Answer:
a) rCn = 1176
b) 2352
Step-by-step explanation:
a)Each committee should be formed with 3 members ( no two members could be of the same state) then
Let´s fix a senator for any of the 50 states so in the new condition we need to combined 49 senators in groups of 2 then
rCn = n! / (n - r )! *r!
rCn = 49!/ (49 - 2)!*2!
rCn = 49*48*47! / 47!*2!
rCn = 49*48 /2
rCn = 1176
So we can choose in 1176 different ways a senator for a given state
b) To answer this question we have to note, that, 1176 is the number of ways a committee can be formed with senators of different sate (taking just one senator for state ) if we have 2 senators we need to multiply that figure by 2.
1176*2 = 2352
find the values of x and y that make k ll j and m ll n
Answer:
x = 80
y = 130
Step-by-step explanation:
The 2 angles are supplementary. so, x-30 + x+50 = 180.
We solve and get 2x = 180-20
x = 80
y = x+50, because of parallel rules.
y = 130
Answer:
x = 80
y = 130
Step-by-step explanation:edge 2020
plz help.... 2|x-3|-5=7
Answer:
x = -3 and x = 9.
Step-by-step explanation:
2|x - 3| - 5 = 7
2|x - 3| = 12
|x - 3| = 6
x - 3 = 6
x = 9
-(x - 3) = 6
-x + 3 = 6
-x = 3
x = -3
Hope this helps!
Answer:
x=9 x=-3
Step-by-step explanation:
2|x-3|-5=7
Add 5 to each side
2|x-3|-5+5=7+5
2|x-3|=12
Divide by 2
2/2|x-3|=12/2
|x-3|=6
There are two solutions to an absolute value equation, one positive and one negative
x-3 =6 x-3 = -6
Add 3 to each side
x-3+3 = 6+3 x-3+3 = -6+3
x=9 x = -3
The number that is 75% of one less than a number n. As an expression THX!!!! i Promise to mark you brainliset
Answer:
x = [tex]\frac{3}{4}(n-1)[/tex]
Step-by-step explanation:
It's given in the question that '' The number is 75% of one less than a number n"
Let the number is 'x'.
One less than a number 'n' will be = (n - 1)
75% of one less than a number will be = 75% of (n -1)
= [tex]\frac{75}{100}(n-1)[/tex]
= [tex]\frac{3}{4}(n-1)[/tex]
Therefore, the desired expression to get the number 'x' will be,
x = [tex]\frac{3}{4}(n-1)[/tex]
Answer:
3/4(n-1)
Step-by-step explanation:
did it in rsm
Please help. I’ll mark you as brainliest if correct!
Answer:
8lb of the cheaper Candy
17.5lb of the expensive candy
Step-by-step explanation:
Let the cheaper candy be x
let the costly candy be y
X+y = 25.5....equation one
2.2x +7.3y = 25.5(5.7)
2.2x +7.3y = 145.35.....equation two
X+y = 25.5
2.2x +7.3y = 145.35
Solving simultaneously
X= 25.5-y
Substituting value of X into equation two
2.2(25.5-y) + 7.3y = 145.35
56.1 -2.2y +7.3y = 145.35
5.1y = 145.35-56.1
5.1y = 89.25
Y= 89.25/5.1
Y= 17.5
X= 25.5-y
X= 25.5-17.5
X= 8
Identify the correct HYPOTHESES used in a hypothesis test of the following claim and sample data:
Claim: "The average battery life (between charges) of this model of tablet is at least 12 hours."
A random sample of 80 of these tablets is selected, and it is found that their average battery life is 11.58 hours with a standard deviation of 1.93 hours. Test the claim at the 0.05 significance level.
a. H0: p = 12 vs. H1: p < 12
b. H0: ? = 12 vs. H1: ? < 12
c. H0: p = 12 vs. H1: p > 12
d. H0: ? = 12 vs. H1: ? > 12
Answer:
The null hypothesis is ;
H0 ≥ 12
While the alternative hypothesis H1 is ;
H1 < 12
Step-by-step explanation:
Here, we want to correctly identify the null hypothesis H0 and the alternative hypothesis H1
The null hypothesis is as follows ;
H0 ≥ 12
While the alternative hypothesis H1 is ;
H1 < 12
Part F
I NEED HELP!
