According to exponent rules, when we multiply terms with the same base add the exponents. Hence, the correct answer is option D.
Exponent rules are a set of rules that dictate how exponents (numbers written as a superscript) can be manipulated in mathematical operations. Some of the most commonly used exponent rules include:
Product of Powers: When multiplying powers with the same base, you can add the exponents.For example, [tex]x^4 * x^5 = x^{4+5} = x^9[/tex]
The quotient of Powers: When dividing powers with the same base, you can subtract the exponents.For example, [tex]x^7 / x^3 = x^{7-3} = x^4[/tex]
Power of a Power: When raising a power to another power, you can multiply the exponents.For example,[tex](x^3)^5 = x^{3*5} = x^{15}[/tex]
Power of a Product: When raising a product to power, you can raise each factor to that power.For example,[tex](xy)^3 = x^3 * y^3[/tex]
Power of a Quotient: When raising a quotient to a power, you can raise the numerator and denominator to that power separately.For example,[tex](x/y)^3 = x^3 / y^3[/tex]
According to the product of the power rule, we get that we add the exponents when we multiply terms with the same base.
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FInd the simple interest earned on a deposit of $2800 after 5 years at a 2% annual rate.
The simple interest earned on a deposit of $2800 after 5 years at a 2% annual rate is $280.
What is simple interest?It is the interest calculated on the principal at a given rate for a time period.
We have,
P = $2800
T = 5 years
R = 2%
Now,
The formula for simple interest.
SI = PRT/100
Now,
SI = (2800 x 2 x 5) / 100
SI = 28 x 10
SI = $280
Thus,
Simple interest is $280.
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how to find
127.98+35.261
(for my cuz)
The simplification of the given expression after addition would be = 163.241.
What is addition?Addition is the combination of two or more given values and it's one of the major arithmetic operations in mathematics.
The given expression is a s follows;
127.98+35.261 = 163.241
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On March 14 at 1:59, people celebrate Pi Day by eating pie. Why do you
think people celebrate on thi day at thi time?
People celebrate Pi Day on March 14th at 1:59 because this date and time is an easy way to remember the mathematical constant pi (π).
Pi, which is represented by the Greek letter π, is an irrational number that starts with 3.14 and continues for an infinite amount of digits. The numerical value of pi is the ratio of a circle's circumference to its diameter, and is approximately equal to 3.1415926535897932384626433832795. The date and time of March 14th, 1:59 is a way to represent the first four digits of pi (3.14). People celebrate Pi Day by eating pie, making pi-related crafts, and sharing facts about pi. People celebrate Pi Day on March 14th at 1:59 because this date and time is an easy way to remember the mathematical constant pi (π).
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You know your cousin's phone number is
8675309, so you dial that number to call
him. Is person being called a function of phone
number dialed?
Function? Explain.
The person being called is a function of the phone number, as for each phone number, there is only one person associated with the number.
When does a relation represents a function?A relation represents a function when each input value is mapped to a single output value.
The input and output variables for this problem are given as follows:
Input: phone number.Output: person.Each phone number is mapped to a single person, meaning that the relation is in fact a function.
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Another submarine’s descent can be represented as y=-3100xy=−3100x , where y is the elevation and x is time in hours. How long will it take this submarine to make the descent? Explain in detail how you found your answer in Part C
The time taken by the submarine to make the descent when the equation of descent is given is 0.677 hours.
Submarine's descent can be represented by the equation, y = -3100 x
where,
y is elevation
x is time in hours
We need to determine how long it will take this submarine to travel 2,100 feet below the surface of the ocean.
Since the submarine to make the descent to the seafloor 2,100 feet below the surface
So, y = - 2100
y = - 3100x gives
- 2100 = - -3100 x
Divide both sides by -3100,
x = 2100/3100 = 0.677 hours
As a result, the submarine will need 0.677 hours to complete the descent.
