8 and a number increased by 17:
8(x + 17)
Printer Paper Store normally sells laser paper for 89,99 per ream, It has a special, 1
ream free with the purchase of 2. If you buy 2 reams and get 1 free, what is your (a)
cost per ream, and (b) markdown per ream?
The required (a) cost per ream becomes 59.99 and (b) the markdown per ream is 30.
Given that,
Printer Paper Store normally sells laser paper for 89,99 per ream, It has a special, 1 ream free with the purchase of 2. If you buy 2 reams and get 1 free.
In mathematics, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication and division,
Here,
Cost of the 1 ream = 89,99
Cost of the 2 reams = 179.98
According to the question,
Cost of the 3 reams = 179.98
Cost of the one ream among the 3 reams = 179.88/3 = 59.99
markdown per ream = 89.99 - 59.99 = 30
Thus, the required (a) cost per ream becomes 59.99 and (b) the markdown per ream is 30.
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Which of the functions below could have created this graph?OA. F(x)=x²+2x-2OB. F(x)---4C. F(x)=3x²+2x²OD. F(x)=-²
The functions [tex]F(x)=-\frac{1}{2}x^{4}-x^{3}+x+2[/tex] could have created this graph of downward parabola.
Option D is correct because the leading coefficient of given function is negative. That's why it is making the downward parabola.
As we can see from the graph that the the parabola is downward.
And we know that if the leading coefficient is less than zero, thus the graph will be downward parabola.
Lets check all the option:
For option A:
[tex]F(x)=x^{3}+x^{2}+x+1[/tex], this is a cubic polynomial and the graph will be a cubic curve.
For option B:
[tex]F(x)=x^{2}+5[/tex], this is a quadratic polynomial and leading coefficient is positive, so the graph will be upward parabola.
For option C:
[tex]F(x)=x^{4}-2x[/tex], for x = 0, F(x) =0, so it will not intersect the y-axis. Also the graph will be upward parabola.
Hence, the option D, [tex]F(x)=-\frac{1}{2}x^{4}-x^{3}+x+2[/tex], could have created this graph of downward parabola.
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Consider the following function.f(x) = |x − 9|Find the derivative from the left at x = 9. If it does not exist, enter NONE.Find the derivative from the right at x = 9. If it does not exist, enter NONE.
The form of the derivative of the absolute equation is
[tex]\begin{gathered} f(x)=\lvert x-a\rvert \\ \frac{dx}{dy}=\frac{\lvert x-a\rvert}{x-a} \\ \frac{dy}{dx}=\frac{x-a}{\lvert x-a\rvert} \end{gathered}[/tex]For the given function
[tex]f(x)=\lvert x-9\rvert[/tex]We will find the derivative from the left at x = 9
[tex]\frac{dy}{dx}=\frac{x-9}{\lvert x-9\rvert}[/tex]Substitute x by 9
[tex]\begin{gathered} \frac{dy}{dx}=\frac{9-9}{\lvert9-9\rvert} \\ \frac{dy}{dx}=\frac{0}{0} \end{gathered}[/tex]Then dy/dx does not exist (None)
The derivative from right at x = 9
[tex]\frac{dx}{dy}=\frac{\lvert x-9\rvert}{x-9}[/tex]Substitute x by 9
[tex]\begin{gathered} \frac{dx}{dy}=\frac{\lvert9-9\rvert}{9-9} \\ \frac{dx}{dy}=\frac{0}{0} \end{gathered}[/tex]Then dx/dy does not exist (None)
Kyra is participating in a fundraiser walk-a-thon. She walks 3 miles in 45 minutes. If she continues to walk at the same rate, determine how many minutes it will take her to walk 7 miles. Show how you found your answer.
3 milles ---> 45 minutes
7 miles ---> x minutes
then
[tex]\begin{gathered} 3\times x=7\times45 \\ 3x=315 \\ \frac{3x}{3}=\frac{315}{3} \\ x=105 \end{gathered}[/tex]answer: 105 minutes for walk 7 miles
What is nine increased by four and then doubled?
