X is equal 5 in 4 to the power of 2x divided by 8 to the power x is equal to 32.
What is base and power?Raising a base number to an exponent is referred to as "power" in mathematics. It indicates that "base number" and "exponent" are the two fundamental components of powers. The exponent shows how many times the base number has been multiplied, whereas the base number is defined as a number that is multiplied by itself.
In a nutshell, power is a number that has exponents used to express it. It means that the same element has been multiplied repeatedly. In the context of powers, the following specific terminology may be used:
Whenever a number:
Squared = power is 2
cubed = Power is 3
to the power of n = used for powers more than 3
The data given gives as an equation as followed
⇒ [tex]4^{2x}[/tex] ÷ [tex]8^x[/tex] = 32
⇒ [tex](2^2)^{2x}[/tex] ÷ [tex](2^3)^{x}[/tex] = 32
⇒ [tex]2^{4x}[/tex] ÷ [tex]2^{3x}[/tex] = 32
⇒ [tex]2^{(4x - 3x )}[/tex] = 32 (If the base is same in a division, then the powers
⇒ [tex]2^x[/tex] = 32 can simply be subtracted with the base as common)
⇒ 2 = [tex]\sqrt[x]{32}[/tex]
⇒ 2 = [tex]\sqrt[5]{32}[/tex]
Thus, x = 5
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(15 points) Find the number of elements in A1∪A2∪A3 if there are 102 elements in A1, 992 elements in A2 and 9975 elements in A3 in each of the following situations:
(a) The sets are pairwise disjoint.
(b) A1⊆A2⊆A3.
(c) There are 14 elements common to each pair of sets and 4 elements in all three sets.
From the union operation between sets, we have that the number of elements for each case will be as follows:
a) 11069.
b) 9975.
c) 11031.
What is the union operation between sets?The union operation between sets is the set that contains all elements that belong to at least one of the sets.
In item a, if the sets are disjoint, all the elements belong to only one set, and the number of elements in A1∪A2∪A3 is given by:
102 + 992 + 9975 = 11069.
For item b, if they are all contained into A3, the number of elements is the cardinality of A3, given by 9975.
For item c, we have that:
There are 4 elements in all three sets.Hence 14 - 4 = 10 common to A1 and A2 but not A3.Hence 14 - 4 = 10 common to A1 and A3 but not A2.Hence 14 - 4 = 10 common to A2 and A3 but not A1.102 - (4 + 2 x 10) = 78 that belong to only A1.992 - (4 + 2 x 10) = 968 that belong to only A2.9975 - (4 + 2 x 10) = 9951 that belong to only A3.Hence:
n(A1∪A2∪A3) = 4 + 3 x 10 + 78 + 968 + 9951 = 11031.
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Why does the range of this function include negative values? What is the significance of the point where the graph crosses the horizontal axis?
The range is the set of y outputs. In this case, the range is the profit.
A negative profit means the company lost money. This is when the cost is larger than the revenue. For instance, if the revenue was $100 but the cost is $150, then the profit = revenue - cost = 100-150 = -50 to signal they lost $50.
Positive profit means the company made money.
The x intercept represents the break-even point. This is where the company neither loses money, nor gains money. The profit is $0 here.
Answer/Step-by-step explanation:
In order to open a restaurant you have to rent a venue, furnish and decorate it, hire a staff and buy food and drinks. Before serving (selling) any meals you have to spend a lot of money. This is why the negative y-values.
At the point where the line crosses the x-axis (horizontal axis) you now begin to have a positive output to your operation. If you sell enough meals, you will turn a profit. That is, you make enough money to pay all those start-up expenses and still have money left over to keep!
Subtract the polynomials. Indicate the degree of the resulting polynomial.
(10x^4y^2-9x^3y-9y)-(5x^4^y2+10x^3y+12y-8x)
The degree of the resulting polynomial, 5x^4^y² - x^3y - 12y + 8x, after subtraction is: degree 4.
How to Subtract Polynomials?Given, (10x^4y^2 - 9x^3y - 9y) - (5x^4^y2 + 10x^3y + 12y - 8x), to subtract, open the parentheses using the distributive property.
