Answer:
Explanations
Given the following terms
[tex]12x^5u^8and18w^2x^4u^6[/tex]Find the factors of each term
[tex]\begin{gathered} 12x^5u^8=6\cdot2\cdot x^4\cdot x\cdot u^6\cdot u^2 \\ 18w^2x^4u^6=6\cdot3\cdot w^2\cdot x^4\cdot u^6 \end{gathered}[/tex]Next is to get the common factors from both terms. From the factors derived, we can see that the common factors are 6 * x^4 * u^6
Hence the greatest common factor of these two expressions is 6x^4
w = {1/1 € Z1 € Z,t is odd, and It| ≤ 6}|W| = IDetermine the Cardinal Number
Given:
[tex]W=\lbrace t|t\in Z,t\text{ is odd, and \mid t\mid}\leq6\rbrace[/tex]Required:
We need to find |W|.
Explanation:
We need to find the number of terms in the given set W.
We know that Z is the set of integers.
[tex]|t|\leq6\text{ means the absoluate values of the intergers less than or equal to 6,}[/tex][tex]|-6,-5,-4,-2,-1,0,1,2,3,4,5,6|\text{ }\leq6[/tex]Select the odd numbers.
[tex]W=\lbrace-5,-3,-1,1,3,5\rbrace[/tex][tex]|W|=6[/tex]FInal answer
[tex] {(v + 3)}^{2} + 4 =0[/tex]I don't understand
we will solve the following equation
[tex](v+3)^2+4=0[/tex][tex](v+3)=\pm\sqrt[]{-4}[/tex][tex](v+3)=\pm2i[/tex][tex]v=-3\pm2i[/tex]A line is perpendicular to y = - {x + 7and intersects the point (4,2).What is the equation of thisperpendicular line?y = 3x + [?]
The equation of the perpendicular line is given as
[tex]y=3x+\text{?}[/tex]It goes through the point (4, 2). Lets substitute and find the equation.
[tex]\begin{gathered} y=3x+\text{?} \\ 2=3(4)+\text{?} \\ 2=12+\text{?} \\ So,\text{ ?=-10} \\ \\ \text{Equation of Line} \\ y=3x-10 \end{gathered}[/tex]Answery = 3x - 10a department store sells a pair of shoes with an 81% markup if the store bought the pair of shoes for $55.25 ,what's the selling price to the nearest dollar?
Explanation:
First we have to find how much is the markup price, which is 81% of $55.25:
[tex]M.P.=\frac{81}{100}\times55.25=0.81\times55.25=44.7525[/tex]Now we have to add the markup price to the cost of the shoes to find the selling price:
[tex]S.P.=55.25+M.P.=55.25+44.7525=100.0025[/tex]Answer:
The selling price, rounded to the nearest dollar is $100
What is the volume picture attach
VOLUME OF PRISM = cross sectional area X length
The cross sectional area is a triangle
First we will find the area of the triangle
Area of triangle = base X height / 2
[tex]\begin{gathered} A=\frac{bh}{2} \\ b=9 \\ h=7 \\ A=\frac{9\times7}{2} \\ A=31.5m^2 \\ V=A\times l \\ l=5m \\ V=31.5\times5 \\ V=157.5m^3 \end{gathered}[/tex]You measure 50 textbooks' weights, and find they have a mean weight of 77 ounces. Assume the population standard deviation is 12.3 ounces. Based on this, construct a 95% confidence interval for the true population mean textbook weight.Give your answers as decimals, to two places < μ<
Given that:
- You measure 50 textbooks' weights.
- They have a Mean of 77 ounces.
- The Population Standard Deviation is 12.3 ounces.
You need to use the following formula:
[tex]CI=\bar{x}\pm z\frac{\sigma}{\sqrt{n}}[/tex]Where:
- The Sample Mean is:
[tex]\bar{x}[/tex]- The z-value for the corresponding Confidence Interval Level is "z".
- The Sample Standard Deviation is σ.
- The Sample Size is "n".
In this case:
[tex]\begin{gathered} \bar{x}=77 \\ \sigma=12.3 \\ n=50 \end{gathered}[/tex]By definition, for a 95% Confidence Interval:
[tex]z=1.96[/tex]Then, by substituting values and evaluating, you get these two values:
[tex]CI=77+1.96\cdot\frac{12.3}{\sqrt{50}}\approx80.41[/tex][tex]CI=77-1.96\cdot\frac{12.3}{\sqrt{50}}\approx73.59[/tex]Hence, the answer is:
[tex]73.59<\mu<80.41[/tex]The number of houses in Central Village, New York, grows every year according to the function H(t) = 540(1.039)^t . where H represents the number of houses, and i represents the number of years since January 1995. A civil engineering firm has suggested that a new, larger well must be built by the village to supply its water when the number of houses exceeds 1.000. During which year will this first happen?
