The value of the indices given will be
[tex](\sqrt{5}) (\sqrt[3]{5})[/tex] simplifies to give [tex]5^{\frac{5}{6} }[/tex] or [tex]\sqrt[6]{3125}[/tex][tex]\sqrt[6]{3125}[/tex]
How can to simply [tex](\sqrt{5}) (\sqrt[3]{5})[/tex]The indices concept can be used for this simplification. An index is the small number which tells us how many times a term had been multiplied by itself.
[tex](\sqrt{5}) (\sqrt[3]{5}) = 5^{\frac{1}{2} } . 5^{\frac{1}{3} }\\\\(\sqrt{5}) (\sqrt[3]{5}) =5^{\frac{1}{2} +\frac{1}{3} }\\\\(\sqrt{5}) (\sqrt[3]{5}) =5^{\frac{2+3}{6}[/tex]
[tex](\sqrt{5}) (\sqrt[3]{5}) = 5^{\frac{5}{6}} = \sqrt[6]{5^{5} } = \sqrt[6]{3125}[/tex]
Therefore, the result of the simplification is [tex]5^{\frac{5}{6} }[/tex] or [tex]\sqrt[6]{3125}[/tex]
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A 250 N force acts on a 20 kg object. What would be the acceleration of the object?
Answer:
a = 12.5 m/s2
Step-by-step explanation:
anwser 12.5
Simplify the expression 7(6t+2)+3-5(t-1).
We are given the following expression:
[tex]7(6t+2)+3-5(t-1)[/tex]To simplify the expression, we will first use the distributive property on the parenthesis, like this:
[tex]7\times6t+7\times2+3-5\times t+5\times1[/tex]Solving the operations:
[tex]42t+14+3-5t+5[/tex]Now we add like terms:
[tex](42t-5t)+(14+3+5)[/tex]Solving the operations:
[tex]37t+22[/tex]This is the most simplified form of the equation
calcula la suma de los quince primeros multiplos de 9
Answer:
Step-by-step explanation:
9*(15/2)[2+14] = 9*15*16 = 2160.
In gym class, a student can do 40 sit-ups in 60 seconds and 100 sit-ups in 150 seconds.
Graph the proportional relationship.
graph with x axis labeled time seconds and y axis labeled sit ups, with a line from 0 comma 0 going through 90 comma 60
graph with x axis labeled time seconds and y axis labeled sit ups, with a line from 0 comma 0 going through 60 comma 30
graph with x axis labeled time seconds and y axis labeled sit ups, with a line from 0 comma 0 going through 60 comma 50
graph with x axis labeled time seconds and y axis labeled sit ups, with a line from 0 comma 0 going through 90 comma 30
Answer:
(a) graph with line through (90, 60)
Step-by-step explanation:
You want a graph of the proportional relationship between sit-ups and seconds if a student can do 40 sit-ups in 60 seconds.
GraphSeconds are plotted on the x-axis, and sit-ups are plotted on the y-axis The graph will match that shown in the attachment.
<95141404393>
identify the mapping diagram that represents the relation and determine whether the relation is a function
F is the correct answer (option A) that is, the relation is like many to one. So, it is a function.
Given mapping diagram that represents the relation.
We have to determine whether the relation is a function.
(-8, -6), (-5, 2), (-8, 1), (7, 3)
Here,
Domain = (-8, -5, 7)
Range = (-6, 2, 1, 3)
A function is a relation where each input has only one output.
Here,
F. The relation is like many to one. So, it is a function.
G. The relation is many to one. So, it is a function.
H. The relation is one to many. It is not a function.
G. The relation is one to many. It is not a function.
So, F is the correct answer (option A) that is, the relation is like many to one. So, it is a function.
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Complete both transformations below.
Then enter the final coordinates of the figure.