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a tank holds 4000 liters of water in which 100 grams of salt have been dissolved. saltwater with a concentration of 1 grams/liter is pumped in at 10 liters/minute and the well mixed saltwater solution is pumped out at the same rate. write initial the value problem for:
The mass of salt in the tank at time t.
dS/dt = 10 - S/400
S(0) = 100 grams
The solution is S(t) = 4000 - 3900[tex]e^{\frac{-t}{400}}[/tex]
A tank holds water V(0) = 4000 liters in which salt S(0) = 100 grams.
So dS/dt = S(in) - S(out)
S(in) = 1 × 10 = 10 gram/liters
S(out) = S/V × 10 = 10S/V gram/liters
V = V(0) + q(in) - q(out)
V = 4000 + 10t - 10t
V = 4000 liters
dS/dt = 10 - 10S/V
dS/dt = 10 - 10S/4000
dS/dt = 10 - S/400
Now given; S(0) = 100.
Here, p(t) = 1/400, q(t) = 10
[tex]\int p(t)dt = \int\frac{1}{400}dt[/tex][tex]\int p(t)dt = \frac{1}{400}t[/tex]
[tex]\mu=e^{\int p(t)dt}[/tex]
[tex]\mu=e^{\frac{t}{400}}[/tex]
So, S(t) = [tex]\frac{\int\mu q(t)dt+C}{\mu}[/tex]
S(t) = [tex]\frac{\int e^{\frac{t}{400}} \cdot10dt+C}{e^{\frac{t}{400}}}[/tex]
S(t) = [tex]e^{\frac{-t}{400}} \left({\int e^{\frac{t}{400}} \cdot10dt+C}\right)[/tex]
S(t) = [tex]e^{\frac{-t}{400}} \left({10\times\frac{e^{\frac{t}{400}}}{1/400} +C}\right)[/tex]
S(t) = [tex]e^{\frac{-t}{400}} \left({4000\times{e^{\frac{t}{400}} +C}\right)[/tex]
Now solving the bracket
S(t) = 4000 + [tex]e^{\frac{-t}{400}}[/tex]C.....(1)
At S(0) = 100
100 = 4000 + [tex]e^{\frac{-0}{400}}[/tex] C
100 = 4000 + [tex]e^{0}[/tex] C
100 = 4000 + C
Subtract 4000 on both side, we get
C = -3900
Now S(t) = 4000 - 3900[tex]e^{\frac{-t}{400}}[/tex]
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The complete question is:
A tank holds 4000 liters of water in which 100 grams of salt have been dissolved. Saltwater with a concentration of 1 grams/liter is pumped in at 10 liters/minute and the well mixed saltwater solution is pumped out at the same rate. Write initial the value problem for:
The mass of salt in the tank at time t.
dS/dt =
S(0) =
The solution is S(t) =
Which equation can be used to describe the relationship between x and y in the table below?
Answer: i think y = x + 5
Step-by-step explanation:
If the quotient of three times a number and five is increased by
four, the result is no more than 34.
Answer: We can start by using algebra to represent the given information. Let's call the number we're trying to find "x".
We know that:
quotient = (3x)/5
quotient + 4 <= 34
We can simplify the first equation:
(3x)/5 + 4 <= 34
We can then solve this inequality for x:
(3x)/5 + 4 <= 34
3x/5 <= 30
3x <= 150
x <= 50
So the quotient of three times a number and five is no more than 34 if that number is less than or equal to 50.
Step-by-step explanation:
Seorang mengendarai mobil dengan kecepatan 72 km/jam, tiba-tiba melihat seorang anak kecil di tengah jalan pada jarak 50 m dimukanya. Jika mobil direm dengan perlambatan maksimum sebesar 4 m/s2 , maka terjadi peristiwa ....
