Answer:
6. 184.275 gr
7. 72 km
8. 368000 cm
Explanation:
To make these conversions, we need to know the following relationships:
1 ounce = 28.35 gr
1 mile = 1.6 km
1 km = 100000 cm
Then, we can convert each expression as follows:
6.5 oz x 28.35gr / 1 oz = 184.275 gr
45 mi x 1.6 km / 1 mi = 72 km
2.3 mi x 1.6 km/ 1 mi = 3.68 km x 100000 cm/ 1km = 368000 cm
Therefore, the answers are:
6. 184.275 gr
7. 72 km
8. 368000 cm
Which function could represent the height in feet, h, of a soccer ball t seconds after being kicked from an initial height of 1 foot?
Let h is the height of the ball after t seconds
The acceleration upward = -32 feet/sec.^2
This situation must be represented by a quadratic function
The form of the function is:
[tex]h=ut+\frac{1}{2}at^2+h_0[/tex]u is the initial velocity
a is the acceleration of gravity
t is the time
h0 is the initial height
From the given, the initial height is 1 foot
The acceleration of gravity is a constant value -32 ft/s^2
The initial velocity is unknown
Let us substitute the values given in the function
[tex]\begin{gathered} h=ut+\frac{1}{2}(-32)t^2+1 \\ h=ut-16t^2+1 \end{gathered}[/tex]Let us arrange the terms from greatest power of t
[tex]h=-16t^2+ut+1[/tex]We have only 1 function in the choices similar to our function
[tex]h=-16t^2+25t+1[/tex]The answer is the second choice
Simplify and then evaluate the equation when x=4 and y =2
We need to plug in
x = 4
y = 2
into the expression and simplify/evaluate.
Let's evaluate:
[tex]\begin{gathered} 5x+2(9y-x)-y \\ x=4,y=2 \\ So, \\ 5(4)+2(9(2)-(4))-(2) \\ =20+2(18-4)-2 \\ =20+2(14)-2 \\ =20+28-2 \\ =46 \end{gathered}[/tex]Answer46a vector w has initial point (0,0) and terminal point (-5,-2) write w in the form w=ai+bj
The initial point is (0,0) and the terminal point (-5,-2).
First, graph the points:
Lets say that A= (0,0) and B = (-5,-2)
So my vector w= line(AB)
Use the component form
Replace the values <-5-0, -2-0>
Then <-5,-2>
In the form w=ai+bj
w = -5i -2j
Looking at the graph we have -2 on the y-axis and -5 on the x-axis.
if -x - 3y = 2 and -8x + 10y = 9 are true equations, what would would be the value of -9x + 7y?
To find the value we add both equations:
[tex]\begin{gathered} (-x-3y)+(-8x+10y)=2+9 \\ -9x+7y=11 \end{gathered}[/tex]Therefore the value of the expression given is 11.
Which of the following numbers is irrational? (A)-1.325 (B)√8 (C)2 (D)4
Answer:
(B)√8
Explanation:
Irrational numbers are numbers which when converted to decimal can be written indefinitely without repeating.
Irrational Numbers are numbers that cannot be written as a terminating or repeating decimal.
Examples of Irrational Numbers are:
[tex]\sqrt{2},\text{ }\pi,\text{ }\frac{22}{7},\text{ }\sqrt{5}\text{, etc.}[/tex]From the given options, the number which is irrational is √8.
Determine the degree of the polynomial 2w with exponent of 2+ 2w:
The degree of the polynomial is 2, because the degree of a polynomial is defined as the same as the greater exponent on the polynomial.
In this case, w² is the greater, then the degree is 2.
Suppose that E and F are independent P(E) = 0.8 and P(F) = 0.4What is P(E and F)?
Answer:
P(E and F) = 0.32
Explanation:
Given that E and F are independent, then
P(E and F) is the multiplication of P(E) and P(F).
P(E) = 0.8, and P(F) = 0.4
P(E and F) = 0.8 * 0.4 = 0.32
Solve the equation below 4X. If your answer is not a whole number enter it as a fraction in lowest terms, using the slash mark (/) as the fraction bar x-5=8x+9X=
Simplify the equation x - 5 = 8x + 9 to obtain the value of x.
