Answer: 8/3 and -9/4
Step-by-step explanation:
1. \(\frac{2^{3}}{3} = \frac{2 * 2 * 2}{3} = \frac{8}{3}\)
2. In this problem, when raising a whole fraction to a power, you must both raise the numerator and denominator to that power.
\(-(\frac{3}{2})^2 = -(\frac{3^2}{2^2}) = -(\frac{9}{4}) = -\frac{9}{4}\)
Simplify the expression so there is only one positive power for the base, -5.
Answer:
c
Step-by-step explanation:
it's a property of powers, when the base is the same (-5) , you need to
sum the powers when both terms are multiplyng
subtract the powers when both terms are dividing (numerator power minus denominator power, in that order)
match the figures with thier name =D--------------C
What are three consecutive multiples of 3 if 2/3
of the sum of the first
two numbers is 1 greater than the third number?
The three consecutive multiples of 3 are 15, 18 and 21
To solve this problem
First, let's determine three successive multiples of 3:
The subsequent two would be "x+3" and "x+6" if we call the initial number "x".
Since we are aware that the third number (x+6) is one more than the first two numbers (x + x+3), we can write the following equation:
2/3(x + x+3) = (x+6) + 1
Simplifying this equation, we get:
2/3(2x+3) = x+7
Multiplying both sides by 3, we get:
2(2x+3) = 3(x+7)
Expanding and simplifying, we get:
4x + 6 = 3x + 21
Subtracting 3x and 6 from both sides, we get:
x = 15
Therefore, the three consecutive multiples of 3 are 15, 18 and 21
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What is 569,400 in scientific notation?
Answer:
Step-by-step explanation:
5,69,400,000 = 5.694 x 10^5
A 799.99 television is selling for 13% off. Find the final price of the television if the sales tax is 6%
18-ax=42 solve the equation for x assume a≠0
Answer:
x=-24/a
Step-by-step explanation:
18-ax=42 isolate x by subtracting 18 from both sides to get -ax=24 then divide by a negative 1 to get ax=-24 then divide by a to isolate x to get x=-24/a
Suppose a baker claims that the average bread height is more than 15cm. Several of this customers do not believe him. To persuade his customers that he is right, the baker decides to do a hypothesis test. He bakes 10 loaves of bread. The mean height of the sample loaves is 17 cm with a sample standard deviation of 1.9 cm. The heights of all bread loaves are assumed to be normally distributed. The baker is now interested in obtaining a 95% confidence interval for the true mean height of his loaves. What is the lower bound to this confidence interval? 2 cm (round to 2 decimal places) What is the upper bound to this confidence interval? cm (round to 2 decimal places) For the following situations, use RStudio to find the appropriate t-critical values that would be needed to construct a confidence interval. Round all critical values to the second decimal place. 1. n = 15, confidence level is 95%, x= 35 and s = 2.7, t-critical value- 2, n = 37, confidence level is 99%, x= 82 and s = 5.9 t-critical value- 2 3, n 1009, confidence level is 90%, x 0.9 and s-0.04 t- critical value = 2 2
The correct answer is Confidence interval lower bound: 32.52 cm,Confidence interval upper bound: 37.48 cm
To calculate the confidence interval for the true mean height of the loaves, we can use the t-distribution. Given that the sample size is small (n = 10) and the population standard deviation is unknown, the t-distribution is appropriate for constructing the confidence interval.
The formula for a confidence interval for the population mean (μ) is:
Confidence Interval = sample mean ± (t-critical value) * (sample standard deviation / sqrt(sample size))
For the first situation:
n = 15
Confidence level is 95% (which corresponds to an alpha level of 0.05)
x = 35 (sample mean)
s = 2.7 (sample standard deviation)
Using RStudio or a t-table, we can find the t-critical value. The degrees of freedom for this scenario is (n - 1) = (15 - 1) = 14.
The t-critical value at a 95% confidence level with 14 degrees of freedom is approximately 2.145.