What is the geometric mean of the measures of the line segments A Dand DC? Show your work.
Answer:
The geometric mean of the measures of the line segments AD and DC is 60/13
Step-by-step explanation:
Geometric mean: BD² = AD×DC
BD = √(AD×DC)
hypotenuse/leg = leg/part
ΔADB: AC/12 = 12/AD
AC×AD = 12×12 = 144
AD = 144/AC
ΔBDC: AC/5 = 5/DC
AC×DC = 5×5 = 25
DC = 25/AC
BD = √[(144/AC)(25/AC)]
BD = (12×5)/AC
BD= 60/AC
Apply Pythagoras theorem in ΔABC
AC² = 12² + 5²
AC² = 144+ 25 = 169
AC = √169 = 13
BD = 60/13
The geometric mean of the measures of the line segments AD and DC is BD = 60/13
You decide not to use your car and cycle to work every day.
You calculate that you will cycle 350 miles a month.
How many kilometres is this? (Use 5 miles to approximately 8 km).
km.
Answer:
560 km
Step-by-step explanation:
350x8/5=
350x1.6=
560
Determine whether 52c2y4 is a monomial, binomial, trinomial, or other polynomial.
Answer: Monomial.
Step-by-step explanation:
Ok, when we have a polynomial with only one term, this is a monomial.
If the polynomial has two terms, this is a binomial.
If the polynomial has 3 terms, this is a trinomial.
And so on.
In this particular case we have:
52*c^2*y^4
Where c and y may be variables.
We can see that here we have only one term, so this would be a monomial.
(notice that the number of variables does not affect the type of polynomial in this case, only the number of terms)
Answer:
binomial.
Step-by-step explanation:
The polynomial −50c3z3−41y220z4 has 2 terms, so it is a binomial.
What is x when: |3x–1|=8
Answer:
x=3 or/and x= -7/3
Step-by-step explanation:
3x-1= 8+1= +1
3x = 9
9 divided by 3 is x= 3
3x-1= -8+1= +1
3x = -7
-7 divided by 3 is x= -7/3
Answer:
[tex]\huge\boxed{x=3\ \vee\ x=-\dfrac{7}{3}}[/tex]
Step-by-step explanation:
[tex]|a|=\left\{\begin{array}{ccc}a&\text{for}\ a\geq0\\-a&\text{for}\ a<0\end{array}\right\\\\|a|=k\to a=k\ \vee\ a=-k\ \text{for}\ k>0\\==========================\\\\|3x-1|=8\iff3x-1=8\ \vee\ 3x-1=-8\\\\\begin{array}{cccc}3x-1=8&\vee&3x-1=-8&\text{add 1 to both sides}\\3x-1+1=8+1&\vee&3x-1+1=-8+1\\3x=9&\vee&3x=-7&\text{divide both sides by 3}\\\dfrac{3x}{3}=\dfrac{9}{3}&\vee&\dfrac{3x}{3}=\dfrac{-7}{3}\\x=3&\vee&x=-\dfrac{7}{3}\\\end{array}[/tex]
if my grade is 69% what will my grade be if i got a 3.3 of 4 on a essay and it's worth 25% of my grade?
Answer:
72.4%
Step-by-step explanation:
The essay is 25% of your grade, and the rest is 75% of your grade.
25 (3.3/4) + 75 (0.69) ≈ 72.4
the sum of two consecutive multiples of 5 is 55.what are the multiples
Answer:
25 and 30
Step-by-step explanation:
Let the smaller consecutive multiples of 5 be x. Therefore, other consecutive multiples will be x + 5.
Now as per statement the sum of two consecutive multiples of 5 is 55. To find the multiples. Thus
x + x + 5 = 55
2x + 5 = 55
2x = 55 - 5
2x = 50
x = 50/2
x = 25
This the smaller consecutive multiples of 5 is 25, the other consecutuve multiple is x+ 5, 25 + 5 = 30.