In a group of 60 tudent, 25 play table tenni, 16 do wimming and 22 play cricket, 8 play table tenni and do wimming, 6 play cricket and do wimming, 5 play table tenni and cricket, and 12 tudent do not play any of thee game
12 students do not play any of the games. Number of students who do not play any of the games = 60 - 82 = 12
A group of 60 students, 25 play table tennis, 16 do swimming and 22 play cricket, 8 play table tennis and do swimming, 6 play cricket and do swimming, 5 play table tennis and cricket.
25 play table tennis
16 do swimming
22 play cricket
8 play table tennis and do swimming
6 play cricket and do swimming
5 play table tennis and cricket
Find the number of students who do not play any of the games
Total number of students = 60
Number of students who play any of the games = 25 + 16 + 22 + 8 + 6 + 5 = 82
Number of students who do not play any of the games = 60 - 82 = 12
12 students do not play any of the games.
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A net of a rectangular pyramid is shown. The rectangular base has length 25 ft and width 22 ft. The net of the pyramid has length 74.8 ft and width 70.4 ft. Find the surface area of the pyramid.
The surface area of the pyramid is 5,685 ft².
Solving for the surface area of the pyramid:To find the surface area of the pyramid, we need to find the area of the base and the area of the four triangular faces. Since the base is a rectangle, we can find its area by multiplying the length and width:
length, l = 25 ft
width,w = 22 ft
Area = l x w
Area = 25 ft x 22 ft
Area = 550 ft².
To find the area of each triangular face, we first need to find the slant height of the pyramid, which can be found by using the Pythagorean theorem on the net dimensions. The slant height is the square root of
Net dimensions of the pyramid:
length, l = 74.8 ft
width, w = 70.4 ft
h = [tex]\sqrt{l ^{2} +w^{2} }[/tex]
h = [tex]\sqrt{(74.8^{2} + 70.4^{2} ) }[/tex]
h = 102.7 ft.
Now, we can use the formula for the area of a triangle:
Area = (1/2) x base x height,
where,
base,b = the length of the rectangular base (25 ft)
height = the slant height (102.7 ft).
So, the area of each triangular face is:
A = (1/2) x 25 ft x 102.7 ft
A = 1283.75 ft².
Since there are four triangular faces, the total area of all the triangular faces is:
A= 4 x 1283.75 ft²
A = 5,135 ft².
To find the surface area of the pyramid, we add the area of the base to the area of the triangular faces:
SA= 550 ft² + 5,135 ft² = 5,685 ft².
Hence, the surface area of the pyramid is 5,685 ft².
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The solution to an inequality is graphed on the number
ne.
-5 -4 -3 -2 -1 0 1 2 3 4 5
Mark this and return
What is another way to represent this solution set?
{xx<4.5}
Ox|x≤4.5}
Oxx> 4.5)
O{x|x24.5)
Save and Exit
Next
The solution set to the inequality as represented in another way is {x | x ∈ ≤ 4.5}. The second option is correct from the photo.
Representation of sets into a set builder notation:The set builder form is the representation of components of a set by a statement or an expression. The represented element(s) will be written using a variable, accompanied by a vertical line or colon, then the general attribute of the same represented element. This approach avoids listing the elements as seen in the roster method or the listing method.
From the given sets in roster form:
{-5,-4, -3, -2, -1, 0, 1, 2, 3, 4.5}
The same set above can be denoted by x, where x represents all the elements in the set and can be written as:
= {x | x ∈ ≤ 4.5}
This is read as x is an element of x such that x represent all the values from negative infinity to 4.5.
Therefore, we can conclude that the second option is correct from the photo.
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An acute angle, θ, is in a right triangle such that sin of theta is equal to 2/5. What is the value of cot θ?
Answer:
cotθ=√21/2
Step-by-step explanation:
we have,
sinθ= 2/5= perpendicular/hypotenuse
here,
perpendicular=2
hypotenuse = 5
Now using Pythagorean theorem,
h^2 = p^2+ b^2
(5)^2 = 2^2 +b^2
b= √21
so,
cotθ= base/perpendicular = √21 /2
Hope you like the explanation.
