Answer:
(A)[tex]128^{x/3}[/tex]
(D)[tex](4(2^{1/3}))^x[/tex]
Step-by-step explanation:
We want to determine which of the expression is equivalent to:
[tex]\sqrt[3]{128}^ x[/tex]
By the law of indices:
[tex]\sqrt[3]{128}=128^{1/3}\\$Therefore:\\\sqrt[3]{128}^ x \\=(128^{1/3})^x\\=128^{x/3}[/tex]
Similarly:
[tex]\sqrt[3]{128}^ x \\=\sqrt[3]{64*2}^ x\\=(4\sqrt[3]{2})^ x\\=(4(2^{1/3}))^x[/tex]
The expressions that are equivalent to (∛128)ˣ are; (128)^(x/3) and (4(2^(1/3))ˣ
How to use law of indices?We want to find the expression that is equivalent to (∛128)ˣ
From law of indices, we have that;
(∛128)ˣ = [(128)^(1/3)]ˣ
This can be further expressed as;
(128)^(x/3)
Similarly, we have the simplified expression at;
[(128)^(1/3)]ˣ = (64 * 2)^(x/3)
⇒ (4³ * 2)^(x/3)
⇒ (4(2^(1/3))ˣ
Read more about law of indices at; https://brainly.com/question/11761858
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The table provides on road accidents reported to the police for the days in December
Accidents reported Frequency
0-5 9
6-10 10
11-15 6
16-20 6
Estimate the mean.
Give your answer rounded to 1 DP.
Answer:
[tex]Mean = 9.3[/tex]
Step-by-step explanation:
Given
Let accidents reported be represented by x and the frequency be represented by f
x ----- f
0-5 -- 9
6-10 -- 10
11-15 -- 6
16-20 -- 6
Required
Calculate the Mean;
To calculate the mean of a grouped data, the first step is to calculate the midpoint of the observation;
When x = 0 - 5
Midpoint = 0.5(0 + 5) = 0.5 * 5 = 2.5
When x = 6 - 10
Midpoint = 0.5(6 + 10) = 0.5 * 16 = 8
When x = 11 - 15
Midpoint = 0.5(11 + 15) = 0.5 * 26 = 13
When x = 16 - 20
Midpoint = 0.5(16 + 20) = 0.5 * 36 = 18.
So, the new table is as follows;
x ------- f
2.5 ---- 9
8 ----- 10
13 ------ 6
18 ------ 6
Mean is calculated by ∑fx/∑f
Where ∑fx represent sum of the product of f and x
∑f represent sum of frequency
∑fx = 2.5 * 9 + 8 * 10 + 13 * 6 + 18 * 6
∑fx = 288.5
∑f = 9 + 10 + 6 + 6
∑f = 31
So,
[tex]Mean =\frac{288.5}{31}[/tex]
[tex]Mean = 9.3064516129[/tex]
[tex]Mean = 9.3 (Approximated)[/tex]
Hence, the mean of road accidents in December is 9.3
. Alexandro, o professor de Física, avisou aos alunos que a média bimestral seria calculada conforme o seguinte critério: Adicionam-se as notas obtidas no projeto, na prova e no trabalho em grupo e divide-se o resultado obtido por três. Laura é uma das alunas do professor Alexandre. As notas de Laura: Projeto: 5,0 Prova: 6,5 trabalho em grupo: 9,5. A) Por que o resultado deve ser dividido por 3?
Answer:
É necessário dividir por 3 para calcular a média simples das 3 notas.
Média = 7.
Step-by-step explanation:
O resultado deve ser dividido por três porque três notas com pesos iguais (projeto, prova e trabalho em grupo) foram somadas, portanto para calcular a média bimestral de Laura, a soma das três notas deve ser dividida por 3. A média de Laura é:
[tex]M=\frac{5,0+6,5+9,5}{3}\\ M=7[/tex]
I need help people please help me
Answer:
Each Cup has 3/8
Step-by-step explanation:
Divide
If f(x) = 3x-2 and g(x) = 2x + 1 find (f-g)(x)
Answer:
x-3
Step-by-step explanation:
f(x) = 3x-2
g(x) = 2x + 1
(f-g)(x) = 3x-2 - (2x+1)
Distribute the minus sign
=3x-2-2x-1
Combine like terms
= 3x-2x-2-1
=x-3
Which set of ordered pairs does not represent a function?
Answer:
it is the last one
Step-by-step explanation:
Since a function is based on a set of ordered pairs, where the first element in each pair is from the domain and the second is from the codomain. Also A function is a mapping from a set of inputs (the domain) to a set of possible outputs (the codomain).
