6a7
Step-by-step explanation:
To simplify the expression (2a³) (3a4), you can use the laws of exponents. First, you can multiply the coefficients 2 and 3 to get 6. Then, you can add the exponents of 'a' which gives you a total of 3+4=7. Therefore, the simplified expression is 6a7. It does not have any negative exponents, and it represents the product of two expressions with the same base 'a' and coefficient multiplication.
Answer: 6a7
Step-by-step explanation: Got this right b4.
7. find the values of c that satisfy Rolle's Theorem.
Show steps
The values of c that satisfy Rolle's Theorem is 2.15 or -0.15.
What is the value of c that satisfy Rolle's Theorem?The value of c that satisfies Roll's theorem is calculated as follows;
y = x³ - 3x² - x; [-1, 3]
Based on Roll's theorem conditions, since the function is a polynomial it is continuous.
The derivative is also a polynomial.
y' = 3x² - 6x - 1
The final condition;
y(-1) = (-1)³ - 3(-1)² - (-1)
y(-1) = -1 - 3 + 1
y(-1) = -3
y(3) = (3)³ - 3(3)² - 3
y(3) = 27 - 27 - 3
y(3) = -3
The three conditions of Rolle's theorem is statisfied, so there exists at least one value of c in the interval (-1, 3) such that y'(c) = 0.
y' = 3x² - 6x - 1
y'(c) = 3c² - 6c - 1
3c² - 6c - 1 = 0
Solve the quadratic equation using formula method;
a = 3, b = -6, c = -1
c = 2.15 or - 0.15
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A 1.75 litre bottle of water is poured into 250 ml paper cups. How many paper cups can be filled?
Answer:
The answer to your problem is, 7
Step-by-step explanation:
First you can either convert;
ml to liter
liter to ml
I will use liter to ml.
1.75 liters in ml is 1750 ml
So we can then divide, 1750 / 250 = 7
Which is the answer
Thus the answer to your problem is, 7
Simplify \sqrt{2} \cdot \sqrt{6} \cdot \sqrt{110} \cdot \sqrt{120} \cdot \sqrt{450} \cdot \sqrt{520}
The simplification of the given expression is equal to 192524.3.
The expression is equal to,
√2 × √6 × √110 × √120 × √450 × √520
Simplify this expression by first simplifying the square roots under the radical signs,
√2 = √(2 × 1)
= √2 × √1
√6 = √(2 × 3)
= √2 × √3
√110 = √(2 × 5 × 11)
= √2 × √5 × √11
√120 = √(2 × 2 × 2 × 3 × 5)
= 2√2 × √3 × √5
√450 = √(2 × 3² × 5²)
= √2 × (3 × 5)²
= 15√2
√520 = √(2³ × 5 × 13)
= 2√2 ×√5 × √13
Substituting these simplifications back into the original expression, we have,
√2 × √6 × √110 × √120 × √450 × √520
= √2 × √2 × √3 × √2 × √5 × √11 × 2√2 × √3 × √5 × 15√2 × 2√2 ×√5 × √13
= 2⁵ × 3² × 5²√(5 × 11 × 13)
= 7200√715
= 192524.3
Therefore, the simplification value of √2 × √6 × √110 × √120 × √450 × √520 is equal to 192524.3.
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The above question is incomplete, the complete question is:
Simplify
√2 × √6 × √110 × √120 × √450 × √520
Please help 50 points
Answer:
2(5(11) + 5(2.5) + 11(2.5))
= 2(55 + 12.5 + 27.5) = 2(55 + 40) = 2(95)
= 190 square centimeters
Select all the correct answers. What are the solutions to this equation? 2 x 2 = - 10 x + 12 x = - 6 x = - 2 x = 1 x = - 3 x = 6
Answer:
The correct solutions to the equation 2x^2 = -10x + 12 are x = -2 and x = 3.
Step-by-step explanation:
Identify the pairs of supplementary angles.
Choose all that apply.
A. RQS and SQR
B. SQT and SQR
C. TQP and RQP
D. SQR and RQP
E. PQR and RQP
F. SQT and TQP
G. TQP and PQT
H. SQR and TQP
The pairs of supplementary angles are;
B. <SQT and <SQR
C. <TQP and <RQP
D. <SQR and <RQP
F. <SQT and <TQP
What are supplementary angles?Two or more angles are referred to as supplementary angles if they add up to 180^o. Therefore the sum of angles is equal to the sum of angles on a straight line.