[tex]\begin{gathered} x-5=8x+9 \\ x-8x=9+5 \\ -7x=14 \\ x=\frac{14}{-7} \\ =-2 \end{gathered}[/tex]So x = -2.
Which of the following represents the LCM of 98 ab^ 3 and 231 a^ 3 ?
The Least Common Multiple (LCM) for 98 and 231, notation LCM (98, 231), is 3234.
Solution by using the division method:
This method consists of grouping by separating the numbers that will be decomposed on the right side by commas while on the left side we put the prime numbers that divide any of the numbers on the right side. We starting with the lowest prime numbers, divide all the row of numbers by a prime number that is evenly divisible into 'at least one' of the numbers. We stop when it is no longer possible to divide (the the last row of results is all 1's). See below how it works step-by-step.
2 | 98, 231
3 | 49, 231
7 | 49, 77
7 | 7, 11
11 | 1, 11
1 | 1, 1
The LCM is the product of the prime numbers in the first column, so:
LCM = 2 . 3 . 7 . 7 . 11 = 3234
Solution by listing multiples:
This method consists of listing the multiples of all the numbers that we want to find the LCM. Multiples of a number are calculated by multiplying that number by the natural numbers 2, 3, 4, ..., etc. See below:
* The multiples of 98 are 98, 196, 294, 392, 490, 588, ..., 3234
* The multiples of 231 are 231, 462, 693, 924, 1155, ..., 3234
Because 3234 is the first number to appear on both lists of multiples, 3234 is the LCM of 98 and 231.
Hence the answer is The Least Common Multiple (LCM) for 98 and 231, notation LCM (98, 231), is 3234.
To learn more about LCM click here https://brainly.com/question/233244
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A shipment of 10 computers contains 4 with defects. Find the probability that a sample of size 4, drawn from the 10, will not contain a defective computer,The probability is:
ANSWER
[tex]P=\frac{81}{625}[/tex]EXPLANATION
There are 4 defects out of 10 total computers. This means that there are 6 computers without defects.
The probability that 1 computer selected will not be defective is the total number of non-defective computers divided by the total number of computers:
[tex]P(one-without-defect)=\frac{6}{10}[/tex]Therefore, if a sample of 4 computers is selected, the probability that the sample will not contain a defective computer is:
[tex]\begin{gathered} P=\frac{6}{10}\cdot\frac{6}{10}\cdot\frac{6}{10}\cdot\frac{6}{10}=(\frac{6}{10})^4 \\ P=\frac{81}{625} \end{gathered}[/tex]Find an equation of the line that has a slope of -1 and a y intercept of 2. Write your answer in the formy = mx + b.
Based on the information the equation would be:
y = -1x + 2
m=slope
b= y-intercept
Ben earned $400 dollars last month.He worked 3 days in the first week andalso worked 2 days in the secondweek. How much does he earn eachday?
Given Data:
Ben earned $400 last month.
Since in the academic calendar the last month was July consisting of 31 days.
Therefore the amount earned per day can be calculated as
[tex]\frac{400}{31}[/tex]Now, He worked 3 days in the first week and 2 days in the second week.
So the total number of working days is 5.
Therefore the amount earned for 5 days will be
[tex]\frac{400}{31}\times5=64.51[/tex]Therefore the amount for 6 days is approximate $65.
And Hence for each day it is $13.
i need help with this question parts c d and e
ANSWER :
c. None
d. 0
e. (-1, 0)
EXPLANATION :
c. Values of x in which f(x) = -2
From the illustration, the graph does not pass through the y = -2
So there's NO values of x that will give f(x) = -2
d. Values of x in which f(x) = -3
From the illustration, when x = 0, f(x) will be -3
So the value of x is 0
e. x-intercepts are the points in which the graph intersects the x-axis.
In this case, the graph intersects at point (-1, 0)
Can someone please help me do #6 and #8 please
#6:
As it's a rhombus, the diagonal is a bisector, so:
med 2 = 27
med 3 = 27
and
med 5 = 27
med 4 = med 1
Also, the sum of interior angles of a triangle is 180 degrees. Then:
27 + 27 + med 1 = 180
med 1 = 126
med 4 = 126
What is the future value of an ordinary annuity of ₱38,000 per year, for 7 years, at 8% interest compounded annually?