The last one doesn't show the correct inputs and outputs
4 Student is 20% of ____ students
I need the answer please help me I don't want to fail my math class
Answer:
4 Student is 20% of 20 students
Step-by-step explanation:
if 4 = 20% then 1 = 5% to get a hundred percent then you need to multiply by 20
so 20
4 Student is 20% of 20 students
Answer:
4 Student is 20% of _20___ students
Step-by-step explanation:
20% of x = 4
20% = 0.20
of means multiplication so
0.2 * x = 4
x = 4 / 0.2 = 40 /2 =20
Find the slope of the line that passes through (10, 3) and (1, 10).
Simplify your answer and write it as a proper fraction, improper fraction, or integer.
Answer: -7/9
Step-by-step explanation:
10-3
1-10
The slope of the line is - 7/9
please see the attached picture for full solution
Hope it helps
Good luck on your assignment
How do i graph the quadratic function f (x)=-(x-3)(x+1)
Answers:
It's basically Inside, Outside, Outside, Inside. (I. O.O.I.)
Explanations:
Given
[tex]f(x)=-(x-3)(x+1)[/tex]
Distribute the (-1) to (x-3)
[tex]f(x)=(-x+3)(x+1)[/tex]
Now let's work the I. O. O. I.
Inside:
[tex](-x)(x)=-x^2[/tex]
Outside:
[tex](-x)(1)=-x[/tex]
Outside:
[tex](3)(x)=3x[/tex]
Inside:
[tex](3)(1)=3[/tex]
Add both the outsides (-x) and (3x) together
[tex]-x+3x=2x[/tex]
Your new equations is now.
[tex]f(x)=-x^2+2x-3[/tex]
3a+2b=9 and 8x+6y=60
what is the value of 9a+6b
what is the value of 4x+3y
Answer:
The Value of 9a+6b is 27. and the value of 4x+3y is 30.
Explanation
1)
3a+2b=9
multiplying both by side by 3
or, 3×( 3a+2b)=3×9
Hence, 9a+6b=27
2)
8x+6y=60
Dividing both by side by 2
or, (8x+6y)/2 = 60/2
Hence, 4x+3y=30
Plzz give an example
how do you round to the nearest cubic
Answer:
I'm assuming that you mean "Cubic Unit". I will use inches in this example, but this will work with other units as well.
Let's say that the volume of a figure was 124.86 cubic inches.
Rounding to the nearest cubic inch is the same thing as rounding to the nearest whole number.
Locate the 'ones' place:
124.86
Check next door:
124.86
If the next door number is greater than or equal to 5, then we round up. If it's less than 5, we round down.
8 is greater then 5. Therefore, we would round up.
So, 124.86 cubic inches to the nearest cubic inch is 125 in³.
124.86in³ ≈ 125in³
What is the product (40 + (-10))((36 + (-9))(32 + (-8))...(-32 + 8)(-36 + 9)(-40 + 10) where the first number in each factor is decreasing by 4 and second number in each factor is increasing by 1?
Answer:
0
Step-by-step explanation:
The first number is 40 and decreases by 4 in each factor, and the second number is -10 and increases by 1 in each factor.
The first number is positive and decreases by 10% its value in each factor, and the second number is negative and increases by 10% its absolute value in each factor. That means we will have a factor where both numbers are 0 (in the 11th value, we will have the first number 40 - 4*10 = 0 and the second number -10 + 1*10 = 0), so the factor will be 0 + 0 = 0, and then whole product will be zero.
HELP ASAP!!1 Write the phrase as a rate in simplest form. 320 miles on 34 gallons a. 160miles/ 17 gallons b. 160miles/ 34 gallons c. 320gallons/ 34 miles d. 320miles/ 34 gallons e. 160gallons/17 gallons
Answer: c( 320 gallons/34 miles or d( 320 miles/34 gallons
hope it helps..
Which of the following is an angle shown in the drawing?
Answer:
ABE
DBC
CBE
Step-by-step explanation:
They all have B as the middle one, and B is the vertex
I think
Joey and Nolan are each solving the equation 13x - 42 = 18 - 7x.
Joey's first step was to rewrite the equation as 20x - 42 = 18 while Nolan's first step was to rewrite the
equation as 13x = 60 - 7x.
Who is correctly applying the addition property of equality in the first step of his work?
A. Only Joey
B. Only Nolan
C. Both Joey and Nolan
D. Neither Joey nor Nolan
Answer:
First step=13x+7x=18+42
Step-by-step explanation:
13x-42=18-7x
First step
It is to collect like terms of the equation
13x+7x=18+42
20x=60
x=60/20
x=3
Tracy has a cell phone plan that provides 250 free minutes each month for a flat rate of $29.