The consecutive multiple numbers of 5 are 25 and 30
Answer the two consecutive multiples of 5 are 25 and 30
Answer:
25 and 30.
Step-by-step explanation:
Let the smaller consecutive multiple of 5 be 'x'. So, the other multiple will be x + 5.
Now, the statement is the sum of two consecutive multiples of 5 is 55. To find the multiples, we must simplify as below.
x + x + 5 = 55
2x + 5 = 55
2x = 55 - 5
2x = 50
x = 50/2
x = 25
We observe that the smaller consecutive is 25, so the other multiple is x+ 5, 25 + 5 = 30.
(Hope this helps and please mark as the brainliest)
The Cambridge Power and Light Company selected a random sample of 20 residential customers. Following are the amounts, to the nearest dollar, the customers were charged for electrical service last month:
53 49 54 50 21 46 75 45 63 76 61 63 36 34 54 63 37 62 66 62
(a) Compute the arithmetic mean.(Round your answer to 2 decimal places. Omit the "$" sign in your response.)
The mean is $
(b) Indicate whether it is a statistic or a parameter.
Answer:
a) the mean is $53.50
b) it is a statistic
Step-by-step explanation:
mean = ∑fx/∑f
∑f = 20
mean = (sum of the terms) ÷ (number of terms)
mean = (53+49+54+50+21+46+75+45+63+76+61+63+36+34+54+63+37+62+66+62) ÷ 20 = 1070/20
=$53.50
b) it is statistics because it is a random sample of 20 residential customers not the actual population
Graph parallelogram ABCD on the graph
below with vertices A(2,0), B(7,0), C(10,3),
D (5,3). What is the area of parallelogram
ABCD?
Answer: 25 square units
Step-by-step explanation:
We mark the points, A(2,0), B(7,0), C(10,3), D (5,3). on a graph and then joined them to make parallelogram ABCD as provided in the attachment.
Area of parallelogram = Base x corresponding height
From the figure, base AB = 7 - 2 units = 5 units
corresponding height: h= 5 units
Now , Area of parallelogram ABCD = base AB x corresponding height
= 5 x 5 square units
= 25 square units
Hence, the area of parallelogram ABCD is 25 square units .
Which is the graph of linear inequality x - 2y 2-12?
10
10
10
1034
Help asappp!!!pls
It would have to have a positive slope and the bottom needs to be shaded, since -2y is negative it means we will be dividing by a negative. The inequality sign will switch.
also if it is < then the line is dotted, if it’s the “greater or equal to sign” then the line is not dotted.
dunno if I explained it very well
The shaded region common to both the inequalities represents the solution set of the inequality → x - 2y² < 12.
What is inequality?An inequality is used to compare two or more expressions or numbers.
For example -
2x > 4y + 3
x + y > 3
x - y < 6
Given is the inequality as -
x - 2y² < 12
The given inequality is -
x - 2y² < 12
2y² - x < - 12
2y² < x - 12
y² < (x/2) - 6
[tex]$y < \pm\sqrt{\frac{x}{2}-6 }[/tex]
[tex]$y < \sqrt{\frac{x}{2}-6 }[/tex]
and
[tex]$y < -\sqrt{\frac{x}{2}-6 }[/tex]
Refer to the graph of the equation attached. The shaded region common to both the inequalities represents the solution set of the inequality.
Therefore, the shaded region common to both the inequalities represents the solution set of the inequality → x - 2y² < 12.
To solve more questions on inequality, visit the link-
https://brainly.com/question/11897796
#SPJ7
Determine the zeros of r=2sin5theta
Answer:
[tex]\theta=\frac{n\pi}{5}[/tex]
Step-by-step explanation:
You have the following function:
[tex]r=2sin5\theta[/tex] (1)
In order to find the zeros of the function you equal to zero the equation (1), and then you solve for θ:
[tex]2sin5\theta=0\\\\sin5\theta=0\\\\5\theta=sin^{-1}(0)=n\pi;\ \ \ \ n=0,1,2,3,..\\\\\theta=\frac{n\pi}{5}[/tex]
Then, there are infinite zeros for the function of the equation (1), because n has infinite positive integers values.