Annuities
The future value (FV) of an annuity is given by:
[tex]FV=A\cdot\frac{(1+i)^n-1}{i}[/tex]Where:
A is the value of the annuity or the regular payment
i is the interest rate adjusted to the compounding period
n is the number of periods of the investment (or payment)
The given values are:
A = $38,000
n = 7 years
i = 8% = 0.08
Substituting:
[tex]\begin{gathered} FV=\$38,000\cdot\frac{(1+0.08)^7-1}{0.08} \\ FV=\$38,000\cdot\frac{(1.08)^7-1}{0.08} \\ \text{Calculate:} \\ FV=\$38,000\cdot\frac{0.7138243}{0.08} \\ FV=\$38,000\cdot8.9228 \\ FV=\$339,066.53 \end{gathered}[/tex]The future value is $339,066.53
With cell phones being so common these days, the phone companies are all competing to earn business by offering various calling plans. One of them, Horizon, offers 700 minutes of calls per month for $45.99, and additional minutes are charged at 6 cents per minute. Another company, Stingular, offers 700 minutes for $29.99 per month, and additional minutes are 35 cents each. For how many total minutes of calls per month is Horizon’s plan a better deal?
For the Horizon offer
There is a cost of $45.99 for 700 minutes plus 6 cents for each additional minute
Since 1 dollar = 100 cents, then
6 cents = 6/100 = $0.06
If the total number of minutes is x, then
The total cost will be
[tex]C_H=45.99+(x-700)0.06\rightarrow(1)[/tex]For the Stingular offer
There is a cost of $29.99 for 700 minutes plus 35 cents for each additional minute
35 cents = 35/100 = $0.35
For the same number of minutes x
The total cost will be
[tex]C_S=29.99+(x-700)0.35\rightarrow(2)[/tex]For Horizon to be better that means, it cost less than the cost of Stingular
[tex]\begin{gathered} C_HSubstitute the expressions and solve for x[tex]\begin{gathered} 45.99+(x-700)0.06<29.99+(x-700)0.35 \\ 45.99+0.06x-42<29.99+0.35x-245 \\ (45.99-42)+0.06x<(29.99-245)+0.35x \\ 3.99+0.06x<-215.01+0.35x \end{gathered}[/tex]Add 215.01 to both sides
[tex]\begin{gathered} 3.99+215.01+0.06x<-215.01+215.01+0.35x \\ 219+0.06x<0.35x \end{gathered}[/tex]Subtract 0.06x from both sides
[tex]\begin{gathered} 219+0.06x-0.06x<0.35x-0.06x \\ 219<0.29x \end{gathered}[/tex]Divide both sides by 0.29 to find x
[tex]\begin{gathered} \frac{219}{0.29}<\frac{0.29x}{0.29} \\ 755.17Then x must be greater than 755.17The first whole number greater than 755.17 is 756
The total minutes should be 756 minutes per month for Horizon's to be the better deal.
Which equation can be used to find the solution of (1/4)y+1=64 ? −y−1=3y−1=3−y+1=3y + 1 = 3
1/4 and 64 can be expressed as follows:
[tex]\begin{gathered} \frac{1}{4}=4^{-1} \\ 64=4^3 \end{gathered}[/tex]Substituting into the equation:
[tex]\begin{gathered} (4^{-1})^{y+1}=4^3 \\ 4^{(-1)(y+1)}=4^3 \\ 4^{-y-1}=4^3 \\ -y-1=3 \end{gathered}[/tex]=Volume of a cylinderThe diameter of a cylindrical construction pipe is 6 ft. If the pipe is 25 ft long, what is its volume?Use the value 3.14 for it, and round your answer to the nearest whole number.Be sure to include the correct unit in your answer.
The volume of a cylinder is given by the following formula:
[tex]V=\frac{\pi\cdot h\cdot d^2}{4}[/tex]Where h is the height and d is the diameter.
We can consider the length of the pipe as the height of the cylinder.
Then h=25 ft and d=6 ft. Replace these values in the formula and solve for V:
[tex]\begin{gathered} V=\frac{3.14\cdot25ft\cdot(6ft)^2}{4} \\ V=\frac{3.14\cdot25ft\cdot36ft^2}{4} \\ V=\frac{2826ft^3}{4} \\ V=706.5ft^3 \\ V\approx707ft^3 \end{gathered}[/tex]The volume is 707 ft^3
xP(x)00.2510.0520.1530.55Find the standard deviation of this probability distribution. Give your answer to at least 2 decimal places
The Solution:
Given:
Required:
Find the standard deviation of the probability distribution.