A(-1,3)
B(2,1)
C(1-1)
1) <2,3>
2) Dilate K = 2
A" ([?], [])
B" ([][])
C" ([],[])
Enter
Answer:
A" (2, 12)
B" (8,8)
C" (6, 4)
Step-by-step explanation:
For each point P(x, y) of the image, the translations are as follows:
Translate P(x, y) by <2, 3> [tex]\longrightarrow[/tex] P'(x + 2, y + 3) [tex]\longrightarrow[/tex] P'(x', y')
Dilate P'(x', y') by 2 [tex]\longrightarrow[/tex] P'' (x'', y'') [tex]\longrightarrow[/tex] P(2x', 2y')
Point [tex]\longrightarrow[/tex] Translate <2, 3> [tex]\longrightarrow[/tex] Dilate by 2
A(-1, 3) [tex]\longrightarrow[/tex] A'(-1 +2, 3 + 3) => A'(1, 6) [tex]\longrightarrow[/tex] A''(2, 12)
B(2, 1) [tex]\longrightarrow[/tex] B'(2 + 2, 1 + 3) => B'(4, 4) [tex]\longrightarrow[/tex] B"(8, 8)
C(1, -1) [tex]\longrightarrow[/tex] C'(1 + 2, -1 + 3) => C'(3, 2) [tex]\longrightarrow[/tex] C"(6, 4)
Lottery numbers in a particular state consist of 5 digits. Each lottery cube that is drawn/rolled has six sides, numbered 1-6. How many different lottery numbers are possible? O 720 lottery number O 7776 lottery numbers
As per the concept of probability, there are 7776 different lottery numbers are possible.
Probability:
Probability means the concept that is based on the possible chances of something to happen.
Given,
Lottery numbers in a particular state consist of 5 digits. Each lottery cube that is drawn/rolled has six sides, numbered 1-6.
Here we need to find how many different lottery numbers are possible.
Through the given question we know that,
The number of digits in a lottery ticket = 5
Side in cube = 6
So, in each time they will roll the dice 5 times to get one number.
So, the possible options of that event are,
For the first time we have 6 options
Second time we got 6 options
Third time also we got six option
Fourth time = 6 options
Fifth time = 6 options.
Therefore, it can be written as,
=> 6 x 6 x 6 x 6 x 6
=> 6⁵
=> 7776.
Therefore, there are 7776 different lottery numbers are possible.
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Consideremos la recta y=6x-4.
¿Cuál es la pendiente de una recta paralela a esta recta?
¿Cuál es la pendiente de una recta perpendicular a esta recta?
Pendiente de una recta paralela:
Pendiente de una recta perpendicular:
Slope of a parallel line: 6
Slope of a perpendicular line: -1/6
What is Slope ?
slope, The inclination of a line with respect to the horizontal is measured numerically. The ratio of the vertical to the horizontal distance between any two points on a line, ray, or line segment is known as its slope in analytical geometry ("slope equals rise over run").
Given equation,
y=6x-4
The equation of a line with slope m is given as:
y=mx+c
Rearranging the given equation:
y=(6)x+(-4)
By equating the equations we get,
m= 6
Which is slope of a parallel line
Now any parallel line would have the same slope.
And slope of a perpendicular line would be −1/m.
i.e. m(perpendicular)= -1/6
Hence, Slope of a parallel line is 6 and Slope of a perpendicular line is -1/6
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Write 92.5% in a fraction or mixed number in simplest form
Write an equation describing the relationship of the given variables
3/9 - 6/9 = ?
,,,,,,,,,,,,,,,,,,,,,,,
Answer:
-3/9 or -1/3
Step-by-step explanation:
:]
Answer: -1/3
Step-by-step explanation- To subtract fractions, you first make the the denominators the same. The denominator is the bottom number. To make the denominator the same, you look for the lowest common denominator. Making the answer -1/3
Suppose that a certain basketball athlete earned $17,250,000 to play 80 games, each lasting 48 minutes. (Assume no overtime games.)