Answer:
θ = 0, pi/5, 2pi/5, 3pi/5, 4pi/5 ,pi
Step-by-step explanation:
What is 3/8 + 1/8 + 2/3 + 1/2 equal?
Answer:
5/3
Step-by-step explanation:
3/8 + 1/8 + 2/3 + 1/2
=> [ 3/8 + 1/8 ] + [ 2/3 + 1/2 ]
=> 1/2( or 4/8 ) + 7/6
=> 10/6 or 5/3
Answer:
[tex] \frac{3}{8} + \frac{1}{8} + \frac{2}{3} + \frac{1}{2} [/tex]
Add the fractions with the same common denominator
That's
[tex] \frac{3}{8} + \frac{1}{8} = \frac{4}{8} = \frac{1}{2} [/tex]
So we have
[tex] \frac{1}{2} + \frac{2}{3} + \frac{1}{2} [/tex]
Add the fractions with the same common denominator
That's
[tex] \frac{1}{2} + \frac{1}{2} = \frac{2}{2} = 1[/tex]
We have
[tex] 1 + \frac{2}{3} [/tex]
That's
[tex] \frac{1}{1} + \frac{2}{3} [/tex]
Find the common denominator
The common denominator is 3
[tex] \frac{1}{1} + \frac{2}{3} = \frac{3 + 2}{3} [/tex]
[tex] = \frac{5}{3} \: \: \: \: \: \: or \: \: \: \: \: \: \: 1 \frac{2}{3} [/tex]
Hope this helps you
CAN ANYONE HELP ME PLEASE? Jen Butler has been pricing Speed-Pass train fares for a group trip to New York. Three adults and four children must pay $106. Two adults and three children must pay $75. Find the price of the adult's ticket and the price of a child's ticket.
Answer:
The adult ticket costs $18 and the children ticket costs $13.
Step-by-step explanation:
Let the price of the adult ticket be a.
Let the price of the children ticket be c.
Three adults and four children must pay $106. This implies that:
3a + 4c = 106 _______(1)
Two adults and three children must pay $75. This implies that:
2a + 3c = 75 ________(2)
We have two simultaneous equations:
3a + 4c = 106 _____(1)
2a + 3c = 75 ______(2)
Multiply (1) by 2 and (2) by 3 and subtract (1) from (2):
6a + 9c = 225
- (6a + 8c = 212)
c = $13
Put this value of c in (2):
2a + 3*13 = 75
2a + 39 = 75
=> 2a = 75 - 39
2a = 36
a = 36/2 = $18
Therefore, the adult ticket costs $18 and the children ticket costs $13.
Can someone please help!
Working backwards, on Wednesday morning we have 60 / (1/2) = 120 pounds of ice.
2/3 melts on Tuesday so 120 pounds must be 1/3 of the ice.
120 / (1/3) = 360
Answer: D. 360
How long is the arc formed by a 300 degree central angle in a circle with a radius of 7 cm.?
approximately 36.633 cm if you use pi = 3.14
approximately 36.6519 cm if you use the calculator's stored value of pi
Work Shown:
L = arc length, r = radius, x = central angle in degrees
L = (x/360)*2*pi*r
L = (300/360)*2*pi*7
L = (35/3)pi .... exact arc length in terms of pi
L = (35/3)*3.14
L = 36.633 .... approximate arc length
Keep in mind that I used pi = 3.14 which isn't that great an approximation for pi. If you want to use more digits of pi, then use your calculator's built in version of it to get (35/3)*pi = 36.6519; of course it will depend on which option your teacher prefers.
Which would give a significantly smaller value than 1.19 x 10^-2 and which would give a significantly larger value?
1.19 x 10^-2 + 1.07 x 10^-2 smaller or larger?
1.19 x 10^-2 - 1.07 x 10^-2 smaller or larger?
1.19 x 10^-2 x 1.07 x 10^-2 smaller or larger?
1.19 x 10^-2 / 1.07 x 10^-2 (this problem is division) smaller or larger?