Plugging the values into the formula:
Confidence Interval = 35 ± (2.145) * (2.7 / sqrt(15))
Calculating the confidence interval:
Lower Bound = 35 - (2.145) * (2.7 / sqrt(15)) ≈ 32.52 (rounded to 2 decimal places)
Upper Bound = 35 + (2.145) * (2.7 / sqrt(15)) ≈ 37.48 (rounded to 2 decimal places)
Therefore, the lower bound of the confidence interval is approximately 32.52 cm, and the upper bound is approximately 37.48 cm.
For the second situation:
n = 37
Confidence level is 99% (which corresponds to an alpha level of 0.01)
x = 82 (sample mean)
s = 5.9 (sample standard deviation)
The degrees of freedom for this scenario is (n - 1) = (37 - 1) = 36.
The t-critical value at a 99% confidence level with 36 degrees of freedom is approximately 2.711.
Plugging the values into the formula:
Confidence Interval = 82 ± (2.711) * (5.9 / sqrt(37))
Calculating the confidence interval:
Lower Bound = 82 - (2.711) * (5.9 / sqrt(37)) ≈ 78.20 (rounded to 2 decimal places)
Upper Bound = 82 + (2.711) * (5.9 / sqrt(37)) ≈ 85.80 (rounded to 2 decimal places)
Therefore, the lower bound of the confidence interval is approximately 78.20 cm, and the upper bound is approximately 85.80 cm.
For the third situation:
n = 1009
Confidence level is 90% (which corresponds to an alpha level of 0.10)
x = 0.9 (sample mean)
s = 0.04 (sample standard deviation)
The degrees of freedom for this scenario is (n - 1) = (1009 - 1) = 1008.
The t-critical value at a 90% confidence level with 1008 degrees of freedom is approximately 1.645.
Plugging the values into the formula:
Confidence Interval = 0.9 ± (1.645) * (0.04 / sqrt(1009))
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3. The table below shows the rates for two duplicating companies.
For what number of pages will the two duplicating stores charge the same amount?
Answer:
250 pages
Step-by-step explanation:
Write an expression for the cost of x pages for each of the companies. Then set the expressions equal, and solve for x, the number of pages.
Quick Copy: 5 + 0.06x
Copy Place: 10 + 0.04x
5 + 0.06x = 10 + 0.04x
0.02x = 5
x = 5/0.02
x = 250
Answer: 250 pages
Check
Quick Copy: 5 + 0.06(250) = 5 + 15 = 20
Copy Place: 10 + 0.04(250) = 10 + 10 = 20
For 250 copies, both places cost $20. 250 copies is the correct answer.
what mathematical strenght and skills did you develop in this lesson
Answer:
I have learned a lot in math, although it was years ago on of my favorite things to learn was to multiply and divide. They were not only easy but also fun.
Step-by-step explanation:
A recipe says to use 3 cups of flour to make 48 cookies. What is the constant of proportionality that relates the number of cookies made, y , to the number of cups of flour used, x ?
Answer: 3cups
Step-by-step explanation:
List all of the solutions.
3cups = 48 = y = cups = x =
Answer:
3cups
Step-by-step explanation:
Use GCF to factor
40x+24y-56
Answer:
8(5x+3y-7)
Step-by-step explanation:
I just learned this like 2 months ago lolll
I need help with my math please
Answer:
41-29=12
756+223=979
821-690=131
eleventh, fifteenth, nineteenth
4
2
How many integers satisfy each inequality?
-102
Answer:At integers -2 and -3 the value of the equation is zero, hence satisfies the inequality. So overall 4 integers satisfy the inequality.
i got 1 2 3 4 5 6 7 8 ems in my bank account
Step-by-step explanation:
Fill in the boxes to add the expressions.
(5.19+4m)+(4.18+3.95m) = (4m+_)+(5.19+_)=_
Using common factor method, sum of the given expressions is 17.14m + 9.37
what is common factor ?
In mathematics, a common factor is a factor that two or more numbers have in common. For example, the numbers 12 and 18 have common factors of 1, 2, 3, and 6. The greatest common factor (GCF) is the largest number that divides evenly into two or more numbers.
In algebra, we often use the term "common factor" when referring to expressions. When two or more algebraic expressions have a factor in common, we can use the distributive property to factor out the common factor.