Step 1:
Find the expected value of the probability distribution.
[tex]E(x)=\mu=\sum_{i\mathop{=}0}^3x_iP_(x_i)[/tex][tex]\begin{gathered} \mu=(0\times0.25)+(1\times0.05)+(2\times0.15)+(3\times0.55) \\ \\ \mu=0+0.05+0.30+1.65=2.0 \end{gathered}[/tex]Step 2:
Find the standard deviation.
[tex]Standard\text{ Deviation}=\sqrt{\sum_{i\mathop{=}0}^3(x_i-\mu)^2P_(x_i)}[/tex][tex]=(0-2)^2(0.25)+(1-2)^2(0.05)+(2-2)^2(0.15)+(3-2)^2(0.55)[/tex][tex]=4(0.25)+1(0.05)+0(0.15)+1(0.55)[/tex][tex]=1+0.05+0+0.55=1.60[/tex]Thus, the standard deviation is 1.60
Answer:
1.60
What is the mean absolute deviation (MAD) of the dada set? 2, 5, 6, 12, 15 Enter your answer as a decimal in the box.
To get the mean absolute deviation, we first need the mean of the set. The mean is calculated by the sum of the values divided by the number of data:
[tex]\begin{gathered} \mu=\frac{2+5+6+12+15}{5} \\ \mu=\frac{40}{5} \\ \mu=8 \end{gathered}[/tex]To get the means absolute deviation, we have to get the absolute difference between each data and the mean, sum them up and divide by the number of data:
[tex]\begin{gathered} d_1=|2-8|=|-6|=6 \\ d_2=|5-8|=|-3|=3 \\ d_3=|6-8|=|-2|=2 \\ d_4=|12-8|=|4|=4 \\ d_5=|15-8|=|7|=7 \\ MAD=\frac{6+3+2+4+7}{5}=\frac{22}{5}=4.4 \end{gathered}[/tex]line AB and CD intersect at E. if the measurement of angle AEC = 12x+5 and the measurement of angle DEB = x+49, find the measurement of angle DEB
We will start by drawing the lines and angles:
By the properties of the angles that are opposed by the vertex, we know that the measure of the angle AEC and the measure of the angle DEB are the same.
So we can express:
[tex]\begin{gathered} m\text{AEC}=m\text{DEB} \\ 12x+5=x+49 \\ 12x-x=49-5 \\ 11x=44 \\ x=\frac{44}{11} \\ x=4 \end{gathered}[/tex]So we can calculate DEB as:
[tex]\text{DEB}=x+49=4+49=53[/tex]The angle DEB has a measure of 53 degrees.
Macy is hosting a party to celebrate her son's baptism. There will be 6 children at the
party. Each child will receive 1/3 of a regular size adult portion. How many full adult
portions will be made to feed the 6 children?
Answer:
2
Step-by-step explanation:
three 1/3 makes a whole and there are 6 children so 3 and 3 is 6 so its 2
Suppose that the functions f and g are defined as follows.f(x) = x² +78g(x) =3x5x70Find the compositions ff and g9.Simplify your answers as much as possible.(Assume that your expressions are defined for all x in the domain of the composition. You do not have to indicate the domain.)
ANSWER
[tex]\begin{gathered} (f\cdot f)(x)=x^4+14x^2+49 \\ (g\cdot g)(x)=\frac{64}{9x^2} \end{gathered}[/tex]EXPLANATION
We are given the two functions:
[tex]\begin{gathered} f(x)=x^2+7 \\ g(x)=\frac{8}{3x} \end{gathered}[/tex]To find (f * f)(x), we have to find the product of f(x) with itself.
That is:
[tex](f\cdot f)(x)=f(x)\cdot f(x)[/tex]Therefore, we have:
[tex]\begin{gathered} (f\cdot f)(x)=(x^2+7)(x^2+7) \\ (f\cdot f)(x)=(x^2)(x^2)+(7)(x^2)+(7)(x^2)+(7)(7) \\ (f\cdot f)(x)=x^4+7x^2+7x^2+49 \\ (f\cdot f)(x)=x^4+14x^2+49 \end{gathered}[/tex]We apply the same procedure to (g * g)(x):
[tex]\begin{gathered} (g\cdot g)(x)=(\frac{8}{3x})(\frac{8}{3x}) \\ (g\cdot g)(x)=\frac{64}{9x^2} \end{gathered}[/tex]Those are the answers.