10x^4y^2 - 9x^3y - 9y - 5x^4^y² - 10x^3y - 12y + 8x
Combine like terms together
10x^4y^2 - 5x^4^y² - 9x^3y - 10x^3y - 9y - 12y + 8x
5x^4^y² - x^3y - 12y + 8x
The highest degree is 4. This determines the degree of a polynomial.
Therefore, the degree of the resulting polynomial, 5x^4^y² - x^3y - 12y + 8x, after subtraction is: degree 4.
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1. A market research survey in which 60 consumers were contacted states that 65% of all consumers of a certain product were motivated by the product's advertising. Find the confidence limits for the proportion of consumers motivated by advertising in the population, given a confidence level equal to 0.95.
The confidence limits for the proportion of consumers motivated by advertising in the population, given a confidence level equal to 0.95. is; CI = (0.47, 0.77)
How to find confidence Interval of Proportions?We are given;
Sample Size; n = 60
sample proportion; p' = 65% = 0.65
Confidence level = 0.95
Now, formula for confidence interval of proportion is;
CI = p' ± z√(p(1 - p)/n)
At CL of 95%, z = 1.96Thus;
CI = 0.65 ± 1.96√(0.65(1 - 0.65)/60)
CI = 0.65 ± 1.96√0.00379167
CI = 0.65 ± 0.12
CI = (0.65 - 0.12), (0.65 + 0.12)
CI = (0.47, 0.77)
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[tex] \rm\sum \limits_{n = 2}^{ \infty } \frac{1}{( {n}^{2} - 1 {)}^{2} } \\ [/tex]
Partial fractions:
[tex]\displaystyle \frac1{(n^2-1)^2} = \dfrac14 \left(\frac1{n+1} - \frac1{n-1} + \frac1{(n+1)^2} + \frac1{(n-1)^2}\right)[/tex]
Now evaluate the sums. The first two terms form a telescoping sum,
[tex]\displaystyle \sum_{n=2}^\infty \left(\frac1{n+1} - \frac1{n-1}\right) = \sum_{n=1}^\infty \left(\frac1{n+2} - \frac1n\right) \\\\ ~~~~~~~~ = \lim_{N\to\infty} \sum_{n=1}^N \left(\frac1{n+2} - \frac1n\right) \\\\ ~~~~~~~~ = \lim_{N\to\infty} \left(\frac1{N+2} + \frac1{N+1} - 1 - \frac12\right) \\\\ ~~~~~~~~= -\frac32[/tex]
The others are flavors of [tex]\zeta(2)[/tex].
[tex]\displaystyle \sum_{n=2}^\infty \frac1{(n+1)^2} = \sum_{n=3}^\infty \frac1{n^2} \\\\ ~~~~~~~~~~~~~~~~~ = \sum_{n=1}^\infty \frac1{n^2} - 1 - \frac1{2^2} \\\\ ~~~~~~~~~~~~~~~~~ = \frac{\pi^2}6 - \frac54[/tex]
[tex]\displaystyle \sum_{n=2}^\infty \frac1{(n-1)^2} = \sum_{n=1}^\infty \frac1{n^2} \\\\ ~~~~~~~~~~~~~~~~~ = \frac{\pi^2}6[/tex]
It follows that
[tex]\displaystyle \sum_{n=2}^\infty \frac1{(n^2-1)^2} = \frac14 \left(-\frac32 + \left(\frac{\pi^2}6 - \frac54\right) + \frac{\pi^2}6\right) = \boxed{\frac{\pi^2}{12} - \frac{11}{16}}[/tex]
I really need help on all these questions
The ratio of boys to girls in math class is 2:4. If there are 24 students
in total in the class, how many boys and girls are there?
Answer:
8 boys and 16 girls
Step-by-step explanation:
2 boys plus 4 girls is six and six goes into 24 four times so 2 times four is eight and 4 times four is 16
Answer:
Step-by-step explanation: Since there are 24 students in total and the ratio is 2:4 then divide 24 by (2+4) which is 4. So the amount of boys is 2x4 which is 8. The amount of girls is 4x4 which is 16. 8+16=24
The Sugar Sweet Company will choose from two companies to transport its sugar to market. The first company charges $5500 to rent trucks plus an additional fee of $200.25 for each ton of sugar. The second company charges $5041 to rent trucks plus an additional fee of $225.75 for each ton of sugar.