Tyson must complete 30 hours of community service. She does 2 hours each day. Write a liner equation to represent the hours Tyson has left after x days?
Tyson has (30-2x) hours left after x days .
Linear equation: What is it?A linear equation has the slope-intercept form y = mx + b. Variables in the equation are x and y. When x is 0, the integers m and b provide the line's slope (m) and the value of y. (b).
A first-degree polynomial is described as the sum of a collection of terms, each of which is the product of a constant and the first power of a variable in a linear equation.
She works out for two hours per day for a total of x days.
She has thus worked for two hours.
She has 30 hours left to accomplish, of which she has already worked for two of them.
She now has 30 2 hours to finish the task.
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– 0.2× – 5÷( – 1– – 0.5)
Answer:
Step-by-step explanation:
35
I need help in this problem
The measurement of indicated angle is 20 degree.
What is congruent angle?Congruent angles are those with equal measure. As a result, all angles with equal measure will be referred to as congruent angles.All congruent angles are not supplementary angles in general. Angles that add up to 180 must be supplementary angles. So only right angles and supplementary angles are congruent because they have the same measure and add up to 180.If the corresponding sides and angles of two angles are of equal size, they are said to be congruent. Two angles that are superimposed are also congruent. That is, if they turn and/or move to coincide with each other. The diagonals of a parallelogram also produce congruent vertex angles.Here opposite angles are congruent .
Therefore the indicated angle is 20 degree.
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In 2012, it was estimated that the number of U. S. Households that had dogs as pets was [tex]4. 33 x 10^7[/tex], and the average number of dogs per household was 1. 6. Based on the information, approximately how many dogs were household pets in the U. S. In 2012, in scientific notation?
[tex]2. 71 x 10^7[/tex]
[tex]3. 70 x 10^8[/tex]
[tex]5. 33 x 10^8[/tex]
[tex]6. 93 x 10^7[/tex]
6.93 × 10⁷ dogs were household pets in the U. S. In 2012.
To find the total number of dogs as household pets in the U.S. in 2012, we need to multiply the number of households by the average number of dogs per household.
Number of households = 4.33 × 10⁷
The average number of dogs per household = 1.6
Total number of dogs = (4.33 x 10⁷) × (1.6) = 6.93 × 10⁷
Therefore, approximately 6.93 × 10⁷ dogs were household pets in the U.S. in 2012.
Hence, the correct answer is D.
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39:11
Heights of four-year-olds are Normally distributed, with a mean of 40 inches and a standard deviation of 3 inches. At
his four-year checkup, Marlon's height is measured as taller than 70% of boys his age. How tall is Marlon?
Find the z-table here.
SECCO
38. 4 inches
41. 6 inches
42. 5 inches
43. 8 inches
Marlon's height is 42.52 inches.
Since the heights of four-year-old's are normally distributed with a mean of 40 inches and a standard deviation of 3 inches, we can use the z-score formula to find Marlon's height.
z = (x - mean) / standard deviation
where x is Marlon's height, mean is the population mean of 40 inches, and standard deviation is the population standard deviation of 3 inches.
We know that Marlon's height is taller than 70% of boys his age, so we can find his z-score using the cumulative standard normal distribution table, which tells us the proportion of the population that is less than a given value.
A z-score of 0.84 corresponds to a cumulative probability of 0.70.
So we can substitute this value into the z-score formula:
0.84 = (x - 40) / 3
Solving for x, we get:
x = 40 + (3 * 0.84) = 40 + 2.52 = 42.52 inches
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be sure to answer all parts. a small hole in the wing of a space shuttle requires a 21.9 cm2 patch. (a) what is the patch's area in square kilometers (km2)? enter your answer in scientific notation. (b) if the patching material costs nasa $3.91/in2, what is the cost of the patch to the nearest cent?
(a) The area of the space shuttle is:2.07x10⁻⁹km²
(b) $11.0321 is the cost of the patch.