Answer:
a) [tex]1.19 \times 10^{-2} + 1.07\times 10^{-2}[/tex] is larger than [tex]1.19\times 10^{-2}[/tex]; b) [tex]1.19 \times 10^{-2} - 1.07\times 10^{-2}[/tex] is smaller than [tex]1.19\times 10^{-2}[/tex]; c) [tex](1.19\times 10^{-2})\cdot (1.07\times 10^{-2})[/tex] is smaller than [tex]1.19\times 10^{-2}[/tex]; d) [tex](1.19\times 10^{-2})/ (1.07\times 10^{-2})[/tex] is greater than [tex]1.19\times 10^{-2}[/tex].
Step-by-step explanation:
a) Is [tex]1.19 \times 10^{-2} + 1.07\times 10^{-2}[/tex] smaller or larger?
1) [tex]1.19 \times 10^{-2} + 1.07\times 10^{-2}[/tex] Given.
2) [tex](1.19+1.07)\times 10^{-2}[/tex] Distributive property.
3) [tex]2.26 \times 10^{-2}[/tex] Addition/Result.
[tex]1.19 \times 10^{-2} + 1.07\times 10^{-2}[/tex] is larger than [tex]1.19\times 10^{-2}[/tex].
b) Is [tex]1.19 \times 10^{-2} - 1.07\times 10^{-2}[/tex] smaller or larger?
1) [tex]1.19 \times 10^{-2} - 1.07\times 10^{-2}[/tex] Given.
2) [tex](1.19-1.07)\times 10^{-2}[/tex] Distributive property.
3) [tex][1.19+(-1.07)]\times 10^{-2}[/tex] Subtraction.
4) [tex]0.12\times 10^{-2}[/tex] Addition/Result.
[tex]1.19 \times 10^{-2} - 1.07\times 10^{-2}[/tex] is smaller than [tex]1.19\times 10^{-2}[/tex].
c) Is [tex](1.19\times 10^{-2})\cdot (1.07\times 10^{-2})[/tex] smaller or larger?
1) [tex](1.19\times 10^{-2})\cdot (1.07\times 10^{-2})[/tex] Given.
2) [tex](1.19\times 1.07)\cdot (10^{-2}\times 10^{-2})[/tex] Associative property/Commutative property.
3) [tex]1.27\times 10^{-4}[/tex] Multiplication/ ([tex]a^{b}\cdot a^{c} = a^{b+c}[/tex])/ [tex](-x)\cdot (-y) = x\cdot y[/tex] /Result.
[tex](1.19\times 10^{-2})\cdot (1.07\times 10^{-2})[/tex] is smaller than [tex]1.19\times 10^{-2}[/tex].
d) Is [tex](1.19\times 10^{-2})/ (1.07\times 10^{-2})[/tex] smaller or larger?
1) [tex](1.19\times 10^{-2})/ (1.07\times 10^{-2})[/tex] Given.
2) [tex](1.19\times 10^{-2})\cdot (1.07\times 10^{-2})^{-1}[/tex] Division.
3) [tex](1.19\times 10^{-2})\cdot (1.07\times 10^{2})[/tex] ([tex](a^{b})^{c} = a^{b\cdot c}[/tex]; [tex](-x)\cdot (-y) = x\cdot y[/tex])
4) [tex](1.19\times 1.07)\cdot (10^{-2}\cdot 10^{2})[/tex] Associative property/Commutative property.
5) [tex]1.27[/tex] Multiplication/([tex](a^{b})^{c} = a^{b\cdot c}[/tex]; [tex]a^{0} = 1[/tex])/Modulative property/Result.
[tex](1.19\times 10^{-2})/ (1.07\times 10^{-2})[/tex] is greater than [tex]1.19\times 10^{-2}[/tex].
please help!!!!!!!!!!!!
