Answers
Solution:
[tex]\rightarrow \frac{4^{-3} \times 3^{4} \times 4^{2} }{3^{5} \times 4^{-2} }[/tex]
[tex]\rightarrow 4^{-3 + 2} \times 3^{4 - 5} \times 4^{2} }[/tex]
[tex]\rightarrow 4^{-1} \times 3^{-1} \times 16}[/tex]
[tex]\rightarrow \frac{1}{4} \times \frac{1}{3} \times 16}[/tex]
[tex]\rightarrow \frac{1}{12} \times 16}[/tex]
[tex]\rightarrow \frac{16}{12}[/tex]
[tex]\rightarrow \boxed{\bold{\frac{4}{3} \tex\text{ (Option B)}}}[/tex]
Answer:
[tex]\dfrac43[/tex]
Step-by-step explanation:
[tex]\dfrac{4^{-3}\cdot3^4\cdot4^2}{3^5\cdot4^{-2}}[/tex]
Separate like terms:
[tex]\implies \dfrac{4^{-3}\cdot4^2}{4^{-2}}\cdot \dfrac{3^4}{3^5}[/tex]
Use exponent rule [tex]a^b \cdot a^c=a^{(b+c)}[/tex] :
[tex]\implies \dfrac{4^{(-3+2)}}{4^{-2}}\cdot \dfrac{3^4}{3^5}[/tex]
[tex]\implies \dfrac{4^{-1}}{4^{-2}}\cdot \dfrac{3^4}{3^5}[/tex]
Use exponent rule [tex]\dfrac{a^b}{a^c}=a^{(b-c)}[/tex]
[tex]\implies 4^{(-1--2)}\cdot {3^{(4-5)}[/tex]
[tex]\implies 4^{1}\cdot {3^{-1}[/tex]
Use exponent rule [tex]a^{-1}=\dfrac{1}{a}[/tex]
[tex]\implies 4\cdot \dfrac13[/tex]
[tex]\implies \dfrac43[/tex]
Related Questions
-3 1/2 - [-12 1/4]...............................................
Answers
Answer:
8.75
Step-by-step explanation:
Answer:
8 3/4
Step-by-step explanation:
Find the area of the parallelogram ABCD
А
B
12 cm
-10 cm-
C
D
-30 cm
Answers
Answer:
I think it is 3600
Step-by-step explanation:
2.8x = -9.24
A. 12.04
B. -0.3030
C. -3.3
D. 12.04
Please helppp
Answers
Answer:
Choice c, 3.3
Step-by-step explanation:
To find out the vaule of X, we have to divided -9.24 by 2.8. We have to divided because when X and next to a number, it means to multiply, and the opposite of multiplication is division. To double check to determine whether or not the answer is correct, simply multiply -3.3 by 2.8 and you will get -9.24.
Rassan invests a sum of money in a savings account, with an interest rate of 4%. After 3 years, the balance reaches $1799.78. What is the amount of the initial investment? Round to the nearest whole dollar.
Answers
Answer:
I believe it is $1,607 hope it helps
Find the verte of the quadratic function given below f(x) = (x-4) (x+2)
Answers
Answer:
Vertex at (1,-9)
Step-by-step explanation:
Expand the equation by using foil method.
You should get X^2+2x-4x-8
And then add the like terms.
X^2-2x-8
And use this formula to find the vertex.
X=b/2a
plug in the values
X=-2/2(1)
you should get x=1
Thats the one value.
For another one you have to plug in you X= (value which is 1) in the f(x) which now becomes f(1)
the answer is f(1)=-9
Which of the following correctly simplifies the expression (2².60) ? ² t 79 32 343 0() 이 - 야 (4) 2².0 2²1 77 64 343 2.0 = 0 78
Answers
Answer:
hello
[( 2 ² * 6 ⁰ ) / 7 ] ³
= ( 2 ⁶ * 1 ³) / 7 ³
= ( 64 *1 ) / 343
= 64/343
Step-by-step explanation:
19.) Vernon has a bank account balance of $24.70, and then deposits $30 into his account. What is
his new balance after the deposit?
Answers
-24.7+30=5.3
his new balance is 5.3
Answer:
$54.70
Step-by-step explanation:
take $24.70 and add $30 to it and $24.70+$30=$54.70
What is 3/5×6/5. Move the numbers to the boxes to show answer. If there is no whole number ,put a 0 in the box
Answers
Answer:
72/100
Step-by-step explanation:
hope this helps!
