Answer:
Given:
[tex]\textsf{Mass of Sample A}=2.4 \times 10^{-2}[/tex][tex]\textsf{Mass of Sample B}=3.6 \times 10^{2}[/tex]As the exponent of Sample A is negative, this means that the mass of Sample A is smaller than that of Sample B.
Therefore, to find the proportional relationship between the samples, divide the mass of the larger sample (B) by the mass of the smaller sample (A):
[tex]\begin{aligned}\implies \dfrac{\textsf{Sample B}}{\textsf{Sample A}}=\dfrac{3.6 \times 10^2}{2.4 \times 10^{-2}} & =\dfrac{3.6}{2.4} \times \dfrac{10^2}{10^{-2}}\\\\ & =1.5 \times 10^{(2-(-2))}\\\\& = 1.5 \times 10^4 \end{aligned}[/tex]
To convert the scientific notation [tex]1.5 \times 10^4[/tex] to a decimal, move the decimal point to the right 4 places:
[tex]\implies 1.5000 \times 10^4=15000[/tex]
(If the exponent is positive, move the decimal point to the right. If the exponent is negative, move the decimal point to the left. The number of places to move the decimal point is the numerical value of the exponent).
Therefore, the mass of sample B is 15,000 times the mass of sample A, so Narissa is correct.
4. Use the formula to evaluate the series 3 + 6 + 12 + 24 +48 +96. Sn a₁(1 - r^) 1-r
Answer:
[tex]S_6=189[/tex]
Step-by-step explanation:
This is a geometric series with [tex]a_1=3[/tex] and common ratio [tex]r=2[/tex]. Using the formula [tex]\displaystyle S_n=\frac{a_1(1-r^n)}{1-r}[/tex] to find the sum of the first [tex]n=6[/tex] terms, we have:
[tex]\displaystyle S_n=\frac{a_1(1-r^n)}{1-r}\\\\S_6=\frac{3(1-2^6)}{1-2}\\\\S_6=\frac{3(1-64)}{-1}\\\\S_6=\frac{3(-63)}{-1}\\\\S_6=\frac{-189}{-1}\\\\S_6=189[/tex]
So, the given series works out to be [tex]S_6=189[/tex].
PLEASE HELP ME I NEED HELP
Answer:
5x + 7y = 37
Step-by-step explanation:
I hope it is the answer
There are 24 pictures on a roll of film. Adelle had 84 pictures from her trip home. She said that 12 other pictures were spoiled. How many rolls of film did Adelle use?
Answer:
Total pictures = 84+12 = 96
roll of films = 96 / 24 = 4
she used 4 rolls
You’ll earn points just answer.. I know the answer already I’m just giving points
Answer:
10 inches
Step-by-step explanation:
2+2.25+2.25+2.25+2.5+2.75+2.75+3.25=10!!!!!!!!!
Answer:
thank youuu
Step-by-step explanation:
Pleas help ppppppp pls
Step-by-step explanation:
option A is correct answer
Which data set does this stem-and-leaf plot represent?
7, 0, 6, 2, 8
77, 7, 0, 6, 6, 0, 0, 2, 8
17, 27, 40, 46, 56, 60, 82, 88
40, 88, 82, 46, 56, 60, 17, 60, 27, 17
Answer:
it's 40, 88, 82, 46, 56, 60, 17, 60, 27, 17
can someone answer this question- I will give brainily if it is correct.
Answer:
A
Step-by-step explanation:
since decimals are 10ths and 100ths places, you can translate such into fractions
hope this helps:)
When hired at a new job selling electronics, you are given two pay options: • Option A: Base salary of $10,000 a year with a commission of 9% of your sales • Option B: Base salary of $20,000 a year with a commission of 4% of your sales How much electronics would you need to sell for option A to produce a larger income? Enter your answer as an inequality using the variable x to represent electronics sales in dollars. Do not enter any commas in your answer.
Using linear functions, it is found that the number of electronics that you need to sell for a larger income in option A is x > 200,000.
What is a linear function?A linear function is modeled by:
y = mx + b
In which:
m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function.Considering the base salaries as the intercept and the commissions as the slope, the functions are given by:
A(x) = 10000 + 0.09x.B(x) = 20000 + 0.04x.To produce a larger income in option A, it is needed that:
A(x) > B(x).
Hence:
10000 + 0.09x > 20000 + 0.04x
0.05x > 10000
x > 10000/0.05
x > 200,000
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In an arithmetic sequence, the sum of the second and eighth terms is $5$, and the product of the fourth and fifth terms is also $5$. What is the $20$th term of this sequence?