The amount paid for each is;
1) Amount earned per game = $215625 per game
2) Amount earned per minute played = $4492.1875
3) Amount earned each minute for 2/3 games = $6738.28
4) Amount earned per hour = 4492.1875 * 60 = $269531.25
How to find the rate per game?We are given;
Amount earned by athlete = $17,250,000
Number of games played = 80 Games
Number of minutes per game = 48 minutes
1) Amount earned per game = Amount earned by athlete/Number of games played = 17250000/80 = $215625 per game
2) If he played entire games for the entire minutes;
Amount earned per minute played = 17250000/(80 * 48)
Amount earned per minute played = $4492.1875
3) He played 2/3 of every game. Thus;
Amount earned each minute for 2/3 games = 17250000/((2/3) * 80 * 48)
Amount earned each minute for 2/3 games = $6738.28
4) Since amount earned for every minute is $4492.1875, then we say that;
Amount earned per hour = 4492.1875 * 60 = $269531.25
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How much interest is earned in an investment if $720 is deposited monthly at 7.8% compounded monthly if the term of the investment is 6 years?$__________Round to the nearest cent
Given:
The initial investment is, P = $720.
The rate of interest is, r = 7.8% = 0.078.
The number of years of investment is, t = 6 years.
Explanation:
The general formula to find the compound interest is,
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]Here, n represents the number of times compounded in a year. It is given that the amount is compounded monthly, so the value of n = 12.
To find total amount after 6 years:
Now, substitute the given values in the general equation.
[tex]\begin{gathered} A=720(1+\frac{0.078}{12})^{12(6)} \\ =720(1+0.0065)^{72} \\ =1147.95 \end{gathered}[/tex]Thus, the total amount earned is $1147.95.
To fnd interest amount:
Now, the amount of interest can be calculated as,
[tex]\begin{gathered} I=A-P \\ =1147.95-720 \\ =427.95 \end{gathered}[/tex]Hence, the interest amount earned is $427.95 and the total amount earned is $1147.95.
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The given statement is false: vertical angle do not depend on the line being parallel. A pair of vertical angles are always congruent.
Vertical angle:
Vertical angle means that the angles opposite each other when two lines cross.
Given,
Here we have the diagram and we also know that angle 7 is congruent to angle 5.
Now we need to find the given statement is true or not.
Through the given diagram, we have identified that, the eight angles will together form four pairs of corresponding angles.
Angles 1 and 5 constitutes one of the pairs.
We know that all the corresponding angles are congruent.
All angles that have the same position with regards to the parallel lines and the transversal are corresponding pairs e.g. 3 + 7, 4 + 8 and 2 + 6.
Through that we know that basically, the vertical angles are always congruent, which means that they are equal. So, it is not necessary for them to be parallel.
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question 1.P(A)=0.25 P(B)=0.65 P(A or B)=?a.0.45b.0.2c.0.65d.0.9question 2P(A)=0.45 P(B)=0.35 P(A or B)=?a.0.75b.0.85c.0.8d.0.35
Given,
1)P(A) = 0.25
P(B) = 0.65
The value of P( A or B) is,
[tex]\begin{gathered} P(A\cup B)=P(A)+P(B)_{} \\ P(A\cup B)=0.25+0.65 \\ P(A\cup B)=0.90 \end{gathered}[/tex]Hence, option d is correct.
2)P(A) = 0.45
P(B) = 0.35
The value of P( A or B) is,
[tex]\begin{gathered} P(A\cup B)=P(A)+P(B)_{} \\ P(A\cup B)=0.45+0.35 \\ P(A\cup B)=0.80 \end{gathered}[/tex]Hence, option c is correct.
Simplify the expression 5(-7 + 3k)
The given expression is,
[tex]5(-7+3k)[/tex]Opening the brackets and multiplying each term inside the bracket with 5, we get,
[tex]\begin{gathered} \lbrack5\times(-7)\rbrack+(5\times3k)=-35+15\text{ k} \\ 15k=35 \\ k=\frac{35}{15}=2.33 \end{gathered}[/tex]The simplified expression is 15k = 35 and the value of k is 2.33.