Answer:
Step-by-step explanation:
9+4=
13
13*2=
26
Answer:
Step-by-step explanation:
(9 multiplied by 4) multiplied by 2
= 72
Can’t figure this fraction equation. 5/6 is the fraction getting divided by 2. Answer must be in the simplest form
Solution:
5/6 divided by 2, i.e.
[tex]\frac{5}{6}\div2[/tex]Applying the fraction rule
[tex]\begin{gathered} \frac{a}{b}\div \frac{c}{d}=\frac{a}{b}\times \frac{d}{c} \\ =\frac{5\times\:1}{6\times\:2} \\ =\frac{5}{6\times\:2} \\ =\frac{5}{12} \end{gathered}[/tex]Hence, the answer is 5/12
In 1994, the moose population in a park was measured to be 4930. By 1999, the population was measured again to be 6180. If the population continues to change linearly: A.) Find a formula for the moose population, P, in terms of t, the years since 1990. P(t) B.) What does your model predict the moose population to be in 2006?
We define the following variables for our problem:
P = population of mooses
t = number of years since 1990
m = growth ratio
In terms of the variables that we defined above and the fact that the population of moose in terms of the year is linear, we have the following equation:
[tex]P(t)=m\cdot t+P_0[/tex]Now, we use the data of the problem:
1) In 1994 the moose population was 4930, so we have:
[tex]\begin{gathered} t=1994-1990=4 \\ P(4)=4930 \end{gathered}[/tex]2) In 1999 the moose population was 6180, so we have:
[tex]\begin{gathered} t=1999-1990=9 \\ P(9)=6180 \end{gathered}[/tex]Now, using the data above and the equation for P(t) we construct the following system of equations:
[tex]\begin{gathered} P(4)=m\cdot4+P_0=4930 \\ P(9)=m\cdot9+P_0=6180 \end{gathered}[/tex]We solve the system of equations.
First, we solve the equations for P0:
[tex]\begin{gathered} P_0=4930-4m \\ P_0=6180-9m \end{gathered}[/tex]Now, because the right-hand-side of both equations is equal to P0, we equal them and then we solve for the variable m:
[tex]\begin{gathered} 4930-4m=6180-9m \\ 9m-4m=6180-4930 \\ 5m=1250 \\ m=250 \end{gathered}[/tex]Finally, we replace the value of m in one of the equations of P0 and solve for it:
[tex]\begin{gathered} P_0=4930-4\cdot m \\ P_0=4930-4\cdot250 \\ P_0=3930 \end{gathered}[/tex]A) The formula for the moose population, P, in terms of t, the years since 1990 is:
[tex]P(t)=250t+3930[/tex]B) We want to know the value of the moose population in 2006.
First, we compute the value of t:
[tex]t=2006-1990=16[/tex]Now, we replace the value of t in the equation of P(t) above:
[tex]P(6)=250\cdot16+3930=7930[/tex]Answer: 7930
QRS and SRT are complementary. if m QRS (8x+10)° and m SRT=(8x)°Determine m QRSm QRS=
We are given two complementary angles (QRS and SRT).
Two angles are called complementry if they sum up to 90 degrees.
Therefore, by defination
mQRS + mSRT = 90
(8x+10) + (8x) = 90
8x + 8x + 10 = 90
16x = 90-10
16x = 80
x = 80/16
x = 5
Now, put the values in both the euqations and we will get the values of both the angles.
mQRS = 8x + 10 = 8(5) + 10 = 40 + 10 = 50 degrees
mSRT = 8x = 8(5) = 40 degrees
A researcher wishes to estimate the percentage of adults who support abolishing the penny. What size sample should be obtained if he wishes the estimate to be within 4
percentage points with 95% confidence if
(a) he uses a previous estimate of 38%?
(b) he does not use any prior estimates?
Click here to view the standard normal distribution table (page 1).
Click here to view the standard normal distribution table (page 2).
(a) n =
(b) n=
(Round up to the nearest integer.)
(Round up to the nearest integer.)
The required sample sizes for the confidence intervals are given as follows:
a) Estimate of 38%: 566.
b) No estimate: 601.
How to obtain the required sample sizes?The margin of error for a confidence interval of proportions, using the z-distribution, is calculated as follows:
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
The parameters of the equation are listed as follows:
[tex]\pi[/tex] is the sample proportion, which is also the estimate of the parameter.z is the critical value.n is the sample size.The desired margin of error in this problem is of:
M = 0.04.