Please help me help help me please help help me
We have to solve for x.
We will apply the logarithm properties.
[tex]\begin{gathered} 2^{x-1}=31 \\ \log _2(2^{x-1})=\log _2(31) \\ x-1=\log _2(31) \\ x=\log _2(31)+1 \\ x\approx4.9542+1 \\ x\approx5.9542 \end{gathered}[/tex]Answer: x = 5.9542
. Frankie has $2.75 in coins, all in dimes and nickels. The total number of coinsis 35. If he has d dimes and n nickels, which system models the situation?A)d+n=3510d+5n=2.75B)d+n=2.7510d+5n=35C)d+n=2.755d+10n=35D)d+n=3510d+5n=275
d + n = 35
10d + 25n = 275
Explanation:Note that:
1 dime = $0.1
1 quarter = $0.25
Let the number of dimes be d
Let the number of quarters be n
Frankie has $2.75
0.1d + 0.25n = 2.75
Multiply through by 100
10d + 25n = 275...................(1)
Total number of coins is 35
d + n = 35
Therefore, the system of equations that models the situation is:
d + n = 35
10d + 25n = 275
What is the value of x that makes the following equation true? 3/4 x + 2 = -4
The value of x that satisfy the equation is x=-8
According to Crown ATM Network, the mean ATM withdrawal is $67. Assume thatthe standard deviation for withdrawals is $35. If a randomly sample of 50 ATMwithdrawals is obtained, what is the probability of obtaining a sample meanwithdrawal amount between $70 and $75, rounded to the nearest ten-thousandth (4decimal places)?
We are given the following information
Mean ATM withdrawal = μ = $67
Standard deviation of ATM withdrawal = σ = $35
Sample size = n = 50
The probability of obtaining a sample mean withdrawal amount between $70 and $75 is given by
[tex]\begin{gathered} P(70\le\bar{x}\le75)=P(\frac{\bar{x}-\mu}{\frac{\sigma}{\sqrt[]{n}}}\le z\le\frac{\bar{x}-\mu}{\frac{\sigma}{\sqrt[]{n}}}) \\ P(70\le\bar{x}\le75)=P(\frac{70-67}{\frac{35}{\sqrt[]{50}}}\le z\le\frac{75-67}{\frac{35}{\sqrt[]{50}}}) \end{gathered}[/tex]Factor out the coefficient of the variable term. The expression 3 z + 1 factored is
Suppose you wanted to invest $2500 with a small company owned by a friend of yours that pays 12.2% simple interest on the investment. How long would it take the money to grow to $3500 in this case? Show your work.
We have the following equation
[tex]3500=2500+2500\cdot0.122\cdot t[/tex]where the t is the time we want to know
[tex]\begin{gathered} 1000=2500\cdot0.122\cdot t \\ 1000=305t \\ t=\frac{1000}{305}=3.2786 \end{gathered}[/tex]so we have to wait at least 3 months to our money to increase to 3500
a coffee shop served 24 people before 7:00 a.m. 2/3 had regular coffee 1/8 had decaf and the remaining order specialty coffee how many customers ordered a specialty coffee
Since 2/3 of 24 had regular coffe, then:
[tex]24\cdot\frac{2}{3}=\frac{24\cdot2}{3}=\frac{48}{3}=16[/tex]We have that 16 people had regular coffe. Now for the people that had decaf:
[tex]24\cdot\frac{1}{8}=\frac{24}{8}=3[/tex]There were 3 people that drank decaf. The remaining had the specialty coffe, then:
[tex]24-16-3=24-19=5[/tex]Therefore, 5 people asked for the specialty coffee
A catapult hurls a cantaloupe from a heightof 12 feet at an initial velocity of 47 feetper second.n(t) = -16 t2 + 47t +12
To find the equation we use:
[tex]h(t)=-\frac{1}{2}gt^2+v_0t+h_0[/tex]Where h is the gravity, v0 is the intial velocity and h0 is the initial height.
Then, we replace the values,
[tex]\begin{gathered} g=32\frac{ft}{s^2};v_0=47\frac{ft}{s};h_0=12ft \\ h(t)=-\frac{1}{2}32t^2+47t+12 \\ h(t)=-16t^2+47t+12 \end{gathered}[/tex]How do I Solve for #16? And what’s the description and rule?