According to the question:
To add the expressions (5.19+4m)+(4.18+3.95m), we can first group the like terms:
(5.19 + 4.18) + (4m + 3.95m)
9.37 + 7.95m
So, the sum of the expressions is:
(5.19+4m)+(4.18+3.95m) = 9.37 + 7.95m
Now, we can use the distributive property to factor out a common factor of m from 7.95m:
9.37 + 7.95m = 4m + (5.19 + 7.95)m
We can factor out a common factor of 1 from (5.19 + 7.95)m:
4m + (5.19 + 7.95)m = (4 + 5.19 + 7.95)m
Adding the coefficients, we get:
4 + 5.19 + 7.95 = 17.14
Therefore, the sum of the expressions is:
(5.19+4m)+(4.18+3.95m) = (4m+5.19)+(3.95m+4.18)= 17.14m + 9.37.
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What is the y-intercept ??? Please show step by step!!
Need help with my geometry homework grade due to
The surface area of the base ball to the nearest whole number is 26 in²
What is surface area of a sphere?A sphere is defined as the set of all points in three-dimensional Euclidean space that are located at a distance.
The area occupied by a three-dimensional object by its outer surface is called the surface area.
The surface area of a sphere is expressed as;
SA = 4πr²
where r is the radius and it's calculated as;
C = 2πr
9 = 2πr
r = 4.5/π =
SA = 4 π × (4.5/π)²
SA = 81/π
SA = 26 in²( nearest whole number)
Therefore the surface area of the sphere is 26 in²
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ZABD and ZDBC are supplementary angles.
What is the measure of x?
x = [?]°
7D
AK
126
x
B
-С
Angles are not drawn to scale.
Enter
x=102°Answer:
x+78=180 supplementary angle
x=180-78=102
There are 10 cards placed face down on a table. Four of the cards have stars on them and the other 6 are blank. You
win if you draw a card with a star. How can the game be made fair?
The game is already fair.
Add 2 cards with stars,
Add a star to 1 of the blank cards
Take away 2 blank cards
The first one is out, because it isn't fair. We want a 50/50 chance to win. If we add 2 cards with stars, then your chance of winning increases too much(as much as that'd be great). If we take away 2 blank ones, it would be fair, but we want to still have 10 cards. So the only choice left is to add a start to 1 of the blank cards.
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hope it helps
the driveway in front of the brown house is 35 feet long and the driveway of the red house is 7 yards and 9 feet long. which house has a long driveway? by how much
Answer:
The brown house has the longer driveway
Step-by-step explanation:
So we would need to convert both of these units of measurements to feet in order to compare them.
There are 3 feet in 1 yardConverting yards to feet, wee need to multiply the number of yards by 3
7 yards = 21 feetSince the red house has a driveway of 7 yards and 9 feet, we can rewrite this to 21 feet + 9 feet, which is equivalent to 30 feet
Now comparing the two driveways, the 35 ft-long brown driveway is 5 feet longer than the 30 ft-long red driveway.
The brown house has the longer driveway
please help me! will mark the brainliest! no spammers
Answer:
3u • (2u + 7)2
Step-by-step explanation:
3u • (2u + 7) • (2u + 7)
I NEED HELP PLEASEEEEE?!!!!!!!!! ASAPPPP HELP ME))):
Find the length of AN given the figure below:
Applying the two-tangent theorem, the length of AN is: 21 units.
What is the Two-Tangent Theorem?The two-tangent theorem is a geometric theorem that states that if two tangents are drawn to a circle from a point outside the circle, then the lengths of the tangent segments are equal. This theorem is often used in geometry to find the length of tangent segments and to prove the existence of tangents to circles.
More formally, the two-tangent theorem states that if P is a point outside a circle with center O, and if PA and PB are tangents to the circle from point P, then PA = PB. In other words, the lengths of the two tangent segments are equal.
From the image above, AM and AN are two tangents from the same circle. Also, AN is also tangent with 29 - 2y.