The confidence level is of 95%, hence the critical value z is the value of Z that has a p-value of [tex]\frac{1+0.95}{2} = 0.975[/tex], so the critical value is z = 1.96.
For item a, the estimate is of [tex]\pi = 0.38[/tex], hence the sample size is obtained as follows:
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
[tex]0.04 = 1.96\sqrt{\frac{0.38(0.62)}{n}}[/tex]
[tex]0.04\sqrt{n} = 1.96\sqrt{0.38(0.62)}[/tex]
[tex]\sqrt{n} = \frac{1.96\sqrt{0.38(0.62)}}{0.04}[/tex]
[tex](\sqrt{n})^2 = \left(\frac{1.96\sqrt{0.38(0.62)}}{0.04}\right)^2[/tex]
n = 566.
For item b, when there is no estimate, we use [tex]\pi = 0.5[/tex], hence:
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
[tex]0.04 = 1.96\sqrt{\frac{0.5(0.5)}{n}}[/tex]
[tex]0.04\sqrt{n} = 1.96\sqrt{0.5(0.5)}[/tex]
[tex]\sqrt{n} = \frac{1.96\sqrt{0.5(0.5)}}{0.04}[/tex]
[tex](\sqrt{n})^2 = \left(\frac{1.96\sqrt{0.5(0.5)}}{0.04}\right)^2[/tex]
n = 601.
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During a hurricane evacuation from the east coast of Georgia, a family traveled 200 miles west. For part of the trip, they averaged 60 mph, but as the congestion got bad, they had to slow to 10 mph. If the total time ct travel was 6 hours, how many miles did they drive at the reduced speed?
Given:
Total distanced traveled is 200 miles.
speed is 60 mph, but as the congestion got bad, they had to slow to 10 mph.
Time = 6 hours.
Let, x be the travel time at 60 mph
The equation is,
[tex]\begin{gathered} 60x+10(6-x)=200 \\ 60x+60-10x=200 \\ 50x=200-60 \\ 50x=140 \\ x=\frac{140}{50} \\ x=2.8 \end{gathered}[/tex]It mean at the speed of 60 mph, the distance traveled is,
[tex]60x=60(2.8)=168\text{ miles}[/tex]So, the distance traveled for the speed of 10 mph is,
[tex]200-168=32\text{ miles.}[/tex]Answer: The family traveled 32 miles at reduced speed.
The total cost of a jacket and shirt was $75.08 if the price of the jacket was $5.32 less than the shirt what was the price of the jacket
Let 'j' be the cost of the jacket and let 's' be the cost of the shirt. Then, if they cost $75.08, then we have the following expression:
[tex]j+s=75.08[/tex]since the price of the jacket was 5.32 less than the shirt, then, we have:
[tex]j=s-5.32[/tex]using this equation on the first equation, we get the following:
[tex]\begin{gathered} s-5.32+s=75.08 \\ \Rightarrow2s=75.08+5.32=80.40 \\ \Rightarrow s=\frac{80.40}{2}=40.20\rbrack \\ s=40.20 \end{gathered}[/tex]now that we have that the shirt costs $40.20, we can find the price of the jacket:]
[tex]j=40.20-5.32=34.88[/tex]therefore, the price of the jacket is $34.88 and the price of the shirt costs $40.20
Why is the quotient of three divided by one-fifth different from the quotient of one-fifth divided by three? Hello my child needs help with this question could someone help
Solution
We want to get why
[tex]\frac{3}{\text{ \lparen1/5\rparen}}\text{ is different from }\frac{\text{ \lparen1/5\rparen}}{3}[/tex]Reason 1: Commutation Law Does Not Hold For Division (or quotient)
Generally,
[tex]\frac{a}{b}\ne\frac{b}{a}[/tex]Reason 2: Actual Computation
First
[tex]\begin{gathered} \frac{3}{\text{ \lparen1/5\rparen}}=3\div\frac{1}{5} \\ \\ \frac{3}{\text{ \lparen1/5\rparen}}=3\times\frac{5}{1} \\ \\ \frac{3}{\text{ \lparen1/5\rparen}}=15 \end{gathered}[/tex]Secondly