It's show mirror image about the x axis:
For any mirror image about any axis of line the mirror point is same distance back side about the axis that mean:
So A,R,G,W all point image same distance about the axis .
Solve for X. Justify your answer. (9x –13) X Y (4x + 2)° your answer
The triangle shows two sides with single strokes which indicates that the two sides are of equal length.
What we have here is an isosceles triangle. The two base angles subtended by the equal sides are also equal in measure.
This means 9x - 13 = 4x + 2.
[tex]\begin{gathered} 9x-13=4x+2 \\ \text{Collect all like terms} \\ 9x-4x=2+13 \\ 5x=15 \\ \text{Divide both sides by 5} \\ x=3 \\ \text{That means the angles are;} \\ 9x-13 \\ =9(3)-13 \\ =27-13 \\ =14 \\ \text{Also,} \\ 4x+2 \\ =4(3)+2 \\ =12+2 \\ =14 \end{gathered}[/tex]Both base angles measure 14 degrees
translate and solve:the Quotient of a number and 6 minus 3 is 1
Let x be the unknown number. Then the quotient of a number and 6 is:
[tex]\frac{x}{6}[/tex]To this be substract 3:
[tex]\frac{x}{6}-3[/tex]Now, this is 1, then:
[tex]\frac{x}{6}-3=1[/tex]Now we solve the equation,
[tex]\begin{gathered} \frac{x}{6}-3=1 \\ \frac{x}{6}=1+3 \\ \frac{x}{6}=4 \\ x=4\cdot6 \\ x=24 \end{gathered}[/tex]Therefore, x=24.
The Vols scored 14 points less than 3 times the Titans score this weekend. If the sum of their points was 70, find how many each team scored.
We can define some notation at first for this problem. Let V the score for The Vols and T for the Titans last weekend. From the information given we have the following conditions:
[tex]V+T=70\text{ (1)}[/tex][tex]V=3T-14\text{ (2)}[/tex]Now if we replace euqation (2) into (1) we have:
[tex]3T-14+T=70[/tex]And if we solve for T we got:
[tex]4T=84[/tex][tex]T=\frac{84}{4}=21[/tex][tex]V=(3\cdot21)-14=49[/tex]The radius of a circle is 8 kilometers. What is the area of a sector bounded by a 144° arc?Give the exact answer in simplest form. ____ square kilometers. (pi, fraction,)
Given the Circle below with radius r,
[tex]\text{Where r = 8km, }\phi=144^0\text{ and }\pi=\pi[/tex]The formula for the area, A, of the sector is given below as,
[tex]A=\frac{\phi}{360^0}\times\pi r^2[/tex]Substituting for r and the ∅ into the formula above,
[tex]\begin{gathered} A=\frac{144^0}{360^0}\times\pi\times8^2 \\ A=\frac{2}{5}\times\pi\times64=25\frac{3}{5}\pi km^2 \end{gathered}[/tex]Hence, Area A of the sector is 25 3/5 km²
I need help, can you help me, please and thank you!
To determine the lenght in the blueprint we divide the measurements in feet by 8 then:
Living room:
[tex]3\times4[/tex]Kitchen:
[tex]3\times3[/tex]Office:
[tex]3\times2[/tex]Bedroom:
[tex]3\times2[/tex]Bedroom:
[tex]4\times4[/tex]Bathroom:
[tex]4.5\times5[/tex]Factor 10s + 25.Write your answer as a product with a whole number greater than 1.
10s+25
Factor by 5:
5 (2s+5)
Two sides of a triangle are 5 and 15. Which of the following cannot be the third side? A. 6B. 12C. 19D. 20
Given:
Two sides of a triangle are 5 and 15.
To find:
Chose the correct option which cannot be the third side.
Explanation:
The length of a side of a triangle is less than the sum of the lengths of the other two sides and greater than the difference of the lengths of the other two sides.
Here, a sum of the two given sides is:
[tex]5+15=20[/tex]Also, the difference of two given sides,
[tex]15-5=10[/tex]So, the third side must be in between,
[tex]\begin{gathered} 15-5<\text{ third side < 15 +}5 \\ 10<\text{ third side < 20} \end{gathered}[/tex]Therefore, option (A) is not true according to the above property as 6 is less than 10.