Answer:
250 minutes with the flat rate of $29.
[tex]x\leq 250[/tex]
x would be the number of minutes called.
[tex]x-250[/tex]
Tracy would be charged by $0.35 per minute.
[tex]f(x)=29\\ 0\leq x\leq 250[/tex]
[tex]f(x)=0.35(x-250)+29,\\250\leq x\leq ∞[/tex]
Ron had some pens. 3 8 of them were black coloured, 1 4 of them were red coloured and the rest of them were blue coloured. There were 15 blue pens. How many pens did Ron have?
Answer:
40 pens
Step-by-step explanation:
Let the total number of pens Ron had be x.
We need to find the fraction of the pen that were blue.
3/8 of them were black and 1/4 of them were red. This means that the fraction of the pens that were blue is:
1 - (3/8 + 1/4) = 1 - 5/8 = 3/8
There were 15 blue pens. This means that 3/8 of x is 15:
3/8 * x = 15
x = 15 * 8/3 = 40 pens
Ron had 40 pens.
Which is equivalent to v10 3/4?
Answer:
d) [tex](\sqrt[8]{(10} )^{3 x}[/tex]
Step-by-step explanation:
Step(i):-
Given [tex](\sqrt{10} )^{\frac{3 x}{4} }[/tex]
we will use formula
[tex](a)^{m n} = (a^{m} )^{n}[/tex]
[tex](\sqrt{10} )^{\frac{3 x}{4} } =( (10)^{\frac{1}{2} } )^{\frac{3 x}{4} }[/tex]
= [tex]( (10)^{\frac{1}{2} X\frac{3 x}{4} } )[/tex]
= [tex]( (10)^{\frac{3 x}{8} } )[/tex]
= [tex]((10)^{\frac{1}{8} } )^{3x}[/tex]
Step(ii):-
we will apply [tex](a)^{\frac{1}{n} } = \sqrt[n]{a}[/tex]
= [tex](\sqrt[8]{(10} )^{3 x}[/tex]
Point D is located on the segment CE. IF CD = 24 and DE = x and CE - 5x, what is the measure of segment CE?
Answer:
30Step-by-step explanation:
If point D is located on the segment CE, then point C, D and E lies on the same line i.e they are collinear. Mathematically, CD+DE = CE
Given CD = 24 and DE = x and CE = 5x, on substituting this values in the equation we have;
[tex]24+x = 5x\\5x-x = 24\\4x = 24\\x = 24/4\\x = 6[/tex]
Since CE = 5x, CE = 5(6) = 30
The measure of segment CE is 30
Last year, there were “x” students in the Math Club, but this year, there was a 40% increase in membership. Represent this year’s membership in terms of “x”.
Answer:
(x)1.4=Y
Step-by-step explanation:
40% increase of memeber so ita 140% of X
Emily convinced her mom to buy a giant box of her favorite cereal. Her mom doesn't think the box will fit on
their shelf. The volume of the box is 10,000 cm3. The base of the box is 25 cm by 10 cm.
How tall is the box of cereal?
am
Answer:
40cm
Step-by-step explanation:
A box is normally in the shape of a cube
formula of volume of a cube;
We want to find the height(tallness)
Volume=LengthxWidthxHeight
10000=25x10xHeight
10000=250H. (divide both side by 250 to remain with H only)
10000/250=250H/250
40cm=Height
Anna has 2 purple lipsticks, 3 red lipsticks and 3 pink lipsticks in her kit. She picks one lipstick, record its color, puts it back in the kit and draws another lipstick. What is the probability of taking out a purple lipstick followed by the red lipstick?
Answer:
9/64Step-by-step explanation:
This is a probability problem on selection with replacement, that is the sample size does not change after each selection or event.
Given data
2 purple lipsticks,
3 red lipsticks and
3 pink lipsticks
The sample space s=(2,3,3)
The sample size= 8
1. the probability of taking a purple lipstick Pr(purple)= [tex]\frac{3}{8} \\[/tex]
2.the probability of taking a red lipstick Pr(red)= [tex]\frac{3}{8}[/tex]
probability of taking out a purple lipstick followed by the red lipstick is
[tex]= \frac{3}{8} * \frac{3}{8} = \frac{9}{64}[/tex]
I will mark you brainliest!!!! What is the first step in adding these equations to eliminate y?
Answer:
I believe D
Step-by-step explanation:
If you multiplied -3 times 3 that would make -9
you can then add 9 + -9 and cross y off
∠A and ∠B are complementary. If m∠B = 64° , what is the measure of ∠A?