[tex]\begin{gathered} \frac{\text{ \lparen1/5\rparen}}{3}=\frac{1}{5}\div3 \\ \\ \frac{\text{ \lparen1/5\rparen}}{3}=\frac{1}{5}\times\frac{1}{3} \\ \\ \frac{\text{ \lparen1/5\rparen}}{3}=\frac{1}{15} \end{gathered}[/tex]It is now obvious that
[tex]\frac{3}{\text{ \lparen1/5\rparen}}\ne\frac{\text{ \lparen1/5\rparen}}{3}[/tex]For the real-valued functions f(x) = 2x+10 and g(x) = x-1, find the composition f•g and specify its domain using interval notation.(f•g)(x)=Domain of f•g: (The 2x+10 is square rooted)
Okay, here we have this:
We need to meke the composition (f•g)(x), so in the function f we will replace x with the function g:
[tex]\begin{gathered} \mleft(f•g\mright)\mleft(x\mright)=\sqrt[]{2(x-1)+10} \\ =\sqrt[]{2x-2+10} \\ =\sqrt[]{2x+8} \end{gathered}[/tex]Now let's find the domain of (f•g)(x):
2X+8≥0
2X≥-8
X≥-4
Finally we obtain the following domain: [-4,∞)
Based on the graph, what is the solution to the system of equations?
The solution of the system of equations is where both lines cross each other.
solution = (0,1)
Parallelogram ABCD was translated to parallelogram AB'C'D'.How many units and in which direction were the x-coordinates of parallelogram ABCD moved?
Number of units: 7
Direction: left of the x coordinate
Explanation:Given:
Parallelogram ABCD was translated to parallelogram AB'C'D'
To find:
the number of units and in which direction were the x-coordinates of parallelogram ABCD moved
To determine the number of units, we will use the diagram below:
From A to A', B to B', C to C' and D to D', the number of units for the movement in the x coordinate is 7. The vertical position didn't change. This means to movement in the coordinate.
The parallelogram ABCD was moved to the left of the x axis to get parallelogram A'B'C'D'
Number of units: 7
Direction: left of the x coordinate
7 units to the left
Part BNow you’ll attempt to copy your original triangle using two of its angles:Choose two of the angles on ∆ABC, and locate the line segment between them. Draw a new line segment, DE¯, parallel to the line segment you located on ∆ABC. You can draw DE¯ of any length and place it anywhere on the coordinate plane, but not on top of ∆ABC.From points D and E, create an angle of the same size as the angles you chose on ∆ABC. Then draw a ray from D and a ray from E through the angles such that the rays intersect. You should now have two angles that are congruent to the angles you chose on ∆ABC.Label the point of intersection of the two rays F, and draw ∆DEF by creating a polygon through points D, E, and F.Take a screenshot of your results, save it, and insert the image in the space below.
Step 1)
We used angles alpha and betta from the original triangle
Step 2)
Then,
Step 3)
Notice that the two triangles are similar due to the AAA postulate. (The length of DE is different than that of AB)
I need help with my math
Given the question
4 (3x -6) + 2x + 18
To simplify the above expression, we will observe the following steps
Step 1: Expand the parenthesis (bracket)
[tex]\begin{gathered} 4(3x-6)+2x+18 \\ \Rightarrow4\times3x-\text{ 4x6 + 2x+18} \\ \Rightarrow12x\text{ -24+2x +18} \end{gathered}[/tex]Step 2: Simplify the expression by collecting like terms
[tex]\Rightarrow\text{ 12x +2x -24+18}[/tex][tex]14x\text{ -6}[/tex]Answer = 14x - 6
the angle t is an acute angle and sin t and cos t are given. use identities to find tan t, csc t, sec t, and cot t. where necessary, rationalizing denominators.