Answer:
csc B = 13/12
Step-by-step explanation:
csc B = 1 / sin B
The sin B is
sin B = opp/ hyp so
csc B = hyp /opp
csc B = 26 / 24
csc B = 13/12
Answer:
13/12
Step-by-step explanation:
sin θ = opposite/ hypotenuse
csc θ = 1/sinθ
csc θ = hypotenuse/opposite
csc (B) = 26/24
csc (B) = 13/12
Write Given f(x)=2−4x−−−−−√ and g(x)=−3x, find the following: a. (g∘f)(x) the domain and range of the function using interval notation.
Answer:
If we have two functions g(x) and f(x)
I suppose that the functions here are:
f(x) = 2 - √(4*x)
g(x) = -3*x
First, let's analyze the functions:
g(x) as not any problem for any value of x, so the domain is the set of all the real numbers.
f(x) has a square root on it, and we know that the square root of a negative number is equal to a complex number, so here we can not have negative values of x.
The domain of f is D = x ∈ {0, ∞}
Then (gof)(x) = g(f(x)) = -3*(2 - √(4*x)) = -6 + 3*√(4*x)
We can see that g(x) does not have any problem, and the problems with f(x) remain there, so the domain of the composition is equal to the domain of f(x):
D = x ∈ {0, ∞}
Find all x in set of real numbers R Superscript 4 that are mapped into the zero vector by the transformation Bold x maps to Upper A Bold x for the given matrix A.
Answer:
[tex]x_3 = \left[\begin{array}{c}4&3&1\\0\end{array}\right][/tex]
Step-by-step explanation:
According to the given situation, The computation of all x in a set of a real number is shown below:
First we have to determine the [tex]\bar x[/tex] so that [tex]A \bar x = 0[/tex]
[tex]\left[\begin{array}{cccc}1&-3&5&-5\\0&1&-3&5\\2&-4&4&-4\end{array}\right][/tex]
Now the augmented matrix is
[tex]\left[\begin{array}{cccc}1&-3&5&-5\ |\ 0\\0&1&-3&5\ |\ 0\\2&-4&4&-4\ |\ 0\end{array}\right][/tex]
After this, we decrease this to reduce the formation of the row echelon
[tex]R_3 = R_3 -2R_1 \rightarrow \left[\begin{array}{cccc}1&-3&5&-5\ |\ 0\\0&1&-3&5\ |\ 0\\0&2&-6&6\ |\ 0\end{array}\right][/tex]
[tex]R_3 = R_3 -2R_2 \rightarrow \left[\begin{array}{cccc}1&-3&5&-5\ |\ 0\\0&1&-3&5\ |\ 0\\0&0&0&-4\ |\ 0\end{array}\right][/tex]
[tex]R_2 = 4R_2 +5R_3 \rightarrow \left[\begin{array}{cccc}1&-3&5&-5\ |\ 0\\0&4&-12&0\ |\ 0\\0&0&0&-4\ |\ 0\end{array}\right][/tex]
[tex]R_2 = \frac{R_2}{4}, R_3 = \frac{R_3}{-4} \rightarrow \left[\begin{array}{cccc}1&-3&5&-5\ |\ 0\\0&1&-3&0\ |\ 0\\0&0&0&1\ |\ 0\end{array}\right][/tex]
[tex]R_1 = R_1 +3 R_2 \rightarrow \left[\begin{array}{cccc}1&0&-4&-5\ |\ 0\\0&1&-3&0\ |\ 0\\0&0&0&-1\ |\ 0\end{array}\right][/tex]
[tex]R_1 = R_1 +5 R_3 \rightarrow \left[\begin{array}{cccc}1&0&-4&0\ |\ 0\\0&1&-3&0\ |\ 0\\0&0&0&-1\ |\ 0\end{array}\right][/tex]
[tex]= x_1 - 4x_3 = 0\\\\x_1 = 4x_3\\\\x_2 - 3x_3 = 0\\\\ x_2 = 3x_3\\\\x_4 = 0[/tex]
[tex]x = \left[\begin{array}{c}4x_3&3x_3&x_3\\0\end{array}\right] \\\\ x_3 = \left[\begin{array}{c}4&3&1\\0\end{array}\right][/tex]
By applying the above matrix, we can easily reach an answer
Kirsten has 9 syrup containers from a local cafe. There are 6 milliliters of syrup per container.