The computation shows that the tons of sugar when they'll have same price is 18 tons.
How to compute the value?The first company charges $5500 to rent trucks plus an additional fee of $200.25. Thai will be:
= 5500 + (200.25 × s)
= 5500 + 200.25s
where s = tons of sugar
The second company charges $5041 to rent trucks plus an additional fee of $225.75 for each ton of sugar. This will be:
5041 + 225.75s
Then we will equate both of them. This will be:
5500 + 200.25s = 5041 + 225.75s
5500 - 5041 = 225.75d - 200.25s
459 = 25.5s
s = 459/25.5
s = 18
At 18 tons, they'll have same price.
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The Sugar Sweet Company will choose from two companies to transport its sugar to market. The first company charges $5500 to rent trucks plus an additional fee of $200.25 for each ton of sugar. The second company charges $5041 to rent trucks plus an additional fee of $225.75 for each ton of sugar. For want mount if sugar do they charge the same price.
A rectangle has side lengths of 7units and (x + 4) units. When multiplied the area is 70 units². Write and solve an equation that will allow you to find the value of x.
Answer:
7(x + 4) = 70
x = 6
Step-by-step explanation:
7(x + 4) = 70 Distribute the 7. Multiply everything inside the parentheses by 7
7x + 28 =70 Subtract 28 from both sides of the equation
7x = 42 Divide both sides by 7
x = 6
a light bulb consumes 2400 watts-hour per day. how many watts-hour does it consume in 5 days and 12 hours
The number of watts it will consume is 436.32
How the calculate the number of watts ?A light bulb consumes 2400 watts/hour
The number of watts it will consume in 5 days 12 hours can be calculated as follows
The first step is to change 5 days 12 hours to hours
120 hours + 12 hours
= 132 hours
The bulb consumes 2400 watts per hour
= 2400/132
= 18.18
The number of watts consumed in 5 days 12 hours is
= 24 × 18.18
= 436.32
Hence the light bulb will consume 436.32 watt-hour in 5 days 12 hours
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help with theses answer please
Answer: correct me if I’m wrong
Step-by-step explanation:
A single 6-sided die is rolled twice. Find the probability of getting a 3 the first time and a 4 the second time. Express the probability as a simplified fraction
Answer:
[tex]\frac{1}{36}[/tex]
Step-by-step explanation:
The first roll. There are six possible answers (1,2,3,4,5,6), but of those 6 answers, there is only one that I want; 3. so, The probability of rolling a 3 is [tex]\frac{1}{6}[/tex]. There is the same probability for rolling a 4.
If I multiply these together I will find the probability that I am looking for.
[tex]\frac{1}{6}[/tex] x [tex]\frac{1}{6}[/tex] = [tex]\frac{1}{36}[/tex]
A survey of 800 school employees yielded the following information 430 were instructors 595 were full time faculty and 340 of the instructors were full time
HELP! daughters struggling with this problem!
The required number of people that are in the US labor force is 0.0086t² + 0.087t + 25.375.
To determine the total number of people available in the US labor force.
In mathematics, it deals with numbers of operations according to the statements.
Here,
As per the data available, the number of Men in the US labor force is M = 0.0016t² + 0.315t + 19.467 and the number of women are W = 0.007t² -0.228t + 5.908.
Total people available in the US labor force,
= Number of women + number of men
= 0.0016t² + 0.315t + 19.467 + 0.007t² -0.228t + 5.908
= 0.0086t² + 0.087t + 25.375.
Thus, the required number of people that are in the US labor force is 0.0086t² + 0.087t + 25.375.
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Goofy ahh questions are hard
Answer:
True sometimes when it is stressful.
Step-by-step explanation:
Answer:
Step-by-step explanation:
your very right
T=A3/2 with out rational exponents
After the conversion, we get T² = 1/3 A
It is given that
T = [tex]A^{\frac{3}{2} }[/tex]
We have to convert the equation without rational exponents
T³ = A²
1/2 T = A³
T² = A³
T² = 1/3A
Therefore we get T² = 1/3 A without using the exponents.