Area of the patch of the space shuttle = 21.9cm²
a) 1 cm=0.00001 km
1cm²=(0.00001 km)²=10⁻¹⁰km²
21.9cm²=21.9x10⁻¹⁰km²=21.9x10⁻⁹km²
the patch's area =21.9x10⁻⁹km²
b) 1 cm = 0.393701 inch
1cm²=0.1550inch²
21.9cm²=21.9x0.1550inch²=3.3945inch²
The cost of patching area = 3.3945inch²
The cost of patching is are: 3.3945inch²
3.25inch²x3.3945inch²=11.0321
the cost of the patch to the nearest cent=11.0321
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Please help me!!! Sorry about small photo!
Answer:
I think 9/10 but I am not sure
If I Got 7 "(tokens or whatever you prefer) a minute for 9 hours/ 540 minutes, how many tokens would I have
An artist connects stained glass pieces with lead strips. In this rectangular window, the strips are cut so that FH = 28 in. Find JG. Complete the explanation
An artist connects stained glass pieces with lead strips and cut the strips so that FH = 28 in and JG = 14 in.
Now, According to the question:
A plane shape, as opposed to a square, with four straight sides and four right angles, particularly one with uneven neighboring sides.
Here, we have
FH ≅ GH
FH = EG = 28in
If diagonals bisect each other then, an artist connects stained glass pieces with lead strips
1/2(EG) = JG
1/2 (28) = JG
14 = JG
Hence, an artist connects stained glass pieces with lead strips and cut the strips so that FH = 28 in and JG = 14 in.
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A shipping container is in the form of a right rectangular prism, with
dimensions of 20 ft by 8 ft by 8 ft 9 in. How many cubic feet of shipped goods
would it hold when it's a quarter full? Round your answer to the nearest tenth
if necessary.
When it's a quarter full, the shipping container holds a volume of 350 cubic feet.
How many cubic feet of shipped goods would it hold when it's a quarter full?Bassically, we want to find one quarter (1/4) of the volume of the rectangular prims.
The dimensions are 20ft by 8ft by (8ft + 9in)
Let's rewrite that last part only using feet.
Remember that 12 in = 1ft
Then:
9 in = (9/12)ft = 0.75 ft
Then we can rewrite the dimensions as:
20ft by 8ft by 8.75 ft
The volume is the product between these numbers, and we want one fourt of the volume, so we need to find:
V = (1/4)*(20ft)*(8 ft)*(8 .75 ft) = 350ft³
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I need help this is due tomorrow!
Used the distributive property a(b+c)=ab+ac, the value of x is x>1/2
Solving inequality using distribution property includes change of inequality signs when multiplied or divided by negative number but, not in the equation.
What is inequality?
An inequality in mathematics depicts the connection between two values in an algebraic statement that are not equal. One of the two variables on the two sides of the inequality may be greater than, greater than or equal to, less than, or less than or equal to another value, according to inequality signals.
Curran:
-4(x-6)< 22
Used the distributive property a(b+c)=ab+ac
-4x+24<22
Then subtracted 24 from bot the sides
-4x<22-24
-4x< -2
Divide both sides by -4 ( inequality changes because of dividing by negative number)
x>1/2
Anjani:
-4(x-6)< 22
Divide both sides by -4
x-6> -22/4
add 6 on both sides
x> -22/4 + 6
x> -11/2 + 6
x> 1/2
Solving inequality using distribution property includes change of inequality signs when multiplied or divided by negative number but, not in the equation.
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Find the lateral area for the prism.
36 in 2
54 in 2
27 in 2
81 in 2
The lateral area for the prism is equal to 54 square inches. (Correct choice: B)
How to determine the lateral area of the prism
Herein we have the case of a prism with five faces, two triangles and three rectangles. The lateral area for the prism is the sume of the areas of the three rectangular faces, whose formula is described below:
Rectangle
A = w · l
Where:
l - Length of the rectangle, in inches.w - Width, in inches.A - Area, in square inches.Finally, we proceed to determine the lateral area of the prism:
A = 3 · (3 in) · (6 in)
A = 54 in²
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Gloria mows her lawn every 12 days and washes
her windows every 20 days. She mowed her lawn
and washed her windows today.