Final answer:
Hence, (A) 6 cannot be the third side.
can u help me with this question
Let:
A = Probability of choose a can of tomato soup
B = Probability of choose a can of cheese soup
P(A) = (Number of cans of tomato soup)/(Total of cans of soup) = 2/10 = 1/5
P(B) = (Number of cans of cheese soup)/(Total of cans of soup) = 2/10 = 1/5
Since A and B are mutually exclusive
P(A ∩ B) = P(A)*P(B) = (1/5)*(1/5) = 1/25
5÷ 1/2=there are halves in one wholethere are halves in 5 wholes 5 is 1/2 of what number?
Answer:
There are 10 halves in 5 wholes
and
5 is 1/2 of 10
there are 2 halves in one whole
[tex]5\text{ }\div\text{ }\frac{1}{2}=10[/tex]Explanation:
Given the operation;
[tex]5\text{ }\div\text{ }\frac{1}{2}[/tex]To solve;
[tex]5\text{ }\div\frac{1}{2}=5\times\frac{2}{1}=\frac{5\times2}{1}=\frac{10}{1}=10[/tex]Therefore;
[tex]5\text{ }\div\text{ }\frac{1}{2}=10[/tex]There are 10 halves in 5 wholes
and
5 is 1/2 of 10
there are 2 halves in one whole
Question 1 Directions: Find the sector area for the circle below. Round to the 145° 18 ft 2
Do you have a picture of your question?
ok
angle = 145
radius = 18 ft
[tex]\begin{gathered} \text{Area = }\frac{\theta}{360}pi(r)^2 \\ \text{Area = }\frac{145}{360}(3.14)(18)^2 \\ \text{Area = (0.402)(3.14)(324)} \\ \text{Area = 409 ft}^2 \end{gathered}[/tex]Well the result from the calculator is 409.77 ft^2
I need to round to the near tenth or hundredth?
Rounding to the nearest tenth = 409.8 ft^2
Rounding to the nearest hundred = 409.77 ft^2
if the equation has the two numbers like that witch one would I use to solve the problem or would I do -10 + 30 and use that number to do 0+30 kinda like that
SOLUTION
When x = 0, y is
[tex]\begin{gathered} y=-10(0)+30 \\ y=0+30 \\ y=30 \end{gathered}[/tex]When x = 1, y is
[tex]\begin{gathered} y=-10(1)+30 \\ y=-10+30 \\ y=20 \end{gathered}[/tex]When x = 3, y is
[tex]\begin{gathered} y=-10(3)+30 \\ y=-30+30 \\ y=0 \end{gathered}[/tex]So the table is shown below
Hii I really need help with this question I don’t understand , I have to determine the intercept of the line but I don’t know how?
Given:-
An image.
To find the points intercept:-
The point on the x-axis is (-10,0). we call this the x-intercept.
The point on the y-axis is (0,-45). we call this the y-intercept.
So this is the required solution.
Kofi and Ama together invest 52million in a business and agree to share the profit in the ratio of their investment. kofi received 5million and Ama received 8million as profit at the end of the first year. How much did each invest
let their ratio of investment
[tex]x\colon y[/tex]then
[tex]x+y=52[/tex]again
[tex]\begin{gathered} \frac{x}{y}=\frac{5}{8} \\ 8x=5y \end{gathered}[/tex]Now
[tex]\begin{gathered} 8x+8y=416 \\ 5y+8y=416 \\ 13y=416 \\ y=32 \end{gathered}[/tex]So
[tex]x=\frac{5\times32}{8}=20[/tex]So kofi invest 20 million and ama invest 32 million each
i just need someone to match the answers to the questions, not an explanation .
Given
Properties
Find
Correct Match of given properties
Explanation
47) 25.36 = 36.25 - Commutative Property of Multiplication
48) (-29).1=-29 - Identity property of multiplication
49) 15(2+7) = 15.2 = 15.7 - Distributive Property of multiplication over addition
50) 31 + (-31) = 0 - Inverse property of addition
51) (17 + 3) + 19 = 17 + (3 + 19) - Associative property of addition
52) -51 + 0 = -51 - Identity property of addition
53) (5/7)(7/5) = 1 - Inverse property of multiplication
54) 8 + 21 = 21 + 8 - Commutative property of addition
55) (6.9).13 = 6.(9.13) - Associative property of Multiplication
Final Answer
47) Commutative Property of Multiplication
48) Identity property of multiplication
49) Distributive Property of multiplication over addition
50) Inverse property of addition
51) Associative property of addition
52) Identity property of addition
53) Inverse property of multiplication
54) Commutative property of addition
55) Associative property of Multiplication