Answer:
10
Step-by-step explanation:
Let $a_n$ be the $n$th term of this sequence. We know $a_2 + a_8 = 5$, and that forces $a_5 = \dfrac 5 2$, the average of these terms.
Then $a_4a_5 = 5$ gives us $a_4 = 2$.
The common difference is $\dfrac 1 2$, and in general, $a_n = \dfrac n 2$.
Therefore the $20$th term is $\dfrac{20}{2} = \boxed{10}$.
The 20th term of the arithmetic sequence will be equal to [tex]T_{20}=10[/tex]
What is arthematic sequence?Arthematic sequence is the type of the number series in which the difference between the first and the second term is always constant in the whole series.
Let [tex]$a_n$[/tex] be the nth term of this sequence.
We know
[tex]$a_2 + a_8 = 5$[/tex], and that forces [tex]$a_5 = \dfrac 5 2$[/tex], the average of these terms.
Then [tex]$a_4a_5 = 5$[/tex] gives us [tex]a_4 = 2$.[/tex]
The common difference is [tex]\dfrac 1 2$,[/tex]and in general, [tex]$a_n = \dfrac n 2$[/tex].
Therefore the 20th term is
[tex]T_{20}=$\dfrac{20}{2} = \boxed{10}$.[/tex]
Hence the 20th term of the arithmetic sequence will be equal to [tex]T_{20}=10[/tex]
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Use the box plots comparing the number of boy dogs and number of girl dogs attending doggy daycare each day for a month to answer the questions.
The boxplots 1 and 2 represent the distribution of data using a five number summary for the male and the female attendance.
What will be the solution?(a) The IQR of the male's data
The first box plot represents the male's boxplot.
So, we have:
Upper quartile (Q3) = 14
Lower quartile (Q1) = 2
The IQR is the difference between the above values
IQR = Q3 - Q1
So, we have:
IQR = 14 - 2 = 12
So: the IQR for the males' data is 12
(b) The difference in the median values
From the first and second boxplots, we have:
Median male = 10
Median female = 18
The difference (d) between these values is
d = 18 - 10
d = 8
So: the difference between the median values of each data set is 8
(c) The distribution of data
This is dependent on whether the dataset has an outlier or not.
From the figure, we have:
Male's data: presence of an outlier - use median
Female's data: absence of an outlier - use mean
So: the male dataset is measured by median, while the mean is a better measure of center for the female's data
(d) Reason for outliers
A possible reason for outliers is sampling problems
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Max is creating a playlist and can have at most 180 minutes of music. He currently has 45 minutes. How many more minutes of music could Max include in the playlist?
Answer:
max could still add 135 minutes of music into his playlist
Step-by-step explanation:
180 - 45 = 135
Answer:
So we know that Max's playlist can have at most 180 minutes of music meaning that our amount of music cannot exceed that number. We are also given that Max already has 45 minutes of music on there so we need to subtract that from 180 minutes to see how much we have left.
[tex]180\ minutes - 45\ minutes[/tex]
[tex]135\ minutes[/tex]
Max still has 135 minutes left on his playlist that he can fill up.
Hope this helps! Let me know if you have any questions
A random sample of 87 eighth grade students’ scores on a national mathematics assessment
test has a mean score of 283. The test results prompts a state school administrator to declare
that the mean score for the eighth graders on the exam is more than 280. Assume the
population deviation is 37. At α = 0.14, is there enough evidence to support the administrator’s
claim?
There is not enough evidence to support the administrator’s claim and the true mean is not significantly greater than 280.
What is a statistical hypothesis?A hypothesis to test the given parameters requires that we determine if the mean score of the eighth graders is more than 283, thus:
The null hypothesis:
[tex]\mathbf{H_o \leq 283}[/tex]
The alternative hypothesis:
[tex]\mathbf{H_i > 283}[/tex]
From the population deviation, the Z test for the true mean can be computed as:
[tex]\mathbf{Z = \dfrac{\hat X - \mu _o}{\dfrac{\sigma}{\sqrt{n}}}}[/tex]
[tex]\mathbf{Z = \dfrac{283 -280}{\dfrac{37}{\sqrt{87}}}}[/tex]
Z = 0.756
Note that, since we are carrying out a right-tailed test, the p-value for the test statistics is expressed as follows:
P(z > 0.756)
P = 0.225
Since the P-value is greater than the significance level at α = 0.14, we can conclude that there is not enough evidence to support the administrator’s claim and the true mean is not significantly greater than 280.
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1,000 km = 1 mm
True or False
Answer: Heavily false. False by a long shot.
Step-by-step explanation: 1,000 kilometers is equivalent to 1e+9 millimeters. This is nine zeros after 1. So, this can be simplified as 1,000,000,000 milimeters, or rather, 1 billion millimeters. You can calculate this yourself by multiplying 1000 by 1,000,000 (1km = 1,000,000 mm.)