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+87 + (4 + 8) = (7 + 4) + what property is
Answer:
87+(4+8)=(7+4)+x
87+12=11+x
87+12-11=x
88=x
Answer Question a),b) and c)
Answer:
a. leisure
b. £189
c.£ 1610
Step-by-step explanation:
In a box of highlighters there are 8 which have dried up and will not write. the box contains 10 red, 15 blue, 5 green and 10 yellow highlighters. Two
highlighters are randomly picked without replacement in succession from the
box. Find the probability that the highlighters are of the different colours.
The probability that it will be a blue highlighters is 3 / 10.
In statistics, what does a probability mean?
Simply put, probability is the likelihood that something will occur. When we don't know how an event will turn out, we can discuss the likelihood or likelihood of several outcomes. Statistics is the study of events that follow a probability distribution.the highlighters which are dried up and will not write or eight
number of red highlighters = 10
number of blue highlighters 15
number of green highlighters = 5
number of yellow highlighters = 10
therefore the total number highlighters in the box
= 10 + 10 + 15 + 5 + 10 = 50
probability of Blue = number of blue highlighters
Total number of highlighters
= 15 /50 = 3/10 = 0.3
the probability that it will be a blue highlighters is 3 / 10
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Mark and Don are planning to sell each of their marble collections at a garage sale. If Don has 5 more than 4 times the number of marbles Mark has, how many does each boy have to sell if the total number of marbles is 95 ?
Mark has 18 and Don has 77 number of marble to sell.
Let’s say Mark has x number of marble and Don’s marble number is y.
According to this problem we have,
Y = 4x +5
And x + y = 95
Or, x + 4x + 5 = 95
Or, 5x = 90
Or, x = 18 and y = 77
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Convert y = 0.25x + 7/8 into standard form.
Answer: -0.25x+y=7/8
Step-by-step explanation:
y = 0.25x + 7/8
-0.25x+y=7/8 ==>Subtract 0.25x from both sides to get the Ax+By=C format
The region [tex]R[/tex] is bounded by the lines [tex]x=2[/tex], [tex]x=3[/tex], [tex]y=-1[/tex], and the curve [tex]y=\frac{1}{2+x^3}[/tex]. Suppose a solid is formed by revolving [tex]R[/tex] about an axis. Use the disk/washer method to set up the integral (or expression involving sums of integrals) giving the volume of the solid formed when [tex]R[/tex] is revolved about [tex]x=-5[/tex].
The curve intersects the vertical lines when
[tex]x=2 \implies y = \dfrac1{2+2^3} = \dfrac1{10}[/tex]
and
[tex]x=3 \implies y = \dfrac1{2+3^3} = \dfrac1{29}[/tex]
Split up the region into washers of thickness [tex]\Delta y[/tex].
For [tex]-1\le y\le\frac1{29}[/tex], the inner and outer radii of each washer will be constant, with outer radius [tex]x=3[/tex] and inner radius [tex]x=2[/tex]. Each washer in this interval will contribute a total volume of
[tex]\pi (3^2 - 2^2) \Delta y = 5\pi\,\Delta y[/tex]
For [tex]\frac1{29} \le y \le \frac1{10}[/tex], the washers will have a varying outer radius of length
[tex]y=\dfrac1{2+x^3} \implies x = \sqrt[3]{\dfrac1y - 2}[/tex]
and inner radius [tex]x=2[/tex]. Their volumes are
[tex]\pi \left(\left(\sqrt[3]{\dfrac1y - 2}\right)^2 - 2^2\right) \, \Delta y = \pi \left(\left(\dfrac1y - 2\right)^{2/3} - 4\right) \, \Delta y[/tex]
Let [tex]\Delta y\to0[/tex]. Then as the number of washers goes to infinity, the total volume of the solid converges to the definite integral
[tex]\displaystyle 5\pi \int_{-1}^{1/29} dy + \pi \int_{1/29}^{1/10} \left(\left(\dfrac1y - 2\right)^{2/3} - 4\right) \, dy[/tex]
The first integral is trivial, but the second one requires hypergeometric functions to evaluate exactly. With a calculator, we find the approximate volume to be 0.117884.