In isosceles triangle ABC,AB=BC. AB and Bc are called_____a.bases b.verticesc.hypotenused. legs
In an isosceles triangle, there are
2 legs (equal sides)
1 base
The 2 legs are the equal sides
The base is the third side
In the isosceles triangle ABC:
Since AB = BC, then
AB and BC are the legs of the triangle, then
AB and BC are called legs
The answer is d
The safe load, L. of a wooden beam supported at both ends varies jointly as the width, w, the square of the depth, d. and inversely as the length. I. A wooden beam 8 in. wide. 6 in. deep, and 10 ft long holds up 1966 lb. What load would a beam 3 in. wide 9 in. deep and 11 ft long of the same material support? (Round off your answer to the nearest pound.)
The safe load, L of a wooden a beam 3 in. wide 9 in. deep and 11 ft long of the same material support is 307.17
Analyzing the given conditions in the question, we get
The safe load, L is directly proportional to width (w) and square of depth (d²)
also,
L is inversely as length (l) i.e L = k/l
combining the above conditions, we get an equation as:
L = k(wd²/l)
now, for the first case we have been given
w = 8 in
d = 6 in
l = 10 ft
L = 1966 lbs
thus,
1966 lb = k ((8 × 6²)/10)
or
k = 68.26 lbs/(ft.in³)
Now,
Using the calculated value of k to calculate the value of L in the second case
in the second case, we have
w = 3 in
d =9 in
l = 11 ft
Final Safe load L' = 68.26 × (6 × 3²/12)
or
L' =307.17 lb
Therefore, The safe load, L of a wooden a beam 3 in. wide 9 in. deep and 11 ft long of the same material support is 307.17
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Capital Gate Tower is
150 meters tall
(measured vertically
from the ground) and
makes a 72° angle
with the ground. If
you were to climb to
the top and then
accidently drop your
keys, how far from
the base of the tower
would they land?
Answer:
Step-by-step explanation:
[tex]\frac{150}{x} =tan72 \\x=150 cot~72=150 cot(90-18)=150 ~tan ~18 \approx 48.74 ~meteres[/tex]
The cranes shown in the figure are lifting an object that weighs 20,290 pounds. Find the tension in the cable of each crane. (Round your answers to the nearest whole number.)TL= lbsTR= lbs
we have that
TLy+TRy=20,290 ------> equation A
and
sin(24.3)=TLy/TL
TLy=TLsin(24.3) ------> equation B
sin(44.5)=TRy/TR
TRy=TRsin(44.5) ------> equation C
and
TLx=TRx
TLcos(24.3)=TRcos(44.5)
TL=TRcos(44.5)/cos(24.3) --------> equation D
substitute equation B and equation C in equation A
TLsin(24.3)+TRsin(44.5)=20,290 -------> equation E
substitute equation D in equation E
(TRcos(44.5)/cos(24.3))sin(24.3)+TRsin(44.5)=20,290
solve for TR
factor TR
TR[cos(44.5)/cos(24.3))sin(24.3)+sin(44.5)]=20,290
TR=19,835 pounds
Find TL
TL=(19,835)cos(44.5)/cos(24.3)
TL=
damion started solving this equation in an even different way what did he do first
With the help of Linear equation we can say that Damion added 12 on both sides.
What is linear equations?Equations with variables whose maximum power is 1 are said to be linear equations. A linear equation has a straight line as its graph.The given equation was,
12x + 4 = 20x-12If we will add 12 on both sides ,
12x + 16= 20xHence we can say that Damion added 12 to both sides.
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Towson Corporation issued $150,000 of 7% ten year bonds at 103 on the semi-annual interest date. Towson uses the straight line method to amortize any bond premium or discount. What is the amount of bond amortization for each six month period? Answer in whole dollars (no cents).
The amount of bond amortization for each six month period is [tex]\$225[/tex].
In the given question,
Towson Corporation issued [tex]\$150,000[/tex] of [tex]7\%[/tex] ten year bonds at [tex]103[/tex] on the semi-annual interest date.
Towson uses the straight line method to amortize any bond premium or discount.
We have to find the amount of bond amortization for each six month period.