A. 0.31
B 0.52
C 0.56
D 0.26
Answer:
0.56
Step-by-step explanation:
A. Reflect across the x-axis, then shift 10 units up
B. Reflect across the x-axis, then shift 4 units up
OC. Reflect across the x-axis, then shift 6 units up
n Deflect across the wavie then chift & unite un
← PREVIOUS
Answer:
b. reflects across the x-axid then shift 4 units up
Step-by-step explanation:
(5,3)
I'm so confused on what I did wrong
Answer:
[tex]r < 15.5[/tex]
Step-by-step explanation:
Step 1: Add 4.5 to both sides
[tex]r - 4.5 < 11[/tex]
[tex]r - 4.5 + 4.5 < 11 + 4.5[/tex]
[tex]r < 15.5[/tex]
Answer: [tex]r < 15.5[/tex]
I don't really know what you did wrong but it seems like you added 45 to 11 instead of adding 4.5 to 11.
Hope this helps! Let me know if you have any questions
Javier uses 1/8 teaspoon of nutmeg for each loaf of banana bread he makes. How many loaves f banana bread can Javier with 4 teaspoons of nutmeg?
Which of these numbers are relatively prime to 51? Select all that apply. da) 84 Ob) 70 Oc) 62 0d) 30
Answer:
b) 70
c) 62
Step-by-step explanation:
Numbers are relatively prime when they have no factors in common.
__
The factors of 51 are ...
51 = 3×17
The factors of the other numbers are ...
84 = 2²×3×7 . . . . . has a factor of 3 in common with 51
70 = 2×5×7 . . . . . . no factors in common
62 = 2×31 . . . . . . . no factors in common
30 = 2×3×5 . . . . . has a factor of 3 in common with 51
The numbers 70 and 62 are relatively prime to 51.
Vicky has a spinner divided into 9 equal sections that are labeled 1 though 9. She wants to compare the theoretical probability and the experimental probability of spinning an odd number. She spins the spinner 10 times and records the results in this list.
{2, 4, 1, 8, 7, 5, 3, 4, 1, 9}
**Note - There are 3 answers. You must select 3 answers.**
The theoretical probability of spinning an odd number is equal to ______. The experimental probability of spinning an odd number is equal to ______. Therefore, the theoretical probability of spinning an odd number is _____ the experimental probability of spinning an odd number.
Question 7 options:
2/3
3/5
less than
greater than
1/2
5/9
1/5
Suppose you toss a coin and then roll a number cube.
What is the sample space for the compound event?
Question 9 options:
H1 T1 H6 T6
H T 1 2 3 4 5 6
H1 T1 H2 T2 H3 T3 H4 T4 H5 T5 H6 T6
TH1 TH2 TH3 TH4 TH5 TH6
A restaurant is serving a special lunch combo meal that includes a drink, a main dish, and a dessert. Customers can choose from 5 drinks, 6 main dishes, and 3 desserts.
How many different combo meals are possible?
Customers can create ______ different lunch combo meals.
Question 10 options:
36
90
14
120
Frank opens several pea pods & counts the number of peas in each pod. He records the number peas per pod: 7,8,9,10,11 Number of times: 1,4,18,15,2. written as a percent, what is the experiment probability that the pea pod has 9 peas in it? 48.8% 45% 18% 12.5%
The theoretical probability of spinning an odd number is equal to 5/9.
The experimental probability is equal to 3/5.
The theoretical probability of is greater than the experimental probability.
The sample space is H1 T1 H2 T2 H3 T3 H4 T4 H5 T5 H6 T6.
The different combo meals that are possible is 90.
The experiment probability that the pea pod has 9 peas in it is 45%.
What are the probabilities?
Probability is used to determine how likely it is that an event would happen. Experimental probability is based on the result of an experiment that has been carried out multiples times
The theoretical probability of spinning an odd number = odd numbers between 1 and 9 / 9 = 5/9
The experimental probability = number of odd number / sample space
6/10 = 3/5
The different combo meals possible = 6 x 5 x 3 = 90
The experiment probability that the pea pod has 9 peas in it = number of pods with 9 peas / total number of peas
(18/40) x 100 = 45%
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Problem 6.1
Which number is larger?
12x10^9
4x10^9
Answer:
7 7^10
1 5^9
yan po yung sagot
sana makatulong
The length of a rectangle is 3 times the
width. Find the dimensions of the
rectangle if its perimeter is 16 cm.