How many rectangles (including squares) are there in a 4x4 square
Answer:
70 squares
Step-by-step explanation:
this is my answer to your question
Answer:
Hello,
100
Step-by-step explanation:
a square 4*4 : wide=4 , lenght=4
number of rectangles= wide*(wide+1)*lenght*(lenght+1) /4 = 4*5*4*5/4=100
Proof:
1 per 1 : 16 (rectangles )
1 per 2: 3*4=12
1 per 3: 2*4=8
1 per 4: 1*4=4 so 4*(4+3+2+1)=4*10=40
2 per 1: 4*3
2 per 2: 3*3
2 per 3: 2*3
2 per 4: 1*3 so 3*(4+3+2+1)=30
3 per 1: 4*2
3 per 2: 3*2
3 per 3: 2*2
3 per 4: 1*2 so 2*(4+3+2+1)=20
4 per 1: 4
4 per 2: 3
4 per 3: 2
4 per 4: 1 so 1*(4+3+2+1)=10
Total=40+30+20+10=(4+3+2+1)*(4+3+2+1)=100
What is the area of a circle with a diameter of 10 inches?What is the area of the circle shown below?
A circle with radius 8 centimeters.
a.
8 pi cm2
c.
StartFraction 16 Over 3 EndFraction pi cm2
b.
16 pi cm2
d.
64 pi cm2
The area of circle of diameter 10 inches is 25π in.² and,
area of circle of radius 8 cm is 64π cm².
How is Area of circle is calculated ?
Area of circle is calculated using formula :
A = πr²
1) It is given that diameter of circle is 10 inches then the radius will be half of it that is :
d = 10 inches
r = 5 inches
Now calculating the area of circle using the above formula :
A = πr²
A = π(5)²
A = 25π in.²
2) It is given that radius of circle is 8 cm then calculating area using above formula :
A = πr²
A = π(8)²
A = 64π cm²
Therefore, the area of circle of diameter 10 inches is 25π in.² and,
area of circle of radius 8 cm is 64π cm².
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the odle show the fraction 2/3 a student uses the model to find the product of 5/2 and 2/3
It should be noted that the product of the fractions 5/2 and 2/3 will be 5/3.
What is a fraction?It should be noted that this is a number that is expressed as a quotient, in which a numerator is divided by a denominator.
Therefore, it should be noted that the product of the fractions 5/2 and 2/3 will be illustrated as thus:
= 5/2 × 2/3
= 5/3.
Therefore, the product of the fractions 5/2 and 2/3 will be 5/3.
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In a photograph, allison stands next to her brother caleb
The actual height of Caleb based on the ratio in the photograph and actual is 48 inches.
What are the ratio and proportion?The ratio is the division of the two numbers.
Proportion is the relation of a variable with another. It could be direct or inverse.
Let's say Allison and Caleb's height in the photograph is A' and C' while in actuality it is A and C.
Since the ratio of height in the photograph will same as the ratio in actual life.
Thereby,
C/A = C'/A'
C/60 = 3.2/4
C = 192/4
C = 48 inches.
Hence "The actual height of Caleb based on the ratio in the photograph and actual is 48 inches".
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Given question is incomplete complete question follows ;
In a photograph, Alison stands next to her brother Caleb. Alison is 4 cm tall in the photograph. Her actual height is 60 in. Caleb is 3.2 cm tall in the photograph.
What is his actual height?
(Show your work)
Square root of 16 multiply by 35
Answer:
140
Step-by-step explanation:
the square root of 16 is 4 so do that times 35
If angle YXZ measures 90 degrees, which statement is true?
O. segment XZ is perpendicular to segment WY
O. WX =XY
O. segment XZ is a perpendicular bisector of segment WY
O. X is the midpoint of segment WY
Answer:
its the first alternative
Jennifer bought 3 4 kg of white rice and 1 8 kg of brown rice. How many kilograms of rice did she buy altogether?
Answer:
52kg
Step-by-step explanation:
it's just sum of the kgs bought
The product of a number and 10