Answer: 54 mL
Step-by-step explanation:
Simply do 9(number of containers)*6(Syrup per container) to get 54 mL of syrup.
Hope it helps <3
Suppose ABC is a right triangle with sides of lengths a, b, and c and right angle at C. Find the unknown side length using the Pythagorean theorem, and then find the values of the six trigonometric functions for angle B. Rationalize denominators when applicable. b=4, c=7
Answer:
Side a^2 = 49 + 16
Side a^2 = 65
Side a = 8.062
sin (B) = 4 / 8.062
cos (B) = 7 / 8.062
tan (B) = 4 / 7
cot (B) = 7 / 4
sec (B) = 8.062 / 7
csc (B) = 8.062 / 4
Step-by-step explanation:
x =x=x, equals ^\circ ∘
Answer:
x = 64
Step-by-step explanation:
A circle equal 360 degrees
180 + 90 + x + 26 = 360
Combine like terms
296+x = 360
Subtract 296 from each side
296+x-296 = 360-296
x = 64
Which number line represents the solution set for the inequality 3(8 - 4x) < 6(x - 5)?
Answer:
x>3
Step-by-step explanation:
Question 12
<
>
1
The tank for a car holds 17 gallons. The gasoline gauge shows the tank is full. How much gas is still in
4
the tank? Give your answer as a whole number or as a mixed fraction reduced to lowest terms.
The question is incomplete! Complete question along with answer and step by step explanation is provided below.
Question:
The tank for a car holds 17 gallons. The gasoline gauge shows the tank is 3/4 full. How much gas is still in the tank?
Give your answer as a whole number or as a mixed fraction reduced to lowest terms.
Answer:
[tex]Gas \: \:left = 12 \frac{3}{4} \: \:gallons \\\\[/tex]
Step-by-step explanation:
The tank for a car holds 17 gallons.
The gasoline gauge of the car shows that the tank is 3/4 full.
We are asked to find the remaining gasoline in the tank.
[tex]Gas \: \:left = \frac{3}{4} \times 17 \\\\Gas \: \:left = \frac{51}{4} \\\\Gas \: \:left = 12 \frac{3}{4} \: \:gallons \\\\[/tex]
Therefore, the remaining gas in the tank is [tex]12\frac{3}{4}[/tex] gallons.
Alternatively:
[tex]1 - \frac{3}{4} = \frac{1}{4}[/tex]
Amount of gasoline consumed = [tex]\frac{1}{4} \times 17 = \frac{17}{4}[/tex]
Amount of gasoline left = total - consumed
Amount of gasoline left = [tex]17 - \frac{17}{4} = 12\frac{3}{4} \:\: gallons[/tex]
find the 10th term of a geometric sequence whose first tow terms are 2 and -8
Answer:
t10 = - 2¹⁹= -524288Step-by-step explanation:
t1=2
t2=-8
r=t2/t1=-8/2=-4
t10=t1*r⁹
t10=2*(-4)⁹= -2*(2²)⁹
t10= -2¹⁹= -524288
Answer:
-524288
Step by step
so use the formula
ar^n-1
so
a is first term
r is common ratio
n is number of terms
so
get r which is -8/2=-4
then apply
2×(-4^9)=answer
not sure
Find three consecutive even integers such that the square of the third is 60 more that the square of the second
Answer:
-4,4,16
Step-by-step explanation:
They are all even integers.
-4^2=16
4^2=16
16^2=256
the square of the third,16 is 256 which is more than the square of the second,4=16
The three consecutive even integers such that the square of the third is 60 more than the square of the second are -18, -16 and -14.
What are integers?Any positive or negative number without fractions or decimal places is known as an integer, often known as a "round number" or "whole number."
Given:
Let the three even consecutive integers are 2n-2, 2n and 2n + 2.
According to the question,
So,
(2n + 2)² = (2n)² - 60
4n² + 4 + 8n = 4n² -60
8n = -64
n = -8
That means, the integers are -18, -16 and -14.
Therefore, the required even integers are -18, -16 and -14.
To learn more about the integers;
brainly.com/question/1768254
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