Answer:
Options 3 and 4 are correct
Step-by-step explanation:
-3>1 is false bc a positive is always greater than a negative
-3=3 is false because a positive is not equal to a negative
1<3 is correct because 1 is less than 3
-3<1 is correct because a negative is always less than a positive.
Answer:
1 < 3
–3 < 1
Step-by-step explanation:
If QR = 3x; LM - 8x -17; and ST = 31 calculate LM.
Answer:
5
Step-by-step explanation:
The midsegment of a trapezoid is equal to one half the sum of the bases.
1. Set up the equation using the midsegment formula: 1/2 (QR + ST)
1/2 (3x + 31) = 8x - 17
2. Solve
1.5x + 15.5 = 8x - 17
32.5 = 6.5x
x = 5
Answer:
[tex]\huge \boxed{23}[/tex]
Step-by-step explanation:
QR < LM < ST
LM is the middle segment, it is in between the length of QR and ST.
LM is also the average or mean of QR and ST.
(QR+ST)/2 = LM
(3x+31)/2 = 8x-17
Multiply both sides by 2.
(2)(3x+31)/2 = (2)8x-17
3x + 31 = 16x - 34
Subtract 16x and 31 from both sides.
3x + 31 - 16x - 31 = 16x - 34 - 16x - 31
-13x = -65
Divide both sides by -13.
(-13x)/-13 = -65/-13
x = 5
Substitute x = 5 for LM.
8(5) - 17
40 - 17
= 23
PLEASE HELP
Two six-sided fair dice are rolled. The probability that at least one number is odd and the sum of the two numbers is even is *blank . The probability that exactly one number is 6 and the product of the two numbers is at most 15 is * blank .
Answer:
1/4
1/3
Step-by-step explanation:
If one number is odd, then the other number must also be odd in order for the sum to be even. There are 3 odd numbers per dice, so the probability is (3/6)² = 1/4.
If one number is 6, the other number must be 1 or 2 for the product to be at most 15. The probability is 2/6 = 1/3.
A square has a perimeter of 24cm. Work out its area.
Answer:
A = 36 cm^2
Step-by-step explanation:
The perimeter of a square is given by
P =4s
24 = 4s
Divide by 4
24/4 = 4s/4
6 =s
The area of a square is
A =s^2
A = 6^2
A = 36 cm^2
Can someone please check my answer? I really need help with this
Answer:
a = – 8
Step-by-step explanation:
From the question:
When P(x) = 2x³ – ax² + 4x – 4 is divided by x – 1, it gives a reminder of 10.
To obtain the value of a, we shall equate x – 1 to 0 as illustrated below:
x – 1 = 0
x = 0 + 1
x = 1
Next, we shall substitute the value of x into 2x³ – ax² + 4x – 4 and equating it to 10 as illustrated below:
2x³ – ax² + 4x – 4 = 10
x = 1
2(1)³ – a(1)² + 4(1) – 4 = 10
2 – a + 4 – 4 = 10
2 – a = 10
Collect like terms
– a = 10 – 2
– a = 8
Divide through by –1
a = – 8
Therefore, the value of a is –8.
A shell of mass 8.0-kg leaves the muzzle of a cannon with a horizontal velocity of 600 m/s. Find the recoil velocity of the cannon, if its mass is 500kg.
Answer:
velocity of recoil velocity of cannon is -9.6 m/sec
Step-by-step explanation:
according to law of conservation of momentum
total momentum of isolated system of body remains constant.
momentum = mass of body* velocity of body.
__________________________________
in the problem the system is
shell + cannon
momentum of shell = 8*600 = 4800 Kg-m/sec
let the velocity of cannon be x m/sec
momentum of cannon = 500*x = 500x Kg-m/sec
initially the system of body is in rest (before the shell is fired) hence, total momentum of the system i is 0
applying conservation of momentum
total momentum before shell fired = total momentum after the shell is fired
0 = momentum of shell + momentum of cannon
4800 + 500x = 0
x = -4800/500 = -9.6
Thus, velocity of recoil velocity of cannon is -9.6 m/sec
here negative sign implies that direction of velocity of cannon is opposite to that of velocity of shell.
Which of the binomials below is a factor of this trinomial?