Answer:
18/25
Step-by-step explanation:
How many 1/4 cup servings are in 3 cups of chololate?
Answers
Answer:
The answer is 12. In 3 cups of chocolate, there are 12 1/4 cup in them.
Step-by-step explanation:
each 1 cup had four 1/4 cup in them. So 4 times 3 cups is 12.
There are 12 servings of 1/4 cup in 3 cups of chocolate.
The term "serving" typically refers to a specified portion or amount of food or drink that is recommended or commonly consumed at one time. It helps in providing a standard measurement for nutritional information and portion control.
To determine the number of 1/4 cup servings in 3 cups of chocolate, we need to calculate the total number of 1/4 cup servings that can be made from the given amount.
1. One cup is equal to 4 quarters (1 cup = 4 × 1/4 cup).
2. To find the number of 1/4 cup servings in 3 cups, multiply 3 cups by the conversion factor (4 × 1/4 cup) for each cup.
3 cups × (4 × 1/4 cup) = 3 cups × 1 cup = 3 cups
Therefore, there are 3 * 4 = 12 servings of 1/4 cup in 3 cups of chocolate.
Learn more about Conversion here:
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#SPJ2
Find the solution set to the following equation. Answer only in numbers.
x^2+ 8x = 0
Answers
[tex]\huge\text{Hey there!}[/tex]
[tex]\mathsf{x^2 + 8x = 0}\\\larg\text{Firstly: FACTOR the LEFT SIDE of the equation}\\\mathsf{\rightarrow x(x + 8) = 0}\\\large\text{Secondly: SET the FACTORS to equal to 0}\\\mathsf{\rightarrow x \approx 0\ or \ x + 8 = 0}\\\large\text{Thirdly: SIMPLIFY}\\\mathsf{\rightarrow x = 0\ or \ x = -8}\\\huge\text{Therefore, your answer is: \boxed{\mathsf{x = 0\ or\ x = -8}}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]Which equation calculates the number of 1/8-foot pieces you can cut from 5 feet of ribbon?
Answers
Private colleges and universities rely on money contributed by individuals and corporations for their operating expenses. Much of this money is put into a fund called an endowment, and the college spends only the interest earned by the fund. A recent survey of 8 private colleges in the United States revealed the following endowments (in millions of dollars): 60.2, 47.0, 235.1, 490.0, 122.6, 177.5, 95.4, and 220.0. Summary statistics yield 180.975 and s143.042. Calculate a 95% confidence interval for the mean endowment of all the private colleges in the United States assuming a normal distribution for the endowments. Round to three decimal places.
Answers
Answer:
The 95% confidence interval [tex] 81.852 < \mu < 280.098 [/tex]
Step-by-step explanation:
From the question we are told that
The sample mean is [tex]\= x = 180.975[/tex]
The standard deviation is [tex]\sigma = 143.042[/tex]
The sample size is n = 8
Given that the confidence level is 95% then the level of significance is
[tex]\alpha =( 100- 95) \%[/tex]
=> [tex]\alpha =0.05[/tex]
Generally from the normal distribution table the critical value of [tex]\frac{\alpha }{2}[/tex] is
[tex]Z_{\frac{\alpha }{2} } = 1.96[/tex]
Generally the margin of error is mathematically represented as
[tex]E = Z_{\frac{\alpha }{2} } * \frac{\sigma }{\sqrt{n} }[/tex]
=> [tex]E = 1.96 * \frac{ 143.042 }{\sqrt{8} }[/tex]
=> [tex]E = 99.123 [/tex]
Generally 95% confidence interval is mathematically represented as
[tex]\= x -E < \mu < \=x +E[/tex]
=> [tex]180.975 -99.123 < p < 180.975 +99.123[/tex]
=> [tex] 81.852 < \mu < 280.098 [/tex]
Using the t-distribution, it is found that the 95% confidence interval for the mean endowment of all the private colleges in the United States assuming a normal distribution for the endowments, in millions of dollars, is (61.39, 300.56).
The information given is:
Sample mean of [tex]\overline{x} = 180.975[/tex].Sample standard deviation of [tex]s = 143.042[/tex]Sample size of [tex]n = 8[/tex].We have the standard deviation for the sample, hence, the t-distribution is used.
The interval is given by:
[tex]\overline{x} \pm t\frac{s}{\sqrt{n}}[/tex]
The critical value for a two-tailed 95% confidence interval with 8 - 1 = 7 df is t = 2.3646.