Recall the following identities:
[tex]\begin{gathered} \tan (t)=\frac{\sin (t)}{\cos (t)} \\ \csc (t)=\frac{1}{\sin (t)} \\ \sec (t)=\frac{1}{\cos (t)} \\ \cot (t)=\frac{\cos (t)}{\sin (t)} \end{gathered}[/tex]Since sin(t)=12/13 and cos(t)=5/13, then:
[tex]\begin{gathered} \tan (t)=\frac{(\frac{12}{13})}{(\frac{5}{13})} \\ =\frac{12}{5} \end{gathered}[/tex][tex]\begin{gathered} \csc (t)=\frac{1}{(\frac{12}{13})} \\ =\frac{13}{12} \end{gathered}[/tex][tex]\begin{gathered} \sec (t)=\frac{1}{(\frac{5}{13})} \\ =\frac{13}{5} \end{gathered}[/tex][tex]\begin{gathered} \cot (t)=\frac{(\frac{5}{13})}{(\frac{12}{13})} \\ =\frac{5}{12} \end{gathered}[/tex]If Vegetable Oil costs $3.47 for 48 ounces, what is the cost of 1 tablespoon of vegetable oil?
A) 7 cents, B) 70 cents C) 4 cents D) $1.40 E) 25 cents
If Vegetable Oil costs $3.47 for 48 ounces, the cost of 1 tablespoon of vegetable oil is 4 cents.
1 tablespoon has alomst 0.5 ounce
If Vegetable Oil costs $3.47 for 48 ounces
Cost of 48 ounces of vegetable oil = $3.47
cost of 1 ounce of vegetable oil = $ 3.47 / 48 = $0.0722
cost of 0.5 ounce of vegetable oil = $0.0722/2 = $0.0361
cost of 0.5 ounce of vegetable oil is $0.0361
1 dollar = 100 cents
0.0361 dollar = 0.0361 x 100 cents
0.0361 dollar = 3.6 cents = 4 cents (approx)
Therefore, if Vegetable Oil costs $3.47 for 48 ounces, the cost of 1 tablespoon of vegetable oil is 4 cents.
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Pythagorean Theorem Task Card #1 A pool table is 9 feet long and 5 feet wide. How far is it from one corner pocket to the diagonally opposite corner pocket? Round to the nearest tenth.
A right triangle is made where the two legs are 9 ft (a) and 5 ft (b), and we have to find the hypotenuse (c). Using Pythagorean Theorem:
c² = a² + b²
c² = 9² + 5²
c² = 81 + 25
c = √106
c ≈ 10.3 ft
5. Julia's test scores on the first four science tests were: 85, 77, 63, 90. Therewill be five tests. She needs an average of at least 80 in order to get a B on herreport card.Part B: What is the minimum score that Julia must earn on her final test in orderto get a B average?
Let the minimum score be x
(85 + 77 + 63 + 90 + x)/5 = 80
315 + x = 400
x = 400 - 315
= 85
Julia must get a minimum score of 85 to get a B average
Latex paint sales for $25 per gallon and will cost you $175 to paint your room if each gallon will cover 330 ft.² how many square feet of wall space do you have in your room
The square feet of wall space in your room if paint cost $25 per gallon and will cost you $175 to paint the room is 2,310 square feet
What is the square feet of wall space in your room?Cost of latex paint per gallon = $25Total cost of paint = $175Square feet covered by each gallon = 330 ft.²Number of latex paint need to paint your room = Total cost of paint / Cost of latex paint per gallon
= $175 / $25
= 7 gallons
Number of square feet of wall space in your room = Number of latex paint need to paint your room × Square feet covered by each gallon
= 7 × 330
= 2,310 square feet
In conclusion, the square feet of wall space in your room is 2,310 square feet
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Stats, Practice Test 5-6 ) There is a class with 6 women and 12 men. a) If I randomly pick 5 students, with replacement. What is the probability that at least 4 of them will be man? b) If I randomly pick 6 students, what is the probability that at least one of them will be a man?
Step 1: Problem
There is a class with 6 women and 12 men. a) If I randomly pick 5 students, with replacement. What is the probability that at least 4 of them will be man? b) If I randomly pick 6 students, what is the probability that at least one of them will be a man?
Step 2: Concept
write an express to 4× + 12 by coming like terms
the initial expression is:
[tex]4x+12[/tex]We can see that they have in common a factor of 4 so we can rewrite it like:
[tex]4(x+3)[/tex]