Step-by-step explanation:
length = 3×width
2×length + 2×width = 16
length + width = 8
we can use the first equation in the second :
3×width + width = 8
4×width = 8
width = 2 cm
therefore,
length = 3×width = 3×2 = 6 cm
find the speed and direction of a plane with a velocity of 〈5,-12〉.
Answer:
Below in bold.
Step-by-step explanation:
Speed = √(5^2 + (-12)^2)
= √169
= 13,
Direction = arctan (5/-12)
= -22.61 degrees ( its in the 4th quadrant)
So we can write the direction as 90 + 22.61
= 112.61 degrees.
Warren's Scores
Absolute Deviation from Mean Score
mean - individual score
0
25
15
10
20
30
10
15
5
25
20
15
20
5
50 dollars is on Emma's way
Step-by-step explanation:
Not math is free okay but only mathematics is free
(53 +9r²s) (12rs²-g³) + (-7r²s +7rs²)
Answer:
(negatively proximity is (31 + 1r¼)car bite
Step-by-step explanation:
Hope it helps
How to solve the square root of x - 1.
Answer:
I know i'm late but I think this might be right, I don't know, I used a website-
Step-by-step explanation:
When
√x-1
STEP
1
:
Isolate the square root on the left hand side
Radical already isolated
√x-1 = 0
STEP
2
:
Eliminate the radical on the left hand side
Raise both sides to the second power
(√x-1)2 = ()2
After squaring
x-1 =
STEP
3
:
Solve the linear equation
Rearranged equation
x -1 = 0
Add 1 to both sides
x = 1
A possible solution is :
x = 1
STEP
4
:
Check that the solution is correct
Original equation
√x-1 =
Plug in 1 for x
√(1)-1 =
Simplify
√0 = 0
Solution checks !!
Solution is:
x = 1
also, want to talk and be friends?
~Dreamer1331~
HELP ASAP!! (NO LINKS) I WILL GIVE BRAINLIEST
The numbers of attendees at the carnival over the last 15 days are 50, 200, 175, 125, 75,
100, 150, 225, 250, 100, 125, 75, 25, 225, and 175. identify the box-and-whisker plot for
the data.
Answer:
The answer is C.
Step-by-step explanation:
From looking at the values you are given. The only one that matchs with your beginning values of 25 and endding values of 250 is answer C. For a more elaborate explanation, please ask another student for more details.
16 km
12 km
What is the length of the hypotenuse? If necessary, round to the nearest tenth.
С
kilometers
If
x
=
−
9
and
y
=
2
, evaluate the following expression:
2
(
y
−
3
x
y
)
I need help on this question and please explain what I got wrong so I understand and what I'm supposed to do.
Answer:
A. 64
Step-by-step explanation:
In this problem, you're trying to find out what b is.
With the information that you have, you know that the answer will be 16, and your denominator (what you'll be dividing by) is 4. What you got wrong in this was thinking of it as "what times 4 equals 16", to which you got the answer 4 because 4*4=16. But, that's not exactly what you're supposed to be doing.
If we looked at it like that in this problem, you'd have b=4, making the equation then look like 4/4=16. This isn't true because 4/4=1.
Instead, to get the correct answer, you'll be multiplying 4, the denominator, by 16, our solution. With this, you'll get the answer A. 64.
If you have any more questions, feel free to reach out for help.
Answer:
We are given an equation of [tex]\frac{b}{4} = 16[/tex] and we need to determine what b is. The way that we would do this is what you did and we would multiply both sides by 4 which would get rid of the 4 in the fraction and this would end up multiplying 16 by 4 giving us [tex]b=64[/tex]. This would best match with option A which is 64.
Hope this helps! Let me know if you have any questions
A rectangle has sides measuring (12x - 2) units and (x + 8) units.
Part A: What is the expression that represents the area of the rectangle? Show your work. (5 points)
Part B: What is the expression that represents the perimeter of the rectangle? Show your work. (5 points)
Part C: What are the degree and classification of the expression obtained in Part A? (3 points)
The area equation is:
A = (12x - 2)*(x + 8)
Which is a polynomial of degree 2, and the perimeter is:
P = 26x + 12
How to write the area of the rectangle?
Remember that for a rectangle of length L and width W, the area is written as:
A = L*W
Here we know that:
L = (12x - 2)
W = (x + 8)
Then the equation for the area is:
A = (12x - 2)*(x + 8).
How to write the perimeter?For a rectangle of length L and width W, the perimeter is:
P = 2*(L + W).
Replacing what we know, we get:
P = 2*(12x - 2 + x + 8) = 2*(13x + 6) = 26x + 12
What are the degree and classification of the area equation?The area equation is:
A = (12x - 2)*(x + 8).
Notice that this is a polynomial that is made of the product of two polynomials of degree 1, so this is a polynomial of degree 2.
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