Cash issued [tex]=\$150,000[/tex]
Rate [tex]=7\%[/tex] ten year bond at [tex]103[/tex] n the semi-annual interest date.
So the cash proceed on issue of bond = Cash issued [tex]\times103[/tex] [tex]/100[/tex]
Cash proceed on issue of bond [tex]=\$150,000\times\frac{103}{100}[/tex]
Firstly simplifying ratio
After simplification of ratio
Cash proceed on issue of bond [tex]=\$150,000\times1.03[/tex]
Now simplifying after multiplication
Cash proceed on issue of bond [tex]=\$154,500[/tex]
Hence, the cash proceed on issue of bond is [tex]\$154,500[/tex].
Now we find the premium that issued in the bond.
Premium on issue of bond [tex]=\$154,500-\$150,000[/tex]
Simplifying
Premium on issue of bond [tex]=\$4,500[/tex]
Hence, the premium on issue of bond is [tex]\$4,500[/tex]
Now finding the amount of bond amortization for each six month period.
Bond Amortization = (Premium on issue of bond/10 years) * 1/2
Bond Amortization [tex]=(\frac{\$4500}{10})\times\frac{1}{2}[/tex]
Simplifying the ratio
Bond Amortization [tex]=\$450\times0.5[/tex]
Bond Amortization [tex]=\$225[/tex]
Hence, the amount of bond amortization for each six month period is [tex]\$225[/tex].
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A stand at the farmers market sells different types of apples, as shown in the table.
Cost ($)
Weight
Apple A Apple B Apple C
4.90
4 lb
1.00
10 oz
0.45
lb
Which type of apple costs the least per pound? Apple A
The cost of Apple A: $1.225
What is Weight?
The weight of an object is the force exerted on it by gravity. Some standard textbooks define weight as a vector quantity, the force of gravity acting on an object. Some define weight as a scalar quantity that is the magnitude of gravity.
Cost of the different types of the apple have been given as,
Apple A = costing $4.90 for 4 lb
Apple B = costing $1.00 for 10 oz
Apple C = costing $0.45 for 1/2 lb
For Apple A,
Since, cost of 4 lb = $4.90
Therefore, cost of 1 lb = 4.90/4
= $1.225
For Apple B,
Since, 1 oz = 0.0625 lb
Therefore, 10 oz = 0.0625 × 10
= 0.625 lb
Since, cost of 10 oz = $1.00
Therefore, cost of 0.625 lb = $1.00
And cost of 1 lb = 1/0.625
= $1.6
For Apple C,
Since, cost of 1/2 lb = $0.45
Therefore, cost of 1 lb = 0.45 × 2
= $0.90
Hence, Cost of Apple A will be the least with $1.225 per pound.
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how far apart is -1 1/3 and 4 2/5 on a number line
Al got an estimate for repairs on his bike. Theparts will cost $17.50, and the parts and labortogether will not be more than $40. Whatinequality shows the possible labor costs, L?
Let's list down the pieces of information given the scenario:
Cost of bike parts = $17.50
Bike parts and labor together = not more than $40/ lesser than or equal to $40.
Let's now generate the equation based on the given information,
Let,
L = Labor cost
[tex]\text{ Cost of parts+Labor Cost }\leq\text{ \$40 ;since the total must not be more than \$40}[/tex][tex]\text{ \$17.50 + L }\leq\text{ \$40 ; inequality showing the possible total cost}[/tex]Let's now generate the inequality showing the possible labor cost, L
[tex]\text{ \$17.50 + L }\leq\text{ \$40 }\rightarrow\text{ L }\leq\text{ \$40 - \$17.50}[/tex][tex]\text{ L }\leq\text{ \$22.50}[/tex]Therefore, the cost of labor must not be more than $22.50.
can you help me find the answer to this question find the area of this figure round your answer to the nearest hundredth use 3.14 to approximate tt. a= ? ft 2
First, let's calculate the area of the triangle.