X^2 + 5x + 6
Answer:
(x + 2) , (x + 3) are factors
Step-by-step explanation:
Given
x² + 5x + 6
Consider the factors of the constant term (+ 6) which sum to give the coefficient of the x- term (+ 5)
The factors are + 2 and + 3, since
2 × 3 = 6 and 2 + 3 = 5 , thus
x² + 5x + 6 = (x + 2)(x + 3)
What am I supposed to do when parentheses are side by side like this?
Answer:
Evaluate each expression inside both grouping symbols, then multiply the result.
Step-by-step explanation:
[tex]\displaystyle (3 - 1)(4 + 2) = (2)(6) = 12[/tex]
G - Grouping Symbols
E - Exponents
M\D - Division & Multiplication [left to right]
S\A - Subtraction & Addition [right to left OR vice versa]
I am joyous to assist you at any time.
In a mathematics class, half of the students scored 89 on an achievement test. With the exception of a few students who scored 48, the remaining students scored 79. Which of the following statements is true about the distribution of scores?
A. The mean is less than the median.
B. The mean and the median are the same.
C. The mean is greater than the mode.
D. The mean is greater than the median.
Answer:
A. The mean is less than the median.
Step-by-step explanation:
Half the students scored 89. The next highest score is 79. So the median is (79 + 89) / 2 = 84.
A few students scored 48, so the mean is slightly lower than the mean of 79 and 89.
Therefore, the mean is less than the median.
Answer:
A. The mean is less than the median.
Step-by-step explanation:
Say that half the students answered 79, and the rest 89.
We'd have a distribution something like this:
79 79 79 89 89 89
The median is in the smack middle. Since we have an even number of scores, the median would be the number between the 2 middle numbers. Here, that's 79 and 89. Thus, the median is 84.
The mean is the "average" of all values. Since we have an equal number of 79s to 89s, the mean would also be in the middle of those values (balancing an equal number on both sides). So, the mean would also be 84.
HOWEVER, we have an unspecified number of 48's.
The distribution looks something like
48 79 79 89 89 89
The median is still the same, smack middle between the 2 values in the middle. 84.
But the mean has changed. We have smaller values on the left. The mean is brought down by these 48 values. It doesn't matter how many, the fact that we have at least 1 will bring the mean, the average, down.
You check 20 batteries.Fourteen of the batteries do not have a charge. What is the experimental probability that the next battery you check does not have a charge?
Answer:
[tex]\dfrac{7}{10}[/tex]
Step-by-step explanation:
Given that
Number of batteries that do not have a charge = 14
Total number of batteries = 20
To find:
Experimental probability that the next battery checked does not have a charge = ?
Solution:
First of all, let us learn about the definition of experimental probability.
Probability is the chances of happening of an event.
Formula for probability of happening of an event E is given as:
[tex]P(E) = \dfrac{\text{Number of favorable cases}}{\text {Total number of cases}}[/tex]
Here we have to find the probability of checking a battery that has no charge.
So, number of favorable cases = Number of batteries that do not have a charge = 14
AND
Total Number of cases = Total number of batteries to be checked = 20
So, the required probability is:
[tex]\dfrac{14}{20} = \bold{\dfrac{7}{10}}[/tex]
The total cost for a bucket of popcorn and 4 movie tickets is $56. The total cost for the same size bucket of popcorn and 6 movie tickets is $80. The cost of a bucket of popcorn is $8. Which equation represents the relationship between y, the total cost of the popcorn and movie tickets, and x, the number of movie tickets that are purchased?
Answer: y=12x+8
Step-by-step explanation:
The relationship between y, the total cost of the popcorn and movie tickets, and x, the number of movie tickets that are purchased will be y = 12x + 8.
How to form an equation?Determine the known quantities and designate the unknown quantity as a variable while trying to set up or construct a linear equation to fit a real-world application.
In other words, an equation is a set of variables that are constrained through a situation or case.
Let's suppose the cost of popcorn is P and the cost of movie tickets is M then
P + 4M = 56
P + 6M = 80
Given that P =$8 hence by putting it to the equation 1
8 + 4M = 56
4M = 48
M = 12 now
Let x number of movie have watch then
y = 12x + 8 will be the formation of the equation.
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Somebody helpppp meeee ???