Then:
[tex]\overline{x} - t\frac{s}{\sqrt{n}} = 180.975 - 2.3646\frac{143.042}{\sqrt{8}} = 61.39[/tex]
[tex]\overline{x} + t\frac{s}{\sqrt{n}} = 180.975 + 2.3646\frac{143.042}{\sqrt{8}} = 300.56[/tex]
The 95% confidence interval for the mean endowment of all the private colleges in the United States assuming a normal distribution for the endowments, in millions of dollars, is (61.39, 300.56).
To learn more about the t-distribution, you can take a look at https://brainly.com/question/25077184
Help math math ASAP ASAP
Answers
Answer:
[tex]\displaystyle y + 2 = 4(x + 1)[/tex]
Step-by-step explanation:
Parallel equations have SIMILAR RATE OF CHANGES [SLOPES], so 4 remains as is as you proceed with plugging the information into the Point-Slope Formula:
[tex]\displaystyle [-1, -2] \\ \\ \boxed{y + 2 = 4(x + 1)}[/tex]
**Remember, all negative symbols give you the OPPOCITE TERMS OF WHAT THEY REALLY ARE, so make sure both operation symbols are correct.
I am joyous to assist you at any time.
What is the mode for this set of data? 34, 36, 56, 58, 58, 58, 61, 62, 62
Answers
Answer:
52
Step-by-step explanation:
Mode is the number that appears the most in the set of data, so we would need to find the number that occurs the most. In this case, it's 52.
Answer:
Your answer whould be 58
Step-by-step explanation:
exmple 67,67,78,78,67,43,34,12, the mobe is 67
The student body of 24 students
wants to elect a president, minister
of Arts, minister of PE department,
and minister of Science. How many
different arrangements are there?
Answers
There are 10,626 ways of arranging the required offices from a body of 24 students.
What is combination?
Combination deals with the way in which a arrangement can be made from a particular lot. In this case, we want to select a president, minister of Arts, minister of PE department, and minister of Science from a body of 24 students.
Hence;
24C4 = 24!/4! (24 - 4)! = 24!/4!20!
So;
24 * 23 * 22 * 21 * 20!/20! * 4 * 3 * 2*1
= 24 * 23 * 22 * 21 / 4 * 3 * 2*1
= 10,626 ways
Learn more about combination: https://brainly.com/question/26852614
How can you solve the equation for 8(-3d+2)=88
Answers
Answer:
-3
Step-by-step explanation:
8(-3d + 2) = 88 divide both sides by 8
-3d + 2 = 11 rest 2 on both sides
-3d = 9 divide both sides by -3
d = -3
Answer:
i think D it's 110 cuz : 8×-3d and 8×2 = -24d+2=88 so D=88+24-2=110
If three angles of a triangle are "(3x - 2) degrees, (8x - 5) degrees, and (7x+7) degrees", then what does "x" equal?
Answers
Answer:
10
Step-by-step explanation:
The sum of the measures of the angles of a triangle.is 180 degrees, so:
3x-2+8x-5+7x+7=180
18x=180
x=10
If we consider the simple random sampling process as an experiment, the sample mean is a. a random variable. b. always zero. c. exactly equal to the population mean. d. always smaller than the population mean.
Answers
The sample mean is an estimate of the population mean.
The sample mean is exactly equal to the population mean
How to determine the true statement
When the population mean is known; the value of the population mean can be used as the sample mean.
This is so because:
The sample mean is an estimate of the population mean.
And it is represented as:
[tex]\bar x = \mu[/tex]
Hence, the true statement is that the sample mean is exactly equal to the population mean
Read more about sample mean at:
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Find the value of xx, yy, and zz in the parallelogram below.
Answers
Answer:
Step-by-step explanation:
What is the total area, in square meters, of the shaded sections of the trapezoid below?
Answers
Answer:
56.16 sqm
Step-by-step explanation:
Area of triangle = 0.5 * base * height
= (0.5 * 7 * 7.2) + (0.5 * 8.6 * 7.2)
= (25.2) + (30.96)
= 56.16
what lines represent parallel to y=6x+2
Answers
Answer:
g
Step-by-step explanation:
Hi please help no links and no fake answers please!
Answers
answer: the student made an error. The first factor, 9, was distributed to only one of the terms inside the parentheses
(6x-1) = (5x+28)
X=?
Answers
x = 29
Answer:
x = 29
Step-by-step explanation:
(6x-1) = (5x+28)
or, 6x-1 = 5x+28
or, 6x-5x = 28+1
or, x = 29
Rosters Chicken advertises "lite" chicken with 30% fewer calories than standard chicken. When the process for "lite" chicken breast production is in control, the average chicken breast contains calories, and the standard deviation in caloric content of the chicken breast population is calories. Rosters wants to design an -chart to monitor the caloric content of chicken breasts, where chicken breasts would be chosen at random to form each sample. a) What are the lower and upper control limits for this chart if these limits are chosen to be four standard deviations from the target? Upper Control Limit () nothing calories (enter your response as an integer).
Answers
Correct question is;
Rosters Chicken advertises "lite" chicken with 30% fewer calories than standard chicken. When the process for "lite" chicken breast production is in control, the average chicken breast contains 450 calories, and the standard deviation in caloric content of the chicken breast population is 20 calories. Rosters wants to design an X-chart to monitor the caloric content of chicken breasts, where 25 chicken breasts would be chosen at random to form each sample. a) What are the lower and upper control limits for this chart if these limits are chosen to be four standard deviations from the target? b) What are the limits with three standard deviations from the target? Upper Control Limit (UCL)calories (enter your response as an integer).
Answer:
A)UCL = 466
LCL = 434
B)UCL = 462
LCL = 438
Step-by-step explanation:
We are given;
Mean;μ = 450
Standard deviation; σ = 20
Sample size; n = 25
A) We are told that these limits are chosen to be four standard deviations from the target.. This means that z-value = 4.
Thus, upper control limit will be the formula;
UCL = μ + 4σ/√n
UCL = 450 + 4(20)/√25
UCL = 450 + 16
UCL = 466
Lower control limit will be;
LCL = μ - 4σ/√n
LCL = 450 - 4(20)/√25
LCL = 450 - 16
LCL = 434
B) We are now told that these limits are chosen to be three standard deviations from the target.
Thus, z = 3
So;
UCL = μ + 3σ/√n
UCL = 450 + 3(20)/√25
UCL = 450 + 12
UCL = 462
Lower control limit will be;
LCL = μ - 3σ/√n
LCL = 450 - 3(20)/√25
LCL = 450 - 12
LCL = 438
Simplify to create an equivalent expression.
8-4(-x+5)
Thank you!
Answers
Question 1 of 15
Ahana swims laps on Tuesday and Thursday mornings. On
Thursday she swims 1 more than twice the number of laps
she swam on Tuesday.
If x represents the number of laps that Ahana swam on Tuesday, select the
expression that represents the total number of laps she swam on Tuesday
and Thursday
O A. 2x + 1
B. 3x + 1
O C. 2x + 2
O D. 3x - 1
Answers
Answer:
3x + 1
Step-by-step explanation:
The table shows several points for function h(x). A 2-column table with 6 rows. Column 1 is labeled x with entries 0, 3, 6, 9, 12, 15. Column 2 is labeled h (X) with entries 1, 6, 12, 2, 8, 9. Which point is on the graph of the inverse function h–1(x)? (0, 1) (6, 3) (9, –15) (12, –8)
Answers
Answer:
B
Step-by-step explanation:
Ed2021
these numbers form an addition and subtraction fact family 6,7,13 choose the fact family formed by these numbers what is the answer
Answers
Answer:
6-13=7 , 7-13=6
6+1=7,7-1=6,
Step-by-step explanation:
which statement best describes the set 14 16 18 20 22
Answers
Answer:
They are adding 2 by each number.
A set of numbers is a group of numbers that are related in one way or the other. The statement that best describes the set is:
The set of even numbers from 14 to 22
Given that:
[tex]Set = 14\ 16\ 18\ 20\ 22[/tex]
From the above set of numbers, we have the following observations
All numbers are evenThe difference between consecutive numbers is 2So, we can describe the set using the following statement:
The set of even numbers from 14 to 22
Read more about set of numbers at:
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can you help me solve for x
Answers
Answer:
x = √80
Step-by-step explanation:
Let's find the hypotenuse of the top side triangle.
Using the Pyth. Theorem:
Let y be the hypotenuse of the top side triangle:
2^2 + 4^2 = y^2
y = √20
Now, the rectangle facing us is formed by two indentical triangles, therefore the bottom side of the triangle is also y = √20 .
Using the Pyth.Theorem again, we can find x:
x^2 + (√20)^2 = 10^2
x = √80 .