Thus, the pair of supplementary angles in the given diagram are;
B. <SQT and <SQR
C. <TQP and <RQP
D. <SQR and <RQP
F. <SQT and <TQP
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The displacement of a train starting from a stop is given by the equation s(t) = 8\sqrt{t}+1 meters. Estimate the instantaneous velocity of the train at t = 9 seconds by considering the average velocities over the intervals [8.5, 9], [8.7, 9], [8.9, 9], [8.99, 9], [9, 9.01], [9, 9.1], [9, 9.3], and [9, 9.5].
The instantaneous velocity of the train at t = 9 seconds is approximately 6.8 m/s
To estimate the instantaneous velocity of the train at t = 9 seconds, we can consider the average velocities over several small intervals of time that include the point t = 9. This is an approximation of the slope of the tangent line to the curve s(t) at t = 9, which is the instantaneous velocity.
We can calculate the average velocity over each interval by dividing the change in displacement by the change in time:
Average velocity from [8.5, 9] = (s(9) - s(8.5)) / (9 - 8.5) = (8√9 + 1 - 8√8.5 + 1) / 0.5 = 6.34 m/s (approx.)
Similarly, we can calculate the average velocities over the other intervals:
[8.7, 9]: 6.48 m/s (approx.)
[8.9, 9]: 6.60 m/s (approx.)
[8.99, 9]: 6.66 m/s (approx.)
[9, 9.01]: 6.67 m/s (approx.)
[9, 9.1]: 6.74 m/s (approx.)
[9, 9.3]: 6.87 m/s (approx.)
[9, 9.5]: 7.00 m/s (approx.)
As we consider smaller intervals closer to t = 9, the average velocities approach a limit, which is the instantaneous velocity at t = 9. In this case, we see that the average velocities are increasing as we approach t = 9, indicating that the instantaneous velocity at t = 9 is also increasing.
Based on these calculations, we can estimate that the instantaneous velocity of the train at t = 9 seconds is approximately 6.8 m/s (averaging the average velocities from [8.99, 9] to [9, 9.5]).
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Pythagorean triples are given by these formulas:
(2²-37, 2zy, z²+37²)
The hypotenuse of a right triangle is 29. The lengths of the legs are whole numbers. List your answers in increasing
order.
The lengths of the two legs are
and
The lengths of the two legs of the right triangle are 58 and 839, in increasing order.
We have,
The formula given is incorrect.
The correct formula for Pythagorean triples with a given integer z is:
(z² - 1², 2z, z² + 1²)
Using this formula, we can find the two legs of the right triangle with hypotenuse 29 as follows:
z² + 1² = 29²
z² + 1 = 29²
z² = 29² - 1
z² = 840
z = √840
z = 28.98
Since z must be an integer, we can try integer values close to 28.98 to find one that works.
Trying z = 29,
a = z² - 1² = 840 - 1 = 839
b = 2z = 58
c = z² + 1² = 840 + 1 = 841
Therefore,
The lengths of the two legs of the right triangle are 58 and 839, in increasing order.
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A summer camp cookout is planned for the campers and their families. There is room for 450 people. Each adult costs $7, and each camper costs $4. There is a maximum budget of $1,150. Write the system of inequalities to represent this real-world scenario, where x is the number of adults and y is the number of campers
The system of inequalities that represents this real-world scenario is:
x + y ≤ 450 (The total people cannot be greater than 450)
7x + 4y ≤ 1150 (total price cap of $1,150)
What is system of inequalities ?
A group of two or more simultaneously true inequalities is referred to as a system of inequalities. A system of inequalities can be solved by finding the set of values that satisfies every one of the inequalities in the system.
Therefore, The system of inequalities that represents this real-world scenario is:
x + y ≤ 450 (The total people cannot be greater than 450)
7x + 4y ≤ 1150 (total price cap of $1,150)
Where x is the number of adults and y is the number of campers.
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Jasmine has a circular swimming pool with a radius of 4.2 meters. What is the circumference of the pool? Use 3.14 for π
. Round to the nearest hundredth if necessary.