[tex]A=\frac{1}{2}b\cdot h[/tex][tex]A=\frac{1}{2}\cdot6\cdot8=\frac{48}{2}=24\text{ ft2}[/tex]Now let's calculate the area of the semicircle.
[tex]A=3.14\cdot\frac{r^2}{2}[/tex][tex]A=3.14\cdot\frac{4^2}{2}=25.12\text{ ft2}[/tex]The total area of the figure is:
24+25.12 ft2 = 49.12 ft2
Explain how you can use addition of groups to show that 4 x ( -3) = 12
The technique of repeated addition involves combining equal groups.
4 x ( -3) = 12.
Repeated addition is the combining of equal groupings. It offers a basis for comprehending multiplication. For instance, 3 x 5 can be expressed as 5 + 5 + 5 to represent 3 groups of 5 counters.
We have been given that
4 x ( -3) = 12
By using repeated addition for multiplication
Add 4 three times or add 3 for times ..
In question negative 3 is given so we add negative 4 , three times
(-4) + (-4) + (-4)
-12.
Or
Add negative 3 , four times
(-3) + (-3 )+ (-3) + (-3)
-12.
Hence, we solved given multiplication by the using repeated addition method.
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10. A recipe calls for 5 cups of flour. If you only have a ½ cup to measure, how many ½ cups will you need for
the recipe?
1messageJosh wants to estimate the mean age in a population of trees. He'll sample n trees and build a 95% confidence interval for the mean age. He doesn't want the margin of error to exceed 3 years. Preliminary data suggests that the standard deviation for the ages of trees in this population is 16 years.Which of these is the smallest approximate sample size required to obtain the desired margin of error?11 trees110 trees144 trees43 trees87 trees
The formula for the margin of error is
[tex]\begin{gathered} \text{MOE}=SE\times critical\text{ value} \\ SE\Rightarrow\text{standard error} \end{gathered}[/tex]The critical value for 95% confidence interval is 1.96
The standard error is
[tex]\begin{gathered} SE=\frac{\sigma}{\sqrt[]{n}} \\ \sigma\Rightarrow standard\text{ deviation} \\ n\Rightarrow\text{sample size} \end{gathered}[/tex]To know which of the list of options will yield approximately the desired margin of error, we will have to calculate the margin of error with the following values
For 110 trees, n= 110, standard dev. =16
[tex]\begin{gathered} SE=\frac{16}{\sqrt[]{110}}=1.53 \\ \text{MOE}=1.53\times1.96=2.9988 \end{gathered}[/tex]For 144 trees, n=144, standard dev=16
[tex]\begin{gathered} SE=\frac{16}{\sqrt[]{144}}=\frac{16}{12}=1.33 \\ \text{MOE}=1.33\times1.96=2.61 \end{gathered}[/tex]For 43 trees, n=43 , standard dev.=16
[tex]\begin{gathered} SE=\frac{16}{\sqrt[]{43}}=2.44 \\ \text{MOE}=2.44\times1.96=4.782 \end{gathered}[/tex]For 87 trees, n= 87, standard dev=16
[tex]\begin{gathered} SE=\frac{16}{\sqrt[]{87}}=1.72 \\ \text{MOE}=1.72\times1.96=3.3712 \end{gathered}[/tex]Hence, from the above calculations, the most prefered is the sample size of 110 trees (because the margin of error of 2.9988 is approximately 3 )
Answer is 110 trees
what value of x is the answer to the equation x - 2 = 16
The value of x is the answer to the equation x - 2 = 16 which is 18.
What is the solution for an equation?An equation is an expression that shows the relationship between two or more numbers and variables. The solution of an equation refers usually to the values of the variables involved in that equation which if substituted in place of that variable would give a true mathematical statement.
We have been given a linear equation as; x - 2 = 16
We need to find the value of x as the answer to the equation x - 2 = 16.
Therefore, we will eliminate the 2.
x - 2 = 16
Add 2 on both sides of the equation;
x - 2 + 2= 16+ 2
Then ;
x = 18
Hence, the value of x is the answer to the equation x - 2 = 16 which is 18.
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