This implies that the three tangents are congruent. Therefore:
6y - 3 = 29 - 2y
6y + 2y = 29 + 3
8y = 32
y = 32/8
y = 4
AN = 6y - 3
Plug in the value of y
AN = 6(4) - 3
AN = 21 units.
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Is there a proportional relationship between x and y?
5
10
6
9
2
Cans of Paint (x)
Bird Houses Painted (y)
15
30
18
27
6
Yes, k =2
Yes, k=3
No
Answer:
Unnnnnnnnnnnnnnnnnnnnnnnnbnbnnnn
Explain with steps please and thank you! :)
Using the information in the given diagram, the value of the missing angle is: m∠1 = 75°
How to find the missing angle?The transverse line theorem states that If two parallel lines are cut by a transversal, then corresponding angles are congruent. Two lines cut by a transversal are parallel IF AND ONLY IF corresponding angles are congruent.
Now, when we draw a horizontal line parallel to lines a and b and directly cutting across the vertex of angle 1, we can see that angle 1 will be composed of two angles.
Now, for the transverse line theorem we can say that:
Angle 1 will be composed of two angles namely:
48 degrees and (180 - 153) degrees.
Thus:
m∠1 = 48° + 27°
m∠1 = 75°
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A company produced in the first quarter 6,905 pieces in the second quarter the same company produced 795 pieces more than in the first quarter under these conditions how many pieces did the company produce in the first semester?
Answer: 14,605 pieces.
Step-by-step explanation:
In the second quarter, the company produced 795 pieces more than in the first quarter.
So, the total pieces produced in the second quarter can be calculated as:
6905 + 795 = 7700
The total pieces produced in the first semester (two quarters) can be calculated as:
6905 + 7700 = 14,605
Therefore, the company produced 14,605 pieces in the first semester.
The number of pieces the company produced in the first semester was 14,605 pieces.
How many?The question asks to calculate how many pieces a company produced in the first semester, considering the production of two quarters.
In the first quarter, the company produced 6,905 pieces, as indicated in the question.
Already in the second quarter, the company produced 795 more pieces than in the first quarter, which means that the production in the second quarter was:
6,905 + 795 = 7,700 pieces.
To know the company's total production in the first semester, just add the productions of the two quarters:
6,905 + 7,700 = 14,605 pieces
Group the terms with variables on one side of the equal sign, and simplify.
5z + 3 = 36z
Answer:
z = 3/31
Step-by-step explanation:
5z + 3 = 36z
subtract 5z on both sides
3 = 31z
divide by 31 on both sides
z = 3/31
Solve the following system of equations.
(15 Points)
x + 3y = -5 & 5y - 10 = -20x
Answer:
( 1 ; -2 )
Step-by-step explanation:
x + 3y = -5..............1
5y - 10 = -20x........2
x = -5 - 3y..............3
5y - 10 = -20( -5 - 3y)
5y - 10 = 100 + 60y
-55y = 110
y = -2
x = 1
How does Mathematics differ from language to language across the world
The answer is explained below.
In order to be considered a language, a system of communication must have vocabulary, grammar, syntax, and people who use and understand it. Mathematics meets this definition of a language. Linguists who don't consider math a language cite its use as a written rather than spoken form of communication.
Mathematics is pure language - the language of science. It is unique among languages in its ability to provide precise expression for every thought or concept that can be formulated in its terms. In a spoken language, there exist words, like "happiness", that defy definition.
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Please help it is algebraic properties of limits!
Answer:
Hi, I'd be happy to help. Is there a photo you can attach of the problem you need help with?
4
Solve the following equation: *
3x + 7 = 5x - 15
Enter your math answer
5
Solve the following equation: *
3(2x - 5) = 9x + 24
Enter your math answer
Answer:
4. x = 11
5. x = -13
Step-by-step explanation:
4. 3x + 7 = 5x - 15
-7 -7
3x = 5x - 22
-5x -5x
-2x = -22
-2x/-2 = -22/-2
x = 11
5. 3(2x - 5) = 9x + 24
6x - 15 = 9x + 24
+15 +15
6x = 9x + 39
-9x -9x
-3x = 39
-3x/-3 = 39/-3
x = -13
Hope this helps, have a great day:)