Help me please don’t use me for pointsthis answer well be 12×
Answer:
9x + 3
Explanation:
Given the below expression;
[tex]1x-7+8x+10[/tex]The 1st to solving the above is to group like terms;
[tex]1x+8x-7+10[/tex]Let's go ahead and evaluate;
[tex]9x+3[/tex]Use the graph to write an equation for f(x).Oy=1(12)Oy=3(4)*Oy=12(4)*Oy=4(3)*
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[tex]\begin{gathered} g(x)=36x-24 \\ g(1)=36(1)-24=36-24=12 \\ g(2)=36(2)-24=72-24=48 \end{gathered}[/tex][tex]y=36x-24[/tex]Can someone please help me solve the following?Please put numbers on graph
Given:
The equation of the hyperbola is given as,
[tex]\frac{y^2}{25}-\frac{x^2}{4}=1........(1)^{}[/tex]The objective is to graph the equation of the hyperbola.
Explanation:
The general equation of hyperbola open in the vertical axis of up and down is,
[tex]\frac{(y-h)^2}{a^2}-\frac{(x-k)^2}{b^2}=1\text{ . . . . . . . .(2)}[/tex]Here, (h,k) represents the center of the hyperbola.
The focal length can be calculated as,
[tex]c=\sqrt[]{a^2+b^2}\text{ . . . . (3)}[/tex]On plugging the values of a and b in equation (3),
[tex]\begin{gathered} c=\sqrt[]{5^2+2^2} \\ =\sqrt[]{25+4} \\ =\sqrt[]{29} \end{gathered}[/tex]The foci can be calculated as,
[tex]\begin{gathered} F(h,k\pm c)=F(0,0\pm\sqrt[]{29}) \\ =F(0,\pm\sqrt[]{29}) \end{gathered}[/tex]The vertices can be calculated as,
[tex]\begin{gathered} V(h,k\pm a)=V(0,0\pm5) \\ =V(0,\pm5) \end{gathered}[/tex]To obtain graph:
The graph of the given hyperbola can be obtained as,
Hence, the graph of the given hyperbola is obtained.
Find the measure of the numbered angles in the rhombus (m1, m2, and m3).
The diagonals of a rhombus intersect at right angles. So, the m<1 is 90 degrees.
The diagonals of a rhombus bisect each vertex angle.
Therefore, the angle of vertex of 24 degree angle angle is 24x2=48.
The opposite angle of 48 degree angle is also 48 degrees. Since the angle is bisected by diagonal,m<2=24 degree.
The sum of opposite angles, 48+48=96.
The sum of other two equal opposite angles, 360-96=264.
The half of 264 is one angle, So, 264/2=132. Again <3=132/2=66.
m<1=90, m<3=66, m<2=24
solve the following equation for x..[tex]5x { }^{2} = 180[/tex]
The square root of 36 has 2 results, one positive and one negative.
[tex]\begin{gathered} x=\sqrt[]{36} \\ x=\pm6 \\ or \\ x_1=6\text{ and }x_2=-6\text{ } \end{gathered}[/tex]How many real solutions does the equation \displaystyle -2x^2-6x+15=2x+5−2x 2 −6x+15=2x+5 have?
-2x² - 6x + 15 = 2x +5
Re-arrange the equation
-2x² - 6x -2x+ 15-5=0
-2x² -8x + 10 = 0
Multiply through by negative one
2x² + 8x - 10 =0
Now;
solve by factorization
Find two numbers such that its product give -20x² and its sum gives 8x and 8x by them
That is;
2x² + 10x - 2x - 10 = 0
2x(x+5) -2(x+5) = 0
(2x - 2) (x+5) = 0
Either 2x - 2 = 0
2x = 2
x= 1
Or
x+5 = 0
x=-5
Hence it has 2 real solutions
Graph the line x= -3 on the axes shown below. Type of line: Choose one
due to the equation that represents the line is a line with no slope defined and is drawn up and down and are parallel to the y-axis.
in this case, since x=-3 it means that this value won't change along the y-axis