Answer:
Step-by-step explanation:
plane parallel to the vertical axis :a rectangle
plane parallel to the circular base: a circle
plane making an angle with the vertical axis without passing though the base or top surface :an oval
plane making an angle with the vertical axis and passing through the base and top surface :a pair of curved lines connected by straight lines at each of their endpoints
plane making an angle with the vertical axis and passing through either the base or the top surface, but not both: a cut-off section of an oval whose boundary has two endpoints connected by a straight line
A baker has three banana muffin recipes. Recipe AAA uses 333 bananas to make 121212 muffins. Recipe BBB uses 555 bananas to make 242424 muffins. Recipe CCC uses 111111 bananas to make 484848 muffins. Order the recipes by number of bananas per muffin from least to greatest.
Answer:
The order from least to greatest is B, A, C
Step-by-step explanation:
Given
Recipe A = 3 bananas to 12 Muffins
Recipe B = 5 bananas to 24 Muffins
Recipe C = 11 bananas to 48 Muffins
Required
Order the recipe from least to greatest
To solve this, we have to divide the number of bananas by number of muffins; this will give the unit banana per muffin
Recipe A: 3 bananas to 12 Muffins
[tex]A = \frac{3}{12}[/tex]
[tex]A = 0.25[/tex]
Recipe B: 5 bananas to 24 Muffins
[tex]B = \frac{5}{24}[/tex]
[tex]B = 0.2083[/tex]
Recipe C: 11 bananas to 48 Muffins
[tex]C = \frac{11}{48}[/tex]
[tex]C = 0.229167[/tex]
By comparison;
Recipe B (0.2083) is the smallest; followed by Recipe C (0.229167) then Recipe A (0.25)
Hence; the order from least to greatest is B, A, C
Answer:
its BCA
Step-by-step explanation:
What is the product of complex conjugates? (1 point)
the product of complex conjugates is a difference of two squares and is always a real number
the product of complex conjugates may be written in standard form as a+bi where neither a nor b is zero
the product of complex conjugates is the same as the product of opposites
the product of complex conjugates is a sum of two squares and is always a real number
Answer:
A. the product of complex conjugates is a difference of two squares and is always a real number
Step-by-step explanation:
Given a complex number z1 = x+iy where x is the real part and y is the imaginary part.
The conjugate of a complex number is the negative form of the complex number z1 above i.e z2= x-iy (The conjugate is gotten by mere changing of the plus sign in between the terms to a minus sign.
Taking the product of the complex number and its conjugate will give;
z1z2 = (x+iy)(x-iy)
z1z2 = x(x) - ixy + ixy - i²y²
z1z2 = x² - i²y²
.since i² = -1
z1z2 = x²-(-1)y²
z1z2 = x²+y²
The product gave a real function x²+y² since there is no presence of complex number 'i'
It can also be seen that the product of the complex numbers z1z2 is like taking the difference of two square. An example of difference of two square is that of two values a and b which is (a+b)(a-b).
From the above solution, it can be concluded that the product of complex conjugates is a difference of two squares and is always a real number.
please help me for the homework
Answer:
refer to the pic attached
rational number 3 by 40 is equals to
Answer:
6/80, 9/120, 12/160 etc
Answer:
3/40 = 6/80 = 9/120 = 12/160 etc......
Hope it helps
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What us 6+8(4w-7)-(2w+1)
Answer:
30w-51
Step-by-step explanation:
6+8(4w-7)-(2w+1)
Distribute
6 + 32w-56 -2w-1
Combine like terms
32w-2w +6-56 -1
30w-51
Answer:W=1.7
Step-by-step explanation: Simplifying
0 = 6 + 8(4w + -7) + -1(2w + 1)
Reorder the terms:
0 = 6 + 8(-7 + 4w) + -1(2w + 1)
0 = 6 + (-7 * 8 + 4w * 8) + -1(2w + 1)
0 = 6 + (-56 + 32w) + -1(2w + 1)
Reorder the terms:
0 = 6 + -56 + 32w + -1(1 + 2w)
0 = 6 + -56 + 32w + (1 * -1 + 2w * -1)
0 = 6 + -56 + 32w + (-1 + -2w)
Reorder the terms:
0 = 6 + -56 + -1 + 32w + -2w
Combine like terms: 6 + -56 = -50
0 = -50 + -1 + 32w + -2w
Combine like terms: -50 + -1 = -51
0 = -51 + 32w + -2w
Combine like terms: 32w + -2w = 30w
0 = -51 + 30w
Solving
0 = -51 + 30w
Solving for variable 'w'.