__ m
If the radius of Jasmine's swimming pool is 4.2 meter, then it's circumference is 26.4 meters.
The "Circumference" of a circle is known as the distance around the boundary of a circle.
The circumference of a circle is given by the formula : 2 × π × radius,
where π (pi) is a mathematical constant approximately equal to 3.14,
We are given that Jasmine's swimming pool has a radius of 4.2 meters.
So, we can calculate the circumference of the pool as :
⇒ Circumference = 2 × 3.14 × 4.2 meters,
⇒ Circumference ≈ 26.4 meters,
Therefore, the circumference of Jasmine's swimming pool is 26.4 meters.
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Triangle 1 undergoes four different transformations.
The results of these transformations are shown.
1
4
2
5
3
Which statement best describes one of these
transformations?
Triangle 1 is rotated to result in triangle 2.
O Triangle 1 is dilated to result in triangle 3.
O Triangle 1 is reflected to result in triangle 4.
Triangle 1 is stretched to result in triangle 5.
time tables on the map mannnnn
help please i need the answer to thus question
The measure of angle 1 is 107° suing the concepts of corresponding angles and linear pair of angles..
Given a line t which is a transversal line that cuts the two parallel lines m and n.
Here the angle which is linear pair to angle 1 and the angle 73° are corresponding angles.
By the corresponding angle theorem, the corresponding angles formed by two parallel lines cut by a transversal are equal.
So,
Measure of angle which is linear pair to 1 = 73°
Now linear pair of angles are supplementary.
∠1 + 73° = 180°
∠1 = 180° - 73°
∠1 = 107°
Hence the measure of angle 1 is 107°.
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10. The box plot shows donations in dollars to charity.
Describe the shape of the distribution.
Donations to Charity ($)
20 40 60 80 100 120 140 160 180 200 220
The given shape of the distribution is not symmetric.
Given that, a box plot shows donations in dollars to charity.
We need to describe the shape of the distribution.
Donations to Charity ($) =
20 40 60 80 100 120 140 160 180 200 220
so, as we can see,
The shape of the distribution is not symmetric since the lengths of each box and whisker are not the same. There is an outlier at 220.
Hence, the given shape of the distribution is not symmetric.
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Every winter, the math club sells cookie dough to raise money. Last year, they sold 1,080 pounds of cookie dough to 360 people. This year, they predict that they will sell cookie dough to between 460 and 500 people. About how many pounds of cookie dough will they need?
A.
2,880
B.
1,440
C.
720
D.
2,160
The number of pounds of cookie dough needed is 1,440. Therefore, option B is the correct answer.
Given that,
Last year, they sold 1,080 pounds of cookie dough to 360 people.
This means that they sold an average of 3 pounds of cookie dough per person.
Number of pounds of cookie dough = 3 pounds/person × Number of people
Here, 3×460=1,380
3×500=1500
To get a more accurate estimate, we can take the average of these two numbers, which is 1,440 pounds of cookie dough.
Therefore, option B is the correct answer.
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An ice-cream scoop has a shape of spherical cap. An engineer's goal is to maximize the volume of the scoop given that the surface area of the scoop is 36 cm2. Find the radius of the sphere and the height of the spherical cap of maximum volume. (Hint:
the volume of a spherical cap is [tex]Vcap=\frac{1}{3} \pi h^2(3R-h)[/tex], where R is the radius of the sphere and h is the height of the cap). Find the maximum volume of ice-cream scoop.
Write your answer in terms of π.
The radius is 5.316 cm, height is 10.362 cm and Maximum volume is
60.583 cm³.
We have,
Surface area of sphere = 36 cm²
4πr² = 36
πr² = 9
r = 3√π
r= 5.316
Now, Volume spherical cap
= 1/3 πh² (3R- h)
= 1/3π (10.362) (3 (5.316) - 10.362)
= 1/3 π (57.882132)
= 60.583 cm³
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which of the following equations demonstrates the Associative Property of Multiplication?
18(27 • 3) = 18(3 • 27)
8(9 + 2) = 64 + 16
12(17 • 23) = (12 • 17) • 23
18(27 • 3) = 18(81)
Answer:
12 • (17 • 23) = (12 • 17) • 23
Find the 20th term of the following sequence.
-6, -4, -2, 0, ...