26°
36°
11°
64°
Answer: 26
Step-by-step explanation:
Two Angles are Complementary when they add up to 90 degrees (a Right Angle). Then
∠A + ∠B = 90
∠A =90- ∠B
∠A = 26
Answer:
The measure of [tex]\angle A[/tex]:
[tex]\angle A = 26\textdegree[/tex]
Step-by-step explanation:
Since both [tex]\angle A[/tex] and [tex]\angle B[/tex] are complementary (Which they both add up to 90°), and you want to find the measure of
Measure of [tex]\angle A[/tex]: unknown
Measure of [tex]\angle B[/tex]: 64°
Finding the measure of [tex]\angle A[/tex]:
[tex]90 - 64 = 26[/tex]
[tex]\angle A = 26\textdegree[/tex]
So, the measure for [tex]\angle A[/tex] is [tex]26\textdegree[/tex].
Please answer correctly!!!!!! Will mark brainliest !!!!!!!!!!!
Answer:
see below
Step-by-step explanation:
g(x) = sqrt(x+3)
g(-6) = sqrt(-6+3) = sqrt(-3) not a real number not in domain
g(-3) = sqrt(-3+3) = sqrt(0) 0 in domain
g(3) = sqrt(3+3) = sqrt(6) in domain
how do you change a rational number to a decimal
Answer:
see below
Step-by-step explanation:
do long division
for example 42/8 = 5 2/8 =5 1/4 =5.25
Solve the simultaneous equation.
7a+3b=46
4a+5b=69
Answer:
a=1 and b=13
do you need the working out?
the distance between (3,k) and ( 5,6) is 2root2 units then k
Answer:
Step-by-step explanation:
[tex]\sqrt{x} Distance=\sqrt{(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2}}\\\\\sqrt{(5-3)^{2}+(6-k)^{2}}=2\sqrt{2}\\\\\sqrt{(2)^{2}+[(6)^{2}-(2*6*k)+(k)^{2}]}=2\sqrt{2}\\\\\sqrt{4+[36-12k+k^{2}]}=2\sqrt{2}\\\\\sqrt{40-12k+k^{2}}=2\sqrt{2}\\[/tex]
Take square both side
[tex]40-12k+k^{2}=(2\sqrt{2})^{2}\\\\40-12k+k^{2}=4*2\\\\40-12k+k^{2}=8\\\\k^{2}-12k+40-8=0\\\\k^{2}-12k+32=0\\[/tex]
Factorize,
Sum = -12
Product = 32
Factors = -8 , -4
k² - 8k - 4k + (-8)*(-4) = 0
k(k - 8) - 4(k - 8) = 0
(k - 8)(k - 4) = 0
k = 8 or 4
The points are (3,k) and (5,6).
Given, distance = 2√2 units
Applying distance formula,
Distance = √(x2-x1)^2 + (y2-y1)^2
2√2 = √(x2-x1)^2 + (y2-y1)^2
Squaring both sides,
(2√2)^2 = [√(x2-x1)^2 + (y2-y1)^2]^2
8 = (x2-x1)^2 + (y2-y1)^2
8 = (5-3)^2 + (6-k)^2
8 = 2^2 + (6^2 - 2x6xk + k^2)
8 = 4 + 36 - 12k + k^2
8 = 40 - 12k + k^2
= k^2 - 12k + 32 = 0
On factorising,
=> k^2 - 4k - 8k + 32 = 0
=> k(k-4) -8(k-4) = 0
=> (k-4)(k-8) = 0
=> k-4 = 0 , k-8 = 0
=> k = 4 , k = 8
pleaseeeeee right answer struggling
The right answer is of:
option C
please see the attached picture....
Hope it helps.....
Good luck on your assignment.....
In a certain room, there are 28 women and 21 men. What is the ratio of
men to women? What is the ratio of women to the total number of
people?
Answer:
The men to women ratio is 3 : 4The ratio between women to total number of people is 4 : 7Step-by-step explanation:
Men to women ratio = 21 : 28 or 3 : 4
The men to women ratio is 3 : 4
Total people = 21 + 28 = 49 people
The ratio of women to total number of people is
28 : 49 or 4 : 7
The ratio between women to total number of people is 4 : 7
Find t12 term in an arithmetic progression having t3 = 10 and t10 = −4 .
Answer:
t12= -8
Step-by-step explanation:
t3
a+2d=10 (1)
t10
a+9d=-4. (2)
From (1)
a=10-2d. (3)
Sub into (3) into equ (2)
a+9d=-4
10-2d+9d=-4
10+7d=-4
7d=-4-10
7d=-14
Divide both sides by 7
d=-14/7
d= -2
10=a+2d
10=a+2(-2)
10=a-4
10+4=a
14=a
a=14
t12=a+11d
= 14+11(-2)
=14-22
= -8
t12= -8