Move all terms containing w to the left, all other terms to the right.
Add '-30w' to each side of the equation.
0 + -30w = -51 + 30w + -30w
Remove the zero:
-30w = -51 + 30w + -30w
Combine like terms: 30w + -30w = 0
-30w = -51 + 0
-30w = -51
Divide each side by '-30'.
w = 1.7
Simplifying
w = 1.7
If it is now January, what month will it be 500 months from
now?
(a) January
(b) June
(C) September
(d) December
PLEASE HELP MEEE How can a company use a scatter plot to make future sale decisions
Answer:
by tracking data of how much money was made on one product in a certain amount of time
Step-by-step explanation:
what is the period of the function F(x)=2sec(2x+3)
Answer: π
Step-by-step explanation:
The standard form of a secant equation is: y = A sec(Bx - C) + D where
A = AmplitudePeriod (P) = 2π/BC = Phase Shift D = vertical shift (also the center line)Given: F(x) = 2 sec(2x + 3)
↓
B=2
Period = 2π/B
= 2π/2
= π
jacob received $500 for christmas from his parents, he wants to put it into an account that will pay him 7.75% interest each year. if he wants to withdraw all his funds at the end of the year. how much will he withdraw
Answer:
He will have $538.75 after one year.
Step-by-step explanation:
First we need to find how much is 7.75% of 500. We can find it by multiplying 500 x .0775
This equals 38.75
That means after one year, he has $38.75 more.
500+38.75=538.75
He will have $538.75 after one year.
1. Draw the graph of f(x) = cos x for 0 I know how to construct the graph but I don’t know how to get the figures. Please help
Answer:
Please refer to the attached figure.
Step-by-step explanation:
Given the function:
[tex]f(x) =cosx \ where\ \{0^\circ\leq x\leq 360^\circ\}[/tex]
OR, the given function can also be written as:
[tex]y = f(x) = cosx[/tex]
We know that graph of cosine is a wave.
and the range of cosine function is [-1, 1]
First of all, let us have a table of values at major values of x.
[tex]x = 0, f(x) = 1\\x = 90, f(x) = 0\\x = 180, f(x) = -1\\x = 270, f(x) = 0\\x = 360, f(x) = 1[/tex]
So, the table of values for f(x) is:
[tex]\begin{center}\begin{tabular}{ c c }x & cosx \\0 & 1 \\90 & 0\\180 & -1\\270 & 0\\360 & 1\\\end{tabular}\end{center}[/tex]
Let us mark these points on the xy coordinate axis where x axis represents value of x and y axis represents value of [tex]f(x) = cosx[/tex] and then join the points using a wave.
Please refer to the attached graph for the answer image.
A small toy car costs $3. A large toy car costs 5 times as much as the small one. Aaron wants to buy one of each. Which equation can he use to find the cost (a) of the two cars?
Answer: He can use 3 x 5 = 15 and 15 + 3.
Step-by-step explanation:
Since a small car is $3, and the large car is 5x the price of the small car, he can use the equation 3 x 5 = 15, because the small car is $3, and the large car is 5x the price. You can use 15 + 3 = 18, because the small car is $3, so you also have to add that.
Here to help!
The equation is x + 5x = 18 , where x is the cost of small toy car and the total cost of the two cars = $ 18
What is an Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the total cost of the two cars be A
Now , the equation will be
Let the cost of the small toy car be = x
The cost of small toy car = $ 3
The cost of the large car = 5 x cost of small toy car
Substituting the values in the equation , we get
The cost of the large car = 5 x 3
The cost of the large car = $ 15
So , the cost of two cars = x + 5x
Substituting the values in the equation , we get
The total cost of the two cars A = 15 + 3
The total cost of the two cars A = $ 18
Therefore , the value of A is $ 18
Hence , the equation is A = x + 5x
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Set A={XIX is an even whole number between 0 and 2) = 0
True? or false?
false
Step-by-step explanation:
false
find the value of x if 64=xmod9
64 = 63 + 1 = 7*9 + 1, so taken modulo 9, 64 is equivalent to x = 1.