How many days from now will it be until she next
mows her lawn and washes her windows on the
same day?
The number of days before she mows the lawn and washes her window on the same day is 60 days.
How many days before she mows her lawn and waters the plant on the same day?The day she would mow the lawn and wash her window on the same day would be the least common multiple of 12 and 20.
A multiple of a number is the product of an integer and that number. A common multiple is a multiple that two or more numbers share. The least common multiple is the smallest multiple that two or more numbers share.
Multiple of 12 = 12, 24, 36, 48, 60, 72, 84, 96, 120
Multiple of 20 = 20, 40, 60, 80, 100, 120, 140, 160, 180, 200
Least common multiple = 60
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Write a ratio in words to compare a whole to a part. Then write the ratio using words. An example is needed
Answer:
A ratio in words compares a whole to a part. For example, the ratio of apples to oranges in a basket is "three to one." This can also be written as "3:1" or "3/1."
Another example: is the ratio of students to teachers in a class is "twenty to one." This can also be written as "20:1" or "20/1."
Step-by-step explanation:
Clare describes her morning at school yesterday: “ I entered the school on the first floor . Then walked up to the third floor floor and stayed for my class for an hour afterwards, I had an hour long class in the basement, and after I went back to the ground level and sat outside to eat my lunch “. Sketch a possible graph of her height from the ground floor as a function of time
The Centers for Disease Control and Prevention (CDC) states that the average height for men and women in the United States is around 5 feet, 9 inches and 5 feet, 4 inches, respectively.
What height do you think is normal?The Centers for Disease Control and Prevention (CDC) states that the average height for men and women in the United States is around 5 feet, 9 inches and 5 feet, 4 inches, respectively.14-year-old boys typically stand 162.4 cm (5 ft 3 in) tall, compared to 159.8 cm for girls (5 ft 2). At this age, you should expect a sizable range in height. Puberty, however, will vary from person to person; some may have already passed through it, while others may not.The Centers for Disease Control and Prevention (CDC) states that the average height for men and women in the United States is around 5 feet, 9 inches and 5 feet, 4 inches, respectively.To learn more about height refer to:
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In a survey, a group of students were asked to name their favorite world language class. There were 25 students who chose "other" languages. How many students participated? french:42. 5% spanish:45 students participated
Spanish 45 and french 42.5. When attempting to solve a Venn diagram with three circles, it is best to start by entering the number of items that the three sets of data have in common.
When attempting to solve a Venn diagram with three circles, it is best to start by entering the number of items that the three sets of data have in common. After that, input how many items are still there in each pair of sets' overlapping zone.
The quantity of each set's leftover pieces should be entered. Lastly, locate any missing numbers using any known totals.
Using a Venn diagram to determine probabilities: The Venn diagram's subset's components should be identified. Figure out the subset's frequency. Work out the larger set's overall frequency.
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FIELD TRIP A school is planning a field trip to a museum. Tickets cost $4 for students and $8 for adult chaperones. There must be at least 1 adult chaperone for every 9 students and no more than 1 adult Up to 100 people may go on the field trip. chaperone for every 4 students. What is the maximum total cost for tickets?
Answer:
The maximum total cost for tickets is $320 + $160 = $480.
Step-by-step explanation:
The maximum number of people that can go on the field trip is 100, so the maximum number of students is 100 - (100/5) = 80 students.
The maximum number of adult chaperones is 1 adult chaperone for every 4 students, so the maximum number of chaperones is 80/4 = 20 chaperones.
The total cost for student tickets is $4 x 80 = $320.
The total cost for adult chaperone tickets is $8 x 20 = $160.
The maximum total cost for tickets is $320 + $160 = $480.
Answer:
the maximum amount for the equation is 320+160=480