32
46
44
Step-by-step explanation:
Arithmetic sequence with d = 2 a1 = -6
a20 = -6 + 2(20-1) = 32
A 10-mile cab ride costs $40. A 15-mile cab ride costs $55. Find the rate of change (cost per mile) for the cab ride
The rate of change for the cab ride is A = $3 per mile
Given data ,
Change in cost = $55 - $40 = $15
Change in distance = 15 miles - 10 miles = 5 miles
Now, we can divide the change in cost by the change in distance to get the rate of change or cost per mile:
Rate of change or cost per mile = Change in cost / Change in distance
A = $15 / 5 miles
A = $3 per mile
Hence , the rate of change or cost per mile for the cab ride is $3 per mile
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I need help with this ?
The equation will have the solution in the form of an imaginary number "i" as: x = (3 ± 2i)/2
What is an imaginary number in a quadratic equationIn a quadratic equation, an imaginary number is a complex number that can arise when trying to take the square root of a negative number.
We shall solve for x in the equation as follows:
(2x + 3)² - 2 = -6
add 2 to both sides
(2x + 3)² = 2 - 6
(2x + 3)² = -4
2x + 3 = √(-4) {taking square root of both sides}
subtract 3 from both sides
2x = 3 ± √(-4)
divide through by 2
x = [3 ± √(-4)]/2
note that: √(-4) = √(1-) × √4 where √(-1) = I, so;
x = (3 ± 2i)/2.
Therefore, the equation will have the solution in the form of an imaginary number "i" as: x = (3 ± 2i)/2
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i need help with this lol
The trio of sides that will make a right triangle are the ones in the first option:
5, 12, and 13.
Which set would make a right triangle?Remember that for any right triangle, the sum of the squares of the two shorter sides must be equal to the square of the longest side.
So for example, for the first option we would have:
5^2 + 12^2 = 13^2
25 + 144 = 169
169 = 169
The equation is true, thus, these sides make a right triangle.
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Which equation is the inverse of 5y+4= (x+3)²+12?
O y = x²+x+1100
y=3± √√5x+ 7/2
O-5-4--(x+3)²--1/
O
O y=-3± √5x+
7
The equation that is the inverse of 5y+4= (x+3)²+12 is y = -3 ± √(5x - 8)
Which equation is the inverse of 5y+4= (x+3)²+12?From the question, we have the following parameters that can be used in our computation:
5y+4= (x+3)²+12
Swap x and y in the equation
So, we have
5x + 4= (y + 3)² + 12
When we make the vairiable y the subject, we have
y = -3 ± √(5x - 8)
Hence, the equation that is the inverse of 5y+4= (x+3)²+12 is y = -3 ± √(5x - 8)
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Find the volume of the triangular prism described below
The volume of the triangular base prims is 21.6 inches cube.
How to find the volume of a triangular base prism?A triangular base prism is a prism with a triangular base. Therefore, let's find the volume of the triangular prism.
volume of a triangular prism = base area × height
Therefore,
base area = 1 / 2 bh
where
b = baseh = heightTherefore, the triangular base has angles 45, 45 and 90 degrees. Using trigonometric ratios let's find the other legs.
tan 45 = opposite / adjacent
tan 45 = x / 6
x = 6 inches
Therefore,
base area = 1 / 2 × 6 × 6
base area = 36 /2
base area = 18 inches²
Hence,
volume of the triangular base prism = 18 × 1.2
volume of the triangular base prism = 21.6 inches³
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Find the area of a parallelogram.
Answer:
60
Step-by-step explanation:
The area of a parallelogram is base x hight.
A = bh
10(b) x 6(h) = 60
A Certain sum of money of simple
interest amount to $$1,300 ire 4 years
and to #11525 in 7 years - Find
the sum and the rate percent
The required rate of simple interest is 1.75%.
Here, we have,
(Principal + Interest) is a straightforward interest equation.
A = P(1 + rt)
Where: A is the sum of the accrued principal and interest.
Principal Amount is P.
I is the interest rate.
r is the annual percentage rate of interest, or R/100.
R is the annual percentage rate of interest; R = r * 100 t is the length of time involved in months or years.
Since I = Prt,
the initial formula A = P(1 + rt) evolved from A = P + I to A = P + Prt,
which may be represented as A = P(1 + rt).