Write an expression that represents an increase of 5% over the
original cost of $d as both a sum and product of d.
Answer:
Sum equation: [tex]d + 0.05d[/tex]
Product equation: [tex]1.05d[/tex]
Step-by-step explanation:
If we have an increase in 5% of d, that means that 5% of d ([tex]0.05\cdot d[/tex]) will be the total amount of money added to it.
However, we need to still count the original price of d, if we increase it by 5%!
So we add d to 0.05d.
[tex]d + 0.05d[/tex] is the sum equation.
Now, we can create the product equation for d by expanding the coefficients for the previous equation, [tex]d + 0.05d[/tex].
[tex]1d + 0.05d[/tex]
We can add like terms here: [tex]1 + 0.05 = 1.05[/tex]! So we can just multiply this by d for our product equation.
[tex]1.05d[/tex]
Hope this helped!
What’s the difference between rational and irrational numbers?
Answer:
rational numbers are perfect squares irrational numbers are non terminating/go on forever
Step-by-step explanation:
Why the answer question now correct
Answer:
461.58 in²
Step-by-step explanation:
The surface area (A) is calculated as
A = area of base + area of curved surface
= πr² + πrl ( r is the radius of base and l is slant height )
= 3.14 × 7² + 3.14 × 7 × 14
= 3.14 × 49 + 3.14 × 98
= 3.14(49 + 98)
= 3.14 ×147
= 461.58 in²
Of the students at Milton Middle School, 120 are girls. If 50% of the students are girls, how many total students are there at Milton Middle school
A new brand of gym shoe claims to add up to 2 inches to an athlete’s vertical leaps. Design an experiment to test this claim.
Describe a sample procedure.
A) Find the average vertical leap of all the athletes in their regular shoes. Give the control group the new shoes and the experimental group a different pair of shoes. Find the average vertical leap of the athletes in both groups. Compare the increases in vertical leap for each group.
B) Find the average vertical leap of all the athletes in their regular shoes. Give the experimental group the new shoes and the control group a different pair of shoes. Find the average vertical leap of the athletes in both groups. Compare the increases in vertical leap for each group.
C) Find the average vertical leap of a group of athletes in their regular shoes. Then give them each the new shoes and find their average vertical leap. Compare the before and after results.
Answer:
The correct option is (B).
Step-by-step explanation:
In this case, we need to test whether the claim made by the new brand of gym shoe is correct or not.
Claim: A new brand of gym shoe claims to add up to 2 inches to an athlete’s vertical leaps.
So, we need to test whether the average vertical leap of all the athletes increased by 2 inches or not after using the new brand of gym shoe.
The sample procedure would be to compute the average vertical leap of a group of athletes in their regular shoes (or a different pair) and the average vertical leap of a group of athletes in their new shoes.
Compare the two averages to see whether the difference is 2 inches or not.
The experimental group would be the one with the new shoes and the control group would be the one with the different pair of shoes.
Thus, the correct option is (B).
Answer:
B) Find the average vertical leap of all the athletes in their regular shoes. Give the experimental group the new shoes and the control group a different pair of shoes. Find the average vertical leap of the athletes in both groups. Compare the increases in vertical leap for each group.
Step-by-step explanation:
Prove that the diagonals of a parallelogram bisect each other. The midpoints are the same point, so the diagonals _____
Answer:
Below
Step-by-step explanation:
To prove that the diagonals bisect each other we should prove that they have a common point.
From the graph we notice that this point is E.
ABCD is a paralellogram, so E is the midpoint of both diagonals.
●●●●●●●●●●●●●●●●●●●●●●●●
Let's start with AC.
● A(0,0)
● C(2a+2b,2c)
● E( (2a+2b+0)/2 , (2c+0)/2)
● E ( a+b, c)
●●●●●●●●●●●●●●●●●●●●●●●●
BD:
● B(2b,2c)
● D(2a,0)
● E ( (2a+2b)/2 , 2c/2)
● E ( a+b ,c)
●●●●●●●●●●●●●●●●●●●●●●●●●
So we conclude that the diagonals bisect each others in E.