Given: Principal is $1,300
Rate is 7% and the amount earned that is A-P is $159.25.
A = P(1 + rt)
Therefore substituting the values in the above mentioned equation, we get:
159.25= 1300(1+r×7)
On solving we get,
r= 1.75%
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complete question:
At the Blue Bank, Barry would earn $159.25 in simple interest in 7 years after depositing $1,300.
What rate of simple interest is offered at the
Blue Bank?
i need help with math
The relationship between the distance that birds fly in relation to the time they do so, is positive.
There are about 3 outliers but for the most part, the relationship is positive.
How to describe the relationship ?The graph which shows the distance that birds fly in relation to the time they do, shows that there is a positive relationship because as the time increases, the distance that the birds have flown also increases.
There are some outliers such as the bird that flew 1 mile in 7 hours but in general, as the time increases, the distance increases as well. There are two clusters of distance as well.
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Swathu buys a new scooter on loan. The loan is for Rs. 90,000 atrase of interest 8% per annum compounded half yearly for 2 years
After two years, Swathu will pay back the debt in full, which comes to Rs. 105287.27.
To find the total amount Swathu will pay back after 2 years on a loan of Rs. 90,000 with an interest rate of 8% per annum compounded half-yearly, we can use the formula for compound interest:
[tex]A = P(1 + r/n)^{nt[/tex]
where:
A = the total amount Swathu will pay back
P = the principal amount borrowed (Rs. 90,000)
r = the annual interest rate (8%)
n = the number of times the interest is compounded per year (2 times, since it is compounded half-yearly)
t = the time period (2 years)
Substituting these values into the formula, we get:
[tex]A = 90,000(1 + 0.08/2)^{2*2}\\\\A = 90,000(1 + 0.04)^4\\\\A = 90,000(1.04)^4\\\\A = 90,000(1.16985856)\\[/tex]
A = 105287.27 (rounded to the nearest tenth)
Therefore, Swathu will pay back a total of Rs. 105287.27 after 2 years on the loan.
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Mrs.lealas living room has an area of 144 square feet.
Her dining room is ⅓ the area of the living room and ⅖ the area of the kitchen. What is the area, in square feet, of the kitchen?
The Area of Kitchen is 120 square feet.
We have,
Area of living room = 144 square feet
So, the dining room
= 1/3 (area of living room)
= 1/3 (144)
= 48 square feet
and, Area of Dining room = 2/5 x Area of kitchen
48 = 2/5 x Area of kitchen
Area of kitchen = 48 x 5/2
Area of Kitchen = 24 x 5
Area of Kitchen = 120 square feet
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What is this equation? 24/x+8, for x=3
Answer:
16
Step-by-step explanation:
24 divided by X(3) is equal to 8, then 8+8 equals 16 (EASY)
can someone help with this
The expected joint frequencies are
Male and Drama = 20Male and Comedy = 40Female and Drama = 75Female and Comedy = 25Calculating the expected joint frequenciesFrom the question, we have the following parameters that can be used in our computation:
The table of values
Also, we have
People = 160
This means that
Male and Drama = 12.5% * 160
Male and Drama = 20
Male and Comedy = 25% * 160
Male and Comedy = 40
Female and Drama = 46.9% * 160
Female and Drama = 75
Female and Comedy = 15.6% * 160
Female and Comedy = 25
In conclusion, we have
Because the expected and the joint frequencies are not the same, gender is not independent of movie type
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The velocity of an object is the distance it travels per unit time. Suppose the velocity of a gliding bird is measured to be 244. cm/s. Calculate the time it will take the bird to travel 1.4 m.
The time it will take the bird to travel 1.4 m is 0.5738 seconds.
What is velocity?In Science and Mathematics, velocity can be defined as the distance covered by an object per unit of time in a specific direction. This ultimately implies that, velocity is a vector quantity because it has both magnitude and direction.
How to calculate the velocity of a physical object?In Mathematics and Science, the velocity of any a physical object can be calculated by using this formula;
Velocity = distance/time
244 cm/s to m = 244/100 = 2.44 cm/s
By making time the subject of formula, we have:
Time = distance/velocity
Time = 1.4/2.44
Time = 0